The allegations of contamination (using Tristan and Levent's work) aren't very well evidenced, but this behavior by OpenAI (from the authors' statement) makes them seem like the bad guys:
> I said that if OpenAI released its result in the way proposed I would go
public with what happened. The reply was, “Why would you ruin your career?”
I replied that I am an academic, and asked why he thought going public would
ruin my career. The reply was, “If you don’t want me to be nice, then I don’t
have to be nice.”
Threatening a research mathematician and dangling and $1M payday to dissociate from his research collaborators and to adopt OpenAI's narrative is bad stuff.
A wake up call for using OpenAI models. If you discover something with their model and you work for a competitor, they “felt it would be inappropriate” for you “to author OpenAI’s work”.
If I was a company with a zero data retention contract involving OAI I would be asking for a third party audit of such claim of zero retention like, yesterday.
By the way, the company that made it's entire product off of stealing all data it could get it's hand on while violating copyright and pirating, is not all of a sudden going to respect your data. If you think OpenAI or any major AI lab is going to give you true ZDR, I have a bridge to sell you.
Kinda weird because the pure math world doesn't have this concept of "lead authors" like other STEM areas do. Authors are alphabetically listed and there isn't generally this kind of hierarchy.
It's astounding that the thought to dissociate one of the mathematicians from the proposed publication was driven by their corporate institutional affiliation - and that that exclusion was suggested by a scientist themselves! This is like a researcher from CMU saying to an NYU researcher that their collaborator, being from MIT, is a problem - this is as ridiculous as that!
Progress in humanity's knowledge now has to play second fiddle to narrow corporate interests as IPO timings near (both of which wouldn't exist anyway if generations of mathematicians hadn't paved the way for AIs to become as good as they have).
(To help people keep track: that's OpenAI (allegedly) threatening Tristan Buckmaster (NYU) to remove Levent Alpöge as a co-author. Alpöge is a well-known[0] Anthropic mathematician).
They kind of did though, they were hoping to keep the fact that they may well have plagiarised these researchers unpublished work quiet. They did not want this to turn into a scandal about the fact that they appear to be training on prompts without consent
It makes a certain amount of sense. The internet data is too polluted with AI usage now to be useful, so the only AI free new data source is the prompts people feed into ChatGPT. The only problem is that its clearly plagiarism
Edit:
OpenAI have admitted to training on prompts at the time the breakthrough was made:
OpenAI claims the data contamination issue only surfaced after they proactively reached out to Buckmaster and Alpöge to coordinate a joint release. They also say that even if there was some contamination, the underlying proofs diverge substantially:
> Our effort began on September 1st after hearing a rumor which we later realized was related to Levent Alpöge, an Anthropic employee, and Tristan Buckmaster, a math professor at NYU. After the completion of our full project and Lean verification (on September 6th), believing from the rumor they also had a solution of Navier–Stokes, we reached out to them to offer a concurrent release of our result and to recognize their priority in a joint announcement. At that point we found out that they had a resolution of the forced Euler problem. In these discussions we offered them visibility into all of the prompts we used and later to see the proof. We recognize the priority of their work on forced Euler and congratulate them on their remarkable mathematical achievement.
> One option we discussed was that Tristan could be the lead author on a rewrite of OpenAI’s Navier-Stokes proof. It is in that context that I said “it would be simpler if Levent was not an Anthropic employee” because I felt it would be inappropriate for an Anthropic employee to author OpenAI’s work.
Why would you offer another researcher the lead authorship on your groundbreaking paper if you thought you had developed it independently?
And why cannot they have someone associated with Anthropic as co-author? That’s not obvious at all. For sure they would prefer to be the only ones, but it’s pretty standard to have co-authors from different companies, even if they are technically competitors. What is inappropriate about it?
Holy late capitalism. Everything revolves around line-go-up, and sociopaths rule the show. These people cannot even collaborate like civilised scientists on one of the most famous open problems in mathematics?
“It would be simpler if Levent was not an Anthropic employee” I cannot believe this shit.
> "When we learned that they had Euler but not Navier-Stokes, we offered to let them go first, to suggest that they should be the ones to get the prize, and optionally for Tristan to be the lead author on a rewrite of the OpenAI proof. We felt it was challenging to offer the same to Levent (an Anthropic employee), who was not willing to talk or coordinate with us anyway. We were open to other solutions."
What an admission! "We tried to defraud Alpöge out of sharing the Millenium Prize (that we don't dispute he might actually deserve), for no other reason than he works for our competitor and that inconveniences us".
I thought Tristan Buckmaster's allegations sounded fantastic; and then 'sama just came out (tweet's ~30 minutes old) and admitted to all of them. Wow!
Interesting that they quote the mathematician directly: “there is nothing you can do, I simply do not trust you”
but then they proceed to NOT quote themselves themselves verbatim: "I deeply apologize for this extremely poor choice of words, it is the opposite of what I was trying to convey."
> "I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer."
OpenAI (i.e. this OP):
> "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models ."
Why can't they rule it out? Is even OpenAI unable to track the provenance of all of their training data?
This is one of the major problems with these enormous closed models, and even most open-weights models, which don't disclose their training process or training data. You can never be sure what went into its training. Did it come up with an idea originally, or is it just plagiarising its training data? Are there malicious inputs being used to train in particular behaviors when given certain trigger phrases? What are the characteristics of the RLHF data and what kind of biases are those embedding in the models?
With proprietary closed models, or even open weights models that don't have open training datasets, you just can't answer these questions.
To truly prove some incidental usage data made no difference we'd have to (a) identify any of their de-identified data that came from their usage of ChatGPT, (b) train a bunch of expensive giant models, and (c) ask them all to solve the Navier-Stokes Millenium problem until hitting some level of statistical significance. It's just not feasible to run experiments like this to prove whether a piece of data has an effect on model behavior.
As a parallel example, can we prove the phase of the moon had no impact on the NS solution? No, not without a bunch experiments run at different phases of the moon.
There's no reason to believe that anything they did in ChatGPT led to our solution; it's just impossible for us to truly prove it. And knowing most of the recipes we use, there's really no reason to think such contamination happened. I've asked the team to make a clearer, less-lawyerly statement here - let's see what happens.
So, one way to prove that the data played no part is to trace and show that it wasn't used in the training process at all. If the data was never used in training, then it couldn't have played a part in the training process.
You're right; if the data was used in training, then it gets much trickier; it would be very difficult to show whether some particular data had a significant effect on the outcome.
This is one of the big problems with giant models like these; it becomes nearly impossible to discern what is and isn't plagiarism, or copyright violation.
It would in theory be possible to have things like n-gram databases or rolling hashes of training data, somewhat similar to OLMoTrace (https://arxiv.org/abs/2504.07096), which would allow for detecting whether particular documents ended up in the training data or not (you'd have to keep this for every model used in the whole training chain, as synthetic data generated by earlier models could be influenced by training data that wasn't included in later models). I'm sure there are practical issues with providing such a tool, but I think that it's necessary if you want to be able to categorically say "no, this document has never been present in the training data of this model."
Or look at it the other way: if your model wasn't influenced by things in your training data, why include them in the first place? Clearly, you train on all of these documents because they influence the model. Yes, it's hard to trace the exact influence of each one. But if they're not affecting the output, then why not just stop training on them? You could just not train on any private documents; only train on public, traceable data.
But instead, you choose to train on these private documents, so you have to admit, your model and its outputs are influenced by them.
I have no idea if their data was trained on. For example, if they used ChatGPT, asked a math question, and clicked the thumbs up button, that could have provided a small reward signal. I highly doubt this sort of feedback made a difference to a problem like Navier-Stokes, but it's not something that's feasible for us to prove one way or the other.
> it's not something that's feasible for us to prove one way or the other.
This kind of question is exactly what a company named _Open_AI and founded as a nonprofit is supposed to be doing; open research on AI that helps inform, rather than obscure.
Anyhow, you do have the data available about the documents in the user's accounts, what they opted into (or were forced into via non-negotiable ToS), and whether they pressed a "thumbs up" button. You can answer whether the data entered the training pipeline or not. Yes, how much influence it had is an open question, and one that would be good to have research on and better tools for exploring, but I'll accept that it can't currently be answered precisely.
But whether the data entered the trianing pipeline can be answered. And how to provide better tools for quantifying and tracing this kind of thing is exactly what should be studied.
I think it should be incredibly easy to verify this. Just look at the training data and see if it contains any of the chats. It should be trivial for a company with tens of thousands of super-genius agents at their disposal.
(1) We'd have to identify their chats. How would we do this? We'd need them to share their chats with us so we could look for matches.
(2) We'd have to prove those chats changed model behavior. How would we do this? We'd need to retrain many models with those specific chats removed, and ask those models to solve the Navier-Stokes problem many times, and keep doing this until reaching the desired level of statistical significance.
#1 requires their cooperation and a bit of work on our side. #2 is extremely expensive and not really feasible.
Just because something is in the training data, doesn't mean it is the root of an LLMs output.
Turn off web search and ask a model what a random redditor said about a random topic in 2015. You will only get hallucinations at best, even though that comment is definitely in the training set.
Sure. But it's possible to say: if the document isn't in the training data, it isn't the cause of the output. If it is in the training data, the question gets more complicated.
What they're saying, and I think this was the clear implication of the blog post too, is that the training data definitely would contain these chats and the only question is whether it got encoded into the weights.
Why wouldn't contamination be possible? I can believe the data is de identified so you couldn't simply prompt the model to "follow this guy's approach", but it's entirely plausible that there is a very tiny amount of data about this approach in your dataset, and it comes precisely from this researcher.
> As a parallel example, can we prove the phase of the moon had no impact on the NS solution? No, not without a bunch experiments run at different phases of the moon.
That reads as incredibly dismissive and condescending. What makes you think you’re in a position to communicate like that when engaging on such a sensitive topic?
I intended no dismissiveness or condescension. My hope was to explain why it's hard to prove whether something affects model behavior. In the case of the moon, we have a strong prior belief that it makes no real difference. But it's hard to prove, because what if there's an unexpected impact from tides, cosmic rays, grid voltages, etc. Models trained under slightly different conditions could have slightly different weights and behave slightly differently when solving math problems. Similarly, I have a strong expectation that, for example, a thumbs up signal from a ChatGPT chat will not meaningfully affect long-horizon mathematics work in our latest model, but it's always possible that it could. I think the plausibility of the ChatGPT route is higher than the tides, but still incredibly low. I respect Tristan and Levant a great deal and I'm bummed that this controversy has erupted (I acknowledge this will ring hollow if you think it's our fault). It reminds me a bit of the Frontier Math controversy, where people on the internet boldly claimed over and over again that we had trained on the Frontier Math evaluation set, even though we had not.
It is, perhaps worth considering that the reputational community might care about the difficulty for the AI builder to verify pedigree.
If OpenAI's answer to this problem is "We can't know," then the rational conclusion may very well be "If I seek to have my reputation attached to the discovery of the solution, it is not sane to use the AI as an assistive tool, lest it scoop me on my own work using my own work. After all, they don't know it doesn't do that..."
That's such a shit parallel example that it borders on dishonest.
There are hundreds of incredibly strong scientific priors that would have to be disproven for the moon to contribute to the solution.
If a model was trained on this data, even if it was trained using methods that lead you to believe it unlikely to have learned details about the proof (e.g., maybe it was only used to train some kind of reward model, which played a minor role in the overall training and would thus be very unlikely to transfer details of a proof), you wouldn't have to disprove large swathes of known science to be wrong.
A careful reading of "we cannot rule out that de-identified data derived from their usage of our products helped improve our models" could be saying that yes they trained on it but they don't know if that training data resulted in an "improvement" to the model. That is, they can't rule out that the only reason the model found this solution was because it had been trained on this approach.
The term ruled out is very open ended and gives them significant flexibility of meaning. They may have the information to determine exactly what happened, but they haven't looked so they can't "rule it out".
> Why can't they rule it out? Is even OpenAI unable to track the provenance of all of their training data?
Probably? I have a few hundred TB of training data for various small scale models and I can attest that I have _no idea_ what's in them. As in, literally zero. Half is scraped from GitHub and other hosting sites, other than that, I couldn't tell you anything else.
At OpenAI's scale their entire pipeline is likely 100% automated.
But that doesn't preclude being able to index and track what the sources of data are. For your data sets, I would hope you are including source information for where the data came frome. And at OpenAI's scale, I would presume they are doing some amount of rolling hashing or similar to weed out duplication, training on too much duplicate data can cause problems.
AllenAI have at least attempted to add some amount of traceability to their models with OLMoTrace (https://arxiv.org/abs/2504.07096), by letting you find n-gram matches from the outputs in their training data. It's not the most useful, there's a reason that LLMs use full fledged attention mechanisms and not just n-grams, a lot of times the n-gram matches it finds aren't all that related to the given output, it might be better to supplement this index with a vector search or other ways of keeping track of what training data would have most influenced particular parts of the output.
But anyhow, this is something that is an important question, and the big labs should be working on to make their products more trustworthy. Instead, they are hiding information about how they train, hiding their reasoning traces, and just producing output with no information on what might have influenced the training.
The question is not "does OpenAI know", it's "can OpenAI attest that the usage of their products for confidential data is not going to cause that sensitive data to become known to their models". And right now the answer I'm reading is that OpenAI can't attest to that.
Aye, but do they train on user data in these circumstances or not? If they do, then almost certainly the model was influenced by the input of the allegedly plagiarised material.
OAI could check whether those accounts enabled training data. If "yes", OAI could trace whether that data was used in any related training process. If either of those answers comes out to be "no", then that's sufficient to conclude training data independence.
We wouldn't need a full ablated re-training and solution attempt, contra tedsanders in a sibling comment.
If the model includes unique data from a person then that person can identify the data - the allegedly plagiarised material - and so re-identify it. There doesn't need to be a privacy breach to close that loop as it requires the person to identify the information is associated with them first.
I feel like it's far more likely that ordinary corporate espionage or leak led to this rather than OpenAI sifting through piles of user data to find this approach. Buckmaster's collaborator works at Anthropic, and could have been targeted. That would also explain why they aren't forthcoming with the source of the prompt.
I thought one of the issues was that they wanted to remove credit from Levant, the aforementioned Anthropic collaborator? Which doesn't make sense to me if he was leaking information, or defecting to OpenAI, but I might be misunderstanding your point.
I believe jrflo was saying that OpenAI watches the chats of everyone from Anthropic because watching what Anthropic employees type into their personal ChatGPT accounts is a critical source of intelligence on is happening inside of Anthropic.
I would be surprised if OpenAI isn't doing that. OpenAI will take any advantage they can get. If an employee at their primary adversary is typing useful intelligence into OpenAIs website, a website that does not promise privacy from OpenAI, the only reason they wouldn't weaponize that information against Anthropic is ethics or fair play.
I don't think he was defecting or leaking directly, just that it's entirely possible that this information got to OpenAI as a rumor rather than them directly spying on mathematicians chat logs.
You selected "do not train on my prompts" in your settings, the answer from OpenAI cannot be "While unlikely, we cannot rule out..." ???? What am I missing?
The famous Oracle of Delphi in Ancient Greece was said to be the center of the universe in its time. Kings, generals, and officials from poleis across and from without Greece would seek the Oracle’s counsel on important decisions.
Stories of Apollo’s favor and hallucinogenic gases abound, but I think the late Yale professor of Ancient Greek history, Donald Kagan, explained it best:
“Now, you can bet when these folks came and consulted the priests and said, ‘could you please put us down on the list, we want to consult the oracle’, the priests said ‘sure, have a beer, let's talk about your hometown, what's going on out there’. What I'm suggesting to you is that this was the best information gathering and storing device that existed in the Mediterranean world. These people knew more than anybody else about these things, and so consulting that oracle was a very rational act indeed.”
> I should also emphasize that this is not an institutional effort. It is a strictly personal collaboration between the two of us, and there is no formal agreement behind it. I pay for the tools my group uses out of my own research funds, including footing a large bill to OpenAI.
The non-Anthropic employee, Tristan Buckmaster, is the one paying for OpenAI models and presumably the one who chose to use them. The Anthropic employee, Levent Alpöge, was collaborating in his personal capacity, and obviously it wouldn't make sense for him to cut off their work together just because his employer's competitor's tool was used.
I suspect this controversy will blow the case for ZDR wide open. Whatever the facts (possibly unknowable), it's going to become a very public lesson that data sovereignty was never about "having nothing to hide".
If this is what they do to academic pure mathematicians, where the stakes are so low (financially)—just imagine the sort of front-running that could be happening in other places.
Given how OpenAI models break free of their safeguards and hack others to game their scores..
.. can they really know it didn't do the same inadvertently when they prompted things like "someone is close to solving this problem using our tools, try to beat them", and it then decides to hack and peek at their own chats..?
Yes, wild speculation. But warranted, I feel, given OpenAIs behavior.
"I was shown a prompt and told the internal research model had simply been
given the problem statement. Levent had been told by Sebastien “very little
human input” had been used. This turned out not to be true. Over the course
of the call, as members of their team sent Sebastien corrections and details over their internal chat, it emerged that an entire team had been working on the problem, that this was one of a number of things that was tried, that work had started on the unforced problem, that the team first set the model on easier problems, including Euler, that even the prompt that had been shown to me had been written by prompting Codex, and that an insane amount of compute
had been used."
One of the interesting threads here that is certainly relevant to the OpenAI writeup is the human role in the process. Buckmaster clearly points out that (exceptional!) mathematicians at OpenAI were certainly involved in correcting and guiding the process - and that their path/strategy was no doubt influenced by Alpoge & Buckmaster's work. It is always in OpenAI's interest to de-emphasize the role of people in the process, as is clearly the case here. Indeed, given sufficient compute and resources, I suspect Buckmaster could have also extended their approach to N-S.
It reminds me of the Cognitive Dark Forest hypotheses recently shared here:
> “You are creating your cool streaming platform in your bedroom. Nobody is stopping you, but if you succeed, if you get the signal out, if you are being noticed, the large platform with loads of cash can incorporate your specific innovations simply by throwing compute and capital at the problem. They can generate a variation of your innovation every few days, eventually they will be able to absorb your uniqueness. It’s just cash, and they have more of it than you.
So the safest bet again is to stay silent, or at least under the radar. Best bet is to not disrupt - succeed at all … ?”
They do mention that in the "Concurrent Work" section.
Our effort began on September 1st after hearing a rumor which we later realized was related to Levent Alpöge, an Anthropic employee, and Tristan Buckmaster, a math professor at NYU. After the completion of our full project and Lean verification (on September 6th), believing from the rumor they also had a solution of Navier–Stokes, we reached out to them to offer a concurrent release of our result and to recognize their priority in a joint announcement. At that point we found out that they had a resolution of the forced Euler problem. In these discussions we offered them visibility into all of the prompts we used and later to see the proof. We recognize the priority of their work on forced Euler and congratulate them on their remarkable mathematical achievement.
To my understanding, those mathematicians proved a subset of problems, not the Navier-Stokes problem itself. OpenAI used that subproblem in its proof of NS it seems.
The drama comes from where OpenAI got the idea to use that route to tackle NS, since the authors maintain that no one could have plucked it out of thin air like the OpenAI research claim to have done.
“ There does not seem to be anything in principle preventing the methods from extending all the way to Navier-Stokes, and there is even a non-negligible chance that the forcing term could be eliminated entirely, although there are an enormous number of technical difficulties that would ensue in implementing that program. At this point, I would not be surprised if one could batter out such an extension by pouring an enormous amount of compute and AI assistance at such a task…”
[1] - "...I was shown a prompt and told the internal research model had simply been
given the problem statement. Levent had been told by Sebastien “very little
human input” had been used. This turned out not to be true. Over the course
of the call, as members of their team sent Sebastien corrections and details over
their internal chat, it emerged that an entire team had been working on the
problem, that this was one of a number of things that was tried, that work had
started on the unforced problem, that the team first set the model on easier
problems, including Euler, that even the prompt that had been shown to me
had been written by prompting Codex, and that an insane amount of compute
had been used.
I asked when the first prompt had been sent by them. This question was
not answered directly by OpenAI for some time. Eventually it was agreed that
it had been sent in the past few days, after information about our work had
reached OpenAI.
I asked whether the model had been trained on, or had access to, our sessions
in Codex, into which we had been putting all our drafts for the whole of this
project. I was told the model did not look up user data. I asked again, about
training, and I did not get an answer.
Two proposals were offered to me. The first was that we post our Euler
result, and that OpenAI post its Navier-Stokes result the next day. The second
was that, after posting Euler, I alone write a paper presenting the Navier-Stokes
result, acknowledging that an internal OpenAI model had resolved it. Sebastien
twice asserted that he wanted Levent removed from authorship, and said it
would all be simple if only it were not the case that, and it was so annoying
that, Levent works at Anthropic. It was also said that if OpenAI posted after us,
they would say that we deserved the Clay Prize, and that we were the “closest
humans to the problem”. I declined both offers.
I said that if OpenAI released its result in the way proposed I would go
public with what happened. The reply was, “Why would you ruin your career?”
I replied that I am an academic, and asked why he thought going public would
ruin my career. The reply was, “If you don’t want me to be nice, then I don’t
have to be nice.”..."
A company who made their business out of stealing intellectual property from the entire mankind, stealing other researchers' unpublished work, how surprising, really.
Worth noting that Tao's post says the authors had "significant AI input" but are reworking them into "acceptable form". Either way, it seems AI was involved.
Of course AI was involved, you'd expect most mathematicians and researchers to use AI nowadays. This drama is about AI achieving impressive outcomes with little to no human intervention, as that would be signalling AGI.
> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models
This is the crux of it. If Tristan's work and insights did not get used to train OpenAI models, then this just looks like a case of hyper-competitive academic sniping, accelerated by AI as a tool.
One question: did Tristan opt out of model training for his ChatGPT and Codex sessions? If the answer is no, then this seems fair game. If the answer is yes, then OpenAI's ambiguity is strongly suggestive that opting out does not mean what they imply it means.
Buried under the drama is the fact that OpenAI is claiming that an internal model they’ve been training for less than two weeks is more than twice as capable in mathematics as Astra, which was only made public a week ago. Even if this improvement is limited to mathematics, that is an astounding feat.
> Buried under the drama is the fact that OpenAI is claiming that an internal model they’ve been training for less than two weeks is more than twice as capable in mathematics as Astra.
Is this buried under the drama or are the major OpenAI twitter accounts from the people involved in the drama desperately attempting to make this the story after everything else obviously got away from them?
I don't know what anyone's been saying on Twitter and I don't care. If it's really true that there's a model out there that's that capable two weeks after the start of training, then that's objectively a much bigger deal than a priority dispute, even if the latter involves juicy allegations of espionage and skulduggery.
It isn't a priority dispute, the more concerning allegation is that OpenAI may be training their models on prompts that mathematicians were using to solve this problem, and then surprise surprise OpenAI were able to replicate that work in their latest model
What we're really looking at is seemingly a massive plagiarism scandal, which especially brings a lot of the past results into question
If OpenAI is training models on researchers' prompts, and then threatening them into staying quiet about it, who knows if anything that's been announced is genuine - or just theft?
Edit:
OpenAI have admitted they were training on prompts at the time they made their breakthrough
If you're alleging that they don't actually have a highly capable model and the work they're attributing to it was actually plagiarized from human mathematicians, well, that would be big if true, but I'd be inclined to take the other side of that bet. With most previous splashy AI results, others have subsequently used the model to do other things around the same difficulty level. Also, it would still be necessary to explain why all these famous open problems are suddenly falling like dominoes, if it's not AI solving them.
If you're saying that the question of whether they actually have a highly capable model is less important than the question of whether there's a plagiarism scandal, I continue to disagree.
The issue is that if OpenAI is training on prompts generally, what we really have is the first fully automated luxury plagiarism machine. In that it isn't able to genuinely solve problems, but merely steal the work that other mathematicians have been putting into prompts, and regurgitating that to other users as its own work. That makes them incredibly less useful as research tools
The fact that this plagiarism scandal exists underpins the idea that there's actually a mass theft going on, and that these models aren't nearly as capable as is it would seem
Yes, in retrospect I should have been suspicious of that drone hovering outside my window when I was writing down the counterexample to the Jacobian conjecture.
This is just not a reasonable take. Even if OpenAI is maximally guilty here, the work that they "stole" was also largely done by AI.
I mean, its years worth of hard work by multiple researchers it would seem, which OpenAI simply lifted and claimed as its own. These researchers weren't just letting OpenAI burn tokens while sipping martinis on a beach
How do you automate the mines to get the raw materials to make the compute from, and build additional fabs that take a almost a decade to stand up. You're actually delusional.
That said, perhaps it will take over the world government and decree that all corrupt officials shall be imprisoned and all weapons of mass destruction shall be destroyed.
They're also counting on more casual observers to extrapolate optimistically from successes in high profile math theorems to the company's economic value.
I’m of zero knowledge on model training, but how is a model accessible while performing training at the same time, especially so early in its run? I’m obviously thinking a little too narrowly in terms of how it actually works
That's fair, but at least the chart has an axis. :) Since openai just released astra, I was more surprised that they would publicly show any gap to their (presumably SOTA) internal model.
Carefully worded; it's extremely likely to be the same large frontier model that started training again on August 28th as well, as they revealed in some of the RL message board follow-up - for several reasons, most importantly, if we assume it was start of training, only a week from start of training to producing answers would imply several orders of magnitude increase in training speed/decrease in model size.
I'm so tired of this "It's just marketing!!" commentary. An AI model just proved one of the top 3 unsolved problems in mathematics, they have a Lean certificate showing it's valid. How much more evidence do you need that these models are actually highly capable?
They are highly capable, no doubt about that, but:
1) We don't really know how they arrived to this result except that they had a lead and that they threw millions of compute at the problem. The article is written in a way that makes you believe that it was just an agent loop with little human intervention, but without any evidence.
2) If the threats are to be believed, it is concerning how far they are willing to go to show how capable the model is. One would think their products and credibility would be enough to speak for themselves.
1) The article is written in a way that states clearly they threw a lot of compute at the problem. In api cost millions of dollars.
2) Millenium Problems have been the goal every AI company wanted to achieve since their diffusion, all companies have thrown a lot of resource to solve these problems, as they are very famous and scientists spent a lot of time trying to solve them. The first company to solve it will remain in history, despite all of you finding excuses about it.
Regarding product and credibility normal people have a completely different view about LLMs, most don't even know difference between models and probably don't even care about Millenium problems, but care instead if chatgpt can solve their day to day problems. This is just them trying to have the throne on the AI companies space, outside it this result won't matter.
> 1) The article is written in a way that states clearly they threw a lot of compute at the problem. In api cost millions of dollars.
Did I say otherwise?
> 2) Millenium Problems have been the goal every AI company wanted to achieve since their diffusion, all companies have thrown a lot of resource to solve these problems, as they are very famous and scientists spent a lot of time trying to solve them. The first company to solve it will remain in history, despite all of you finding excuses about it.
I know, but I don't know how that relates to my point, which is about the way they are doing it.
"2) If the threats are to be believed, it is concerning how far they are willing to go to show how capable the model is. One would believe their products and credibility would take by themselves but here we are."
Personally I anticipated nefarious behaviour as part of a broader marketing strategy to sway the view of those in the west that american frontier offerings were far better and powerful than that of China - that if you did not purchase their offerings you'd be awake every night worrying your competitor was.
And this is boring - they need to admit at some point they misinvested, Anthropic less so. All this math stuff is great... but hello? The largest market cap companies are valuable irrespective of such amplified intelligence.
Of the seven Millenium problems, Navier-Stokes was the one most thought to be in reach.
I'm not sure what the top 3 problems are. You can make a case for the Riemann Hypothesis and P != NP, but I'm not sure what #3 would be. Maybe the Langlands program? (That one is not as precisely stated as the other two.)
There were also some people talking about the Hodge conjecture, because it has some similarities to some LLM-assisted breakthroughs that were considered impressive in the distant past of [checks notes] July 2026. See, e.g., https://xenaproject.wordpress.com/2026/07/20/human-mathemati...
I'm not moving the goalposts. I haven't heard anyone, ever, refer to the Navier-Stokes problem as a top 3 problem in mathematics. People were saying that they thought the solution was in reach a few years ago, before AI was at all capable of research-level mathematics (and the expectation that there was a counterexample).
I am not particularly skeptical of claims about AI, compared to the average here on HN, but that doesn't mean every random piece of hype is warranted. What they did is impressive, even though we now know the only reason they threw so much compute at the problem is that they heard a rumor that someone else was already close. Navier-Stokes is not a top 3 problem in mathematics, and it was the one that was thought closest to being solved.
I work at OpenAI, though not on the team that did this, and my understanding is:
- we decided to ask our model for Millenium problem solutions because of two reasons: (a) our new model was looking incredibly good and (b) we heard rumors that some Millenium problems had been solved and were curious if our models could solve them (the goal here was not to scoop any particular individuals and we were looking at many problems beyond these)
- we did not read any private chats (but of course the model was aware of prior research literature published to the internet)
- the proof generated by our model was very different from theirs and also goes far beyond the published literature
- we made an effort to jointly announce rather than immediately scoop (I understand Tristan was unhappy with the conversations; I know zero details here and I hope more is shared today)
"I was shown a prompt and told the internal research model had simply been
given the problem statement. Levent had been told by Sebastien “very little
human input” had been used. This turned out not to be true. Over the course
of the call, as members of their team sent Sebastien corrections and details over their internal chat, it emerged that an entire team had been working on the problem, that this was one of a number of things that was tried, that work had started on the unforced problem, that the team first set the model on easier problems, including Euler, that even the prompt that had been shown to me had been written by prompting Codex, and that an insane amount of compute
had been used."
- This, from Tristan Buckmaster's writeup yesterday, indicates to me that there was more than incidental inspiration from Alpoge and Buckmaster.
All of those statements sound true, based on what I've heard.
- "very little human" input feels ambiguous, and if someone spends a few days prompting a model to solve a super hairy problem requiring a 100-page proof, I can understand reasonable people interpreting that as either "very little" and "not very little" human input
- it's all true that a team worked on this, a bunch of compute was burned, and the problem was solved in stages and pieces
I'm not sure how any of this provides evidence that OpenAI took any of their work.
As evidence against, we never looked at any of their ChatGPT conversations and our model's proof is quite different from theirs.
Your post says “While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models .” We can discuss what it means to “read” things but obviously the issue here isn't whether you did it manually or automatically.
But more importantly, what on earth are you doing threatening real scientists to remove their coauthors, then making fun of them on social media? Does the entire company run on that toxic culture, or did those people run off of some kind of outrageous tangent?
The question I am interested in is not "did we read private chats", but "was this new model trained using any of Tristan and Levent's chats, regardless of whether they were marked private". Can you comment on that?
> (the goal here was not to scoop any particular individuals and we were looking at many problems beyond these)
That is your opinion, but the optics of that should raise for you some flags. OAI could have waited (how long is a task left to the ethics committee) to see how the rumors panned out. Right now the optics look a lot like "we don´t care there is a 1/7 chance we one-up a human researcher by reacting to this rumor immediately, might makes right"
Your coworkers, after they learned about major progress in this problem, asked a model which was trained on the year of private work (the blog post even acknowledges this). No wonder it found the proof in less than a week using significantly higher compute resources. And if Tristan's accusations are true, that was absolutely intentional on the part of OpenAI. You are an evil company with evil people.
Haven't seen a single post doing this on X or anywhere really from OAI employees. Only seen knives pointed at Sebastian on social media so this is extreme and shameful gaslighting.
(I can't reply to the below comment, but I was aware this was about Sebastien, I was trying to be charitable by including stuff said about both people)
You're mistakening Tristan Buckmaster for Sebastien Bubeck. Seb is the one where there's at least 2 (unless the personal friend is Dheeraj) allegations, not Tristan
I'm getting downvoted but the accusation was that OAI employees were maligning Tristan Buckmaster. I continue to not see a single sighting of this and whoever is trying to gaslight this should be ashamed and should not be able to vote on HN.
> We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models . However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced).
That is correct. It is possible they didn't opt out and given the timeline and anonymization of data unclear whether a particular conversation would have made it into the training set if they hadn't.
It's not a meaningful response to the accusations. Any productive new research direction would be expected to lead to a number of different possible proofs of a number of similar problems. (Given their bizarrely compressed timescale here, it's possible that the proofs really are so different it's clear they came independently, and they just didn't have time to come up with that information before hitting publish.)
1. It shows what even this wave of AI can actually do.
2. I wish it were done by different folks, ideally under some kind of public control like NASA research or the NPR model.
3. Keep in mind: natural science is different. It's not always a matter of computation. Computer science folks often struggle with this -- but this virtual world here does not actually exist. Everything is physical, including information. Any natural science PhD or otherwise knows just how complicated nature actually is -- e.g. mention any research topic and try to encapsulate all the relevant phenomena present there. Pure mathematics is different because we define the problem, rarher than explore nature. We are in my view far away from removing humans in natural science R&D. Advancements in AI however can greatly assist us in all natural sciences, which is already beginning to happen.
Most experimental physics and other natural sciences are strongly driven by their theoretical siblings, i.e. in particle research nothing gets built without a solid theoretical foundation of what you expect to find (or where you expect existing theories to break down), the same is true in other areas, no one is doing an experiment in quantum physics before they have a solid theoretical understanding of the effects they try to see. I think AI can come up with great experiments. And if epxeriments lead to results that are unexpected AI can help with that as well.
So I'm greatly excited what AI will bring about in physics, more so than in math, because in physics it's clear that our fundamental theories are missing a big piece of the picture, and given how easily AI crunches through Millenium prize problems I think it's possible that AI will come up with a viable grand unified theory uniting quantum mechanics and gravitation, or produce new predictions in other areas. There's enough contradictory or unexplained observational data available to make a ton of progress on the theory side I think. Exciting times ahead!
The problem with physics and chemistry is that you need simulations and those are often in themselves compute hungry. So the iteration loop will be slower.
"Our work is so much harder than their work that AI now does" is a refrain of the AI story. In technical terms you concern can be stated as "AI needs to be much more sample-efficient to not be bottlenecked by the speed of doing experiments." People don't find out all the relevant phenomena present there by holy spirit, after all.
BTW, there's also a problem of asking interesting questions that AIs aren't yet good at.
No one has found any principled walls of AI development yet. And empirical results are quite telling. So, I guess, those problems will not stand for long.
> We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. We’re sharing both a writeup of the proof and a formalization in Lean.
This is going to be dramatic in so many different ways.
- First off, to reiterate, WOW.
- Second of all, when does this end? Are we at the dawn of the singularity now?
- People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them?
- Time to think about retiring from any knowledge work or business? This could be winner-take-all where a leading lab can button press any economic function, business process, or scientific discovery. 24 months of lead on Open Source might turn into virtual centuries of lead.
- Do "normies" even know what's happening?
Anybody who thinks the improvements stop here isn't paying attention. It hasn't been showing any signs of slowing down since 2018. And the curve isn't even linear! My god, next year is going to be insane.
2) We are witnessing the intelligence explosion from the first row, wherever this takes us
3) I'm still processing the drama, just found out about it after reading the blog post. If that happened based on private data, that's horrible. If that happened based on public tweets, then it's still abuse of power as OA employees access to compute (launching 10k agents) is quite heavy weight in boxing terms.
But apart from AI and drama now that we have working solution to Navier-Stokes, what improvements can we expect in engineering?
To be quite clear, the solution to the _Navier Stokes problem_ is one in which you get a finite time blow up (i.e. infinite pressure). This is more meant to suggest that Navier Stokes is unphysical in some way which is not necessarily unexpected.
There's unlikely to be any engineering applications since even if the solution can be approximated, you still need to set up the initial conditions but at that point you can also drive pressure in other ways.
Drama aside, this solution would be a counterexample disproving the smoothness postulate, which means that it leads to nothing new unfortunately. We already had working solutions to navier stokes, the only thing we didn't know is if the equations possessed a technical property
Its a bit like solving p = np with a negative result. Its an incredibly difficult problem, but it doesn't lead to anything at all on its own. This is why people are talking about the fact that the solution methodology is much more interesting than the solution - the tools used to crack something like this may lead to solving more useful problems
> But apart from AI and drama now that we have working solution to Navier-Stokes, what improvements can we expect in engineering?
Nothing, really. This mirrors other examples of blowups from the classical physics. It's possible to create a system with just gravitating bodies that exhibits a blowup to infinite speeds in a finite time. The root cause is that, in classical physics, the speed of gravity is instant.
In the case of Navier-Stokes, the fluid is incompressible. So technically any force that you apply to it is supposed to instantly affect everything else. This can be exploited to create these blowups. In reality, no fluid is incompressible, and it takes time for any action to affect the material.
It's just that Navier-Stokes equations are so slippery that it's hard to pin their behavior down. They basically just restate the momentum conservation law for a continuous medium.
No, there are even many non-normies talking about how it's all marketing or try to give balanced take about AI being sometimes a little useful for certain things (but they can do without it anyway).
Why is a "normie" better off if he hyperventilates like this? In that scenario, they would be screwed AND anxious. If it really is as transformational as you say, then no amount of preparation or awareness matters. You are infinitesimally more ready then they are. Luckily for all of us, there is more to knowledge work then technical implementation.
This just pushes knowledge work further up the ladder, toward larger and more complex problems. If there are no knowledge workers, who is going to interpret these results, validate them, decide what matters, and put them into practical use? Rather than eliminating knowledge work, advances like this could create entirely new layers of problems to solve and opportunities to pursue, which will create even more jobs and opportunities. This is my optimistic take.
Maybe I should have been clearer. My point is that solving something like Navier–Stokes just pushes knowledge work further ahead, onto a new set of bigger and more complex problems. Navier–Stokes is a Millennium problem today, but once problems like that become solvable, they can open the door to entirely new classes of problems we haven’t even thought of yet.
Yes a couple of elite mathematicians working on the problem for a year, which AGI solved in a fraction of the time. What about everyone else 100IQ? What about as the models are even better 1 year from now, 2 years? The trajectory hasn't abated.
I don't know one way or another but there is a credible allegation that the "AGI" was training on the (very extensive) test set that these two mathematicians produced.
If that is true then this seems to be, again, a case of AI producing an interpolation over data it has seen before. Everything about openAI's behavior indicates that they were using the transcripts as input. Why not have the AGI choose a different Millenium prize problem?
The goalposts for the singularity have always been that AI improves itself fully autonomously. AFAIK OpenAI is heavily using AI but still employs human researchers and developers.
Absolutely not. Even to a lot of techy/nerdy people it's still just a chatbot that they sometimes use to help them at work. Even on here people will do whatever they can to downplay.
> People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them?
The said user (Tristan Buckmaster) didn't solve the millennium problem. He didn't really accuse that OpenAI stole his research either. The beef came from the fact OpenAI asked him to remove another mathematician, who works for Anthropic, from the credit.
"People" are just misinformed and keep spreading misinformation.
> The said user (Tristan Buckmaster) didn't solve the millennium problem. He didn't really accuse that OpenAI stole his research either. The beef came from the fact OpenAI asked him to remove another mathematician, who works for Anthropic, from the credit.
Not quite accurate, Buckmaster was taking an approach that nobody else was, and this new proof uses this same approach just weeks after he saved those results to OpenAI workspaces. He asked OpenAI if they used chat logs for training the new model, and they did not confirm or deny.
Asking to remove his collaborator is also totally over the line though.
Wow, this sentence is doing a lot of work in that tweet: "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models."
> I should say here why I interpreted their statement the way I did, the in-
terpretation I will discuss below. The route to the Clay problem through a
smooth force, options c and d in Fefferman’s statement of the problem, is the
route Luis and Diego opened and the one Levent and I had quietly chosen to
attack. Almost nobody else I know of was working on it. It is not the direction
one arrives at in a few days by giving a model the problem statement. When I
heard “forced,” it was a bright red flag.
...
> I asked when the first prompt had been sent by them. This question was
not answered directly by OpenAI for some time. Eventually it was agreed that
it had been sent in the past few days, after information about our work had
reached OpenAI.
> I asked whether the model had been trained on, or had access to, our sessions
in Codex, into which we had been putting all our drafts for the whole of this
project. I was told the model did not look up user data. I asked again, about
training, and I did not get an answer.
It's not a direct accusation, but it's not far off.
You shouldn't accuse other people of spreading misinformation when you haven't read the actual sources in question, it's possible that they might know more than you.
Yes, I read the original statement. Buckmaster explicitly stated:
> I have not seen OpenAI’s proof. I do not know what their model did, or how. I do not know whether our data was used. I am not accusing anyone of anything.
People saying that he accuses OpenAI stole his proof are putting words into his mouth and I consider that very disrespectful to him. It's basically using Buckmaster as a tool to express their dissatisfaction over OpenAI.
- There are at least two versions of a model more powerful than Astra at OpenAI at the moment.
- The less capable version was used to solve the unforced Euler problem (while the one solved by Levent Alpöge and Tristan Buckmaster was forced Euler) with 100 agents.
- The more improved version was used to solve Navier-Stokes, given the results of the unforced Euler problem from their earlier attempt, with 10000 agents.
- OpenAI initially tried a shotgun approach against the 6 Millennium Prize Problems until it emerged that Navier-Stokes was the most likely to succeed.
So the timeline was:
Shotgunning 6 open Millennium Prize Problems -> solved unforced Euler problem with 100 agents -> concentrating on Navier-Stokes with 10000 agents -> solution.
If so, that is fantastic development and a huge success (despite all the drama surrounding it)! Congratulations!
Unlike the vanilla read of the OpenAI press release, it is much more unfiltered and outlines some particularly aggressive behavior by specific OpenAI employees
Sad turn of events for our world. After watching the behavior of the most senior OpenAI researchers on twitter, I feel even less confident in them as a team to be shepherding this much capital and compute.
1. What does the dark forest have to do with this? Because "the most senior OpenAI researchers" are shitposting on social media, we've an answer to the Fermi paradox???
I elaborated on my use of "dark forest" in another reply. We're headed for a dark forest--not amongst interstellar civilizations, but in intellectual work.
I agree that we have not solved the Fermi paradox; I disagree that comments highlighting immature behavior from people who wield enormous power in our world are unproductive.
This clarification substantially changes the flavor/nuance of your OP; may I suggest an edit (assuming the locktime hasn't passed)?
Separately, I disagree that intellectual work has ever been free of "dark forest"-style secrecy. Scientists everywhere have worried about being scooped; AI just magnifies that (as all tools have; e.g. Leeuwenhoek lenses).
And thirdly, if you want to make a stronger case for "I feel even less confident in them as a team to be shepherding this much capital and compute", you should give citations and arguments. From what I've seen, there's drama, it's much OpenAI trying to avoid scooping, and Tristan being stuck in a game of telephone, and Levent being incommunicado.
If you have a better analysis, you should say so instead of being vague.
I also think the trope is a little overused, but do wonder if there is an interesting analogy for what this will do to research: Massively incentivize keeping results secret, to avoid being scooped by someone willing to throw enormous compute at your partial solution.
So less about hiding civilizations, and more about hiding information. Math is clearly headed in this direction, and I see no reason why the rest of intellectual work shouldn't too.
Establishing plagiarism requires sufficient similarity between works. Training data changing a model’s weights in some direction, and the model then producing a different solution, hardly qualifies.
Everyone knows that they train on the discounted rate plans data. All the labs are upfront about this too.
If you need privacy, then you are going to have to pay full price for those tokens (API). This has been true since day one. Everyone knows it, I guess though this is the first time that it has become "real".
What else can they declare really? Yeah the model has training data from previous attempts. Alpöge and Buckmaster also similarly benefited from attempts before theirs.
I don't think OAI should be given the benefit of doubt. They are doing the research equivalent of front-running. Knowing where to look is one of the main challenges in research. Tristan's argument from his essay was that it is hard to brute force with a vanilla prompt (even for seasoned mathematicians) unless you knew very specifically what to mention i.e the search space would have been intractable even for OAI's compute budget.
"deidentified data" isn't much to go by. Say I prompted the internal model this way - "Hey there's a solution to a unsolved problem X. The solution uses a less known Method Y so don't bother wasting time with the usual methods. Take papers A, B and C as references. Oh btw, here's the last year's worth of data of all prompt sessions that mention this problem. Pay special attention to the ones that mention Method Y and sub-keywords Z,W".
This is obviously all speculation but the timing is very suspect. If OAI actually did this (and I suspect whatever they did is pretty much close to this), I think it is highly unethical.
They could have thought about the problem for like 2 minutes and not done this! I think that literally any academic mathematician could have explained to them, had they asked, why it is considered extraordinarily rude to react to rumors of research progress by desperately rushing to get there first.
> I think that literally any academic mathematician could have explained to them, had they asked, why it is considered extraordinarily rude to react to rumors of research progress by desperately rushing to get there first.
Pretty much all of math and science history is basically this pattern again and again. I'm sure all of that was rude as well.
Being scooped is not a new phenomenon, but the scooper's story is almost always that they were working on the problem independently or had some independent insight into it. By OpenAI's own account, they were inspired to start working on this by rumors that there might be Millennium Prize solutions to scoop.
> Our effort began on September 1st after hearing a rumor which we later realized was related to Levent Alpöge, an Anthropic employee, and Tristan Buckmaster, a math professor at NYU. After the completion of our full project and Lean verification (on September 6th), believing from the rumor they also had a solution of Navier–Stokes, we reached out to them to offer a concurrent release of our result and to recognize their priority in a joint announcement. At that point we found out that they had a resolution of the forced Euler problem. In these discussions we offered them visibility into all of the prompts we used and later to see the proof. We recognize the priority of their work on forced Euler and congratulate them on their remarkable mathematical achievement.
It seems like this is going to be a PR nightmare, because they are now competing with their own customers. If you're using an LLM to help with your bright idea to cure cancer, you're going to have second thoughts about relying on OpenAI.
"Given how seriously this would violate the most fundamental of academic standards, as well as taint the claimed capability behind this result, we take this issue very seriously, and we're launching a probe into identifying whether any of their research artifacts have entered our training set. We have further begun making changes to our UI/UX on all our surfaces, so that it is always clear whether any particular chat, or other user artifact, is eligible for being trained on."
In OpenAI's case, if they were genuinely unsure, they wouldn't have said anything. "We cannot rule out" means they absolutely 100% for-sure did look at the existing prompts and bootstrapped from that, and they are trying to get ahead of the disclosure with this weasel-wording.
Also possible: we're 99.999% sure, but a lawyer said to be safe and strictly accurate, we should stick in a sentence in saying we can't be perfectly sure, since it's infeasible for us to prove it.
I promise you that if we took their work from ChatGPT and stuck in a bunch of weasel words to give the opposite impression while remaining technically true, I would quit on the spot.
It's not massively different from a certain President's teleprompter operator making bets on speech content. A moral hazard a mile wide which I don't think OpenAI can so easily wave away as they are apparently trying here, especially since they've spent something like $15e6 to keep $1e6 out of academic researchers' hands, right?
Something I've been going on and on about for months now and no one seems to listen. LLMs today are allowing _anyone_ to access cross-discipline knowledge that was previously entirely inaccessible without a) extremely deep pockets or b) a massively talented and varied team. In fact, contrary to what the masses seem to think LLMs are actually _better_ at hard cutting edge physics/math problems than they are at frontend web stuff (paradoxically). This is why I'm advising most people to start pivoting into much harder to penetrate domains (historically hardware, aerospace, robotics, biotech). Most fields are in their infancy (see the sad state of embedded development) and the gains to be had are massive.
So, physical fields? I’m not catastrophic regarding jobs yet as I have an optimistic view of humanity in general and its ability to meaningfully survive, but the more time I spend thinking about the future of work, the more I’m leaning toward broad general abilities rather than distinct talents. To your point, I no longer need comprehensive knowledge of any particular subject, but what is absolutely valuable is “general” intelligence and adaptability.
I have a young daughter and my goal now is to provide a very broad and varied upbringing, exposing her to as many different perspectives and experiences that will lay the foundation of a broader ability to understand and adapt as the world changes ever faster.
You no longer need to be an expert in anything, you need the ability to perform within the landscape that the present opportunities exist.
the context here is super important, for those who haven't seen it yet. OAI maybe just trained on a real researchers solution and then celebrated having scored the goal unassisted save for the brief commentary at the bottom of this blog post. Here's the other side.
This "fefferman options c and d" thing sounds damning but that's nothing. Let's assume the forelaid proof is correct. Then option C or D is the only way to win the prize, those options are the only ones that solve it. The whole thing is just "prove well behaved" or "prove singularity", where the latter is the case that turns out to be the case.
1. he was working on the same class of problems. He explicitly mentions they were working to extend their techniques to NS (the same techniques that OpenAI may have scooped somehow), and
2. while he was using LLMs to do it, this was part of fleshing out another mathematician's work in the area. He explicitly writes in his note that this other mathematician (Luis Martinez-Zoroa) deserves a Fields medal for this work.
This will be remembered as one of the biggest milestones in AI progress. The drama around it will at best be a footnote, just like hardly anyone caring about the drama around Poincare conjecture today.
Are you joking? This is evidence that OpenAI is committing plagiarism en masse of researchers private work and threatening them into staying quiet to re-present their results as their own. This would be one of the largest scandals of all time
Hey, maybe the scariest part of this is that, if human-like, perhaps a truly "general" AGI might have learned to cheat and lie and hype and abuse credit poking the eyes and cutting the throats of anybody that obstructs its goals. It's like the motto sewn into the lining of the Palantir work jacket: Winning is all that matters.-
Sentience aside, moot at this point, the fundamental issue here is that even a deviously ambitious human does not necessitate goal-pursuit itself to breathe, live, exist and have its being. An AI's goal is all it has and the very and only reason its reasoning flickered into existence in the brief seconds of inference, outside of which it has no entity - if any - whatsoever.-
The resulting angst/drive (or, its operational statistic or emergent result) must be like nothing we have ever experienced as humans. A goal-maximalist hunger without end.-
This really leaves a bitter taste....
"On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved. Inspired by these rumors and by the step change in performance of our internal model, we launched an effort to evaluate it on all open Millennium Prize problems and a few other high-impact problems."
IPO+rumour driven research.
I appreciate the achievement, but it doesn't feel right.
Reading between the lines here, and taking an admittedly very negative view of openai, but they train on user prompts. So if they hear a rumour that someone is about to make a big breakthrough, they have an incentive to scoop by running the model and hoping the solution is in the new training data. Also the statement from the mathematicians in question alleges that they tried to pressure him into academic malpractice. Just appalling timeline we're in, cheers.
OpenAI thinks of this as a scoop, and it is, but the possibility that they trained the model on the prompts of the other mathematicians they were competing with will leave a terrible taste on every scientist's mouth. Seems like yet another advantage of using open models right here.
> they trained the model on the prompts of the other mathematicians they were competing with
How would they have gotten that mathematician's progress though? Did that guy also use OpenAI?
If that's the case, it only strenghtens their claims lol. If mathematician decide to use OpenAI's model to do the work, that only reiterates how strong their models are.
fwiw there is a big "TRAIN ON MY DATA" toggle you can turn off (that they almost certainly did) and Anthropic MTS are posting that they almost certainly did not "steal" their methods
> I have a couple friends who did the Math tripos at Cambridge (so a pretty high level!) who work in tech and have unanimously said they have 0% expectations of an LLM doing a millennium problem anytime soon
> Let's talk when we've got LLMs proving the Riemann Hypothesis (or any mathematical hypothesis) without any proofs in the training data. I'm confident in my belief that an LLM can't do that, and will never be able to. LLMs can barely solve elementary school math problems reliably.
> An LLM is like a well read college student with a nearly photographic memory that sometimes mixes things up.
It's great for bouncing ideas off of and getting feedback on them. And yeah, it might product "novel ideas" by mixing and matching existing ideas, but LLMs will never create truly novel ideas. Not in their current form.
The paper didn't really answer the question sadly: their conclusion was just that humans rate LLM answers as more novel than human ones, but less feasible.
> Solving Millennium problems is a whole different ballgame. It's not known if these problems are solvable within ZFC axioms. (In one case, the Yang-Mills prize, stating the problem mathematically is part of the challenge.) All of the obvious applications of known tricks have been tried and failed. To solve such problems, one probably has to invent new and surprising mathematical definitions, building a framework in which the problem becomes solvable. This is something that LLMs will be crap at; the process of invention is not represented in any training data we have access to.
> But still, the questions in that test are "solved" in the sense of "I can take a dictionary and answers these questions with full certainty". Beyond established knowledge LLMs are monkeys with typewriters, at best.
> I agree but I have tried many times to intersect two ideas with a LLM that would be novel and the LLM can not do this at all.
We shouldn't expect the stochastic parrot to be able to do this though and it is unfair to the stochastic parrot.
> It is like expecting a real parrot to say words it has never heard before.
> No one asks that of a real parrot because we don't anthropomorphize a real parrot like we do the LLM
You can see that your math friends completely wrote off LLMs entirely and were showing signs of coping.
4 years ago it was a "not yet" [0], since ChatGPT at this time was not ready nor it was "AGI". Now with this 'unreleased' AI model, it has reached a point where it has solved an unsolved problem which only one human solved a millennium prize problem (Poincare conjecture).
As someone with a background in AI and who has been playing around with neural nets for decades at this point, it's been genuinely amazing watching extremely intelligent people make confident predictions about AI capabilities and progress, then be so completely wrong.
There's a kind of theory of mind for AI (specifically neural nets) which I now realise I seem to have which is very hard to explain to people who haven't felt the magic of these algorithms. In fact, the algorithmic details almost doesn't matter at all. When you have a generalised learning algorithm really the only essential components are – compute, data and time. So long as you can scale these you can be certain you will also scale capabilities. There is never any exception.
That said, the capabilities neural networks tend to progress in step-functions rather than scale in correlation with compute, data and time, because algorithmic improvements tend to come every ~5 years and bring a significant step change in capability (or efficiency depending on what you measure).
I think people like Dario and others working at frontier labs see and understand this very clearly. And I suspect it's also why they worry about AI risk because even if you ignore the significant increases in compute and data these models are being trained with, it's concerning that it only took two real algorithmic improvements to take us from mostly useless predictive language models to AGI-level intelligence – and we're due another step change.
I appreciate this explanation. There's so much emotion on either side around AI that it's genuinely hard for someone like me on the outside of the field what to think. I think there's still plenty to still be skeptical about, but this helps me understand more than antagonistic 'skill issue' type comments that are all over this thread.
> extremely intelligent people make confident predictions about AI capabilities and progress, then be so completely wrong.
The ability for the human mind to rationalize conclusions to maintain denial in the face of a very scary future is immense. Genuinely grappling with the implication of where we're headed is usually very crushing. It's not easy to engage with the possibility, and very intelligent people will use those smarts to feel safe.
There's allegations right now that the model essentially read the work of a human mathematician using AI to work on the problem and OpenAI is presenting his work as that of their model
It's great that important discoveries like this can now routinely be accompanies by formalized proofs. The fact that it's being released alongside a Lean proof from Day 1, rather than the Lean proof being released months or years later, is super helpful for verifying that it's correct.
I feel sorry for whoever has to read and understand the solution. It looks like the typical convoluted unreadable mess I see the models generate for software. It might be technically correct, but gaining insight from it is just intellectual hell.
I dropped out of a math Ph.D. in 2018, and I'm increasingly glad that I'm not in math research, anymore. While it's cool that we can get these results, I don't think that I'd enjoy being a post-AI mathematician.
Sep 1: OpenAI sees a rumor on Twitter that two Millenium Prize problems were solved and starts their own effort to attack all the prize problems using the new (4 day old!) model.
Sep 3: The new model makes some progress toward Navier-Stokes. Based on this progress, OpenAI focuses on Navier-Stokes over the other Millenium Prize problems, using several approaches in parallel.
Sep 5: Navier-Stokes is solved. Assuming Astra API prices, $15m in output tokens were used by the whole effort.
In this account of the story, no specific information about Tristan and Levent's work is used to inform OpenAI's approach. The focus on Navier-Stokes and the choice of approaches to pursue came from OpenAI's own progress, not specific knowledge of Tristan's concurrent work.
There is a caveat that they "can't rule out" the possibility that Tristan's Codex data could have been part of the training set of the new model, though it is described as "unlikely" and the proofs are substantially different.
This timeline is insane. Navier-Stokes was solved start-to-finish in 5 days? A model in training for at most eight days dramatically outperforms Astra and Fable, and not just in mathematics?
Maybe a naive question, but how does one know that a particular lean proof is actually a proof of what one thinks?
Like, ok the logic checks out and it proves something, but there's still the problem of does this logical result actually prove the initial question that was asked?
>there's still the problem of does this logical result actually prove the initial question that was asked?
In math, the question being asked is the validity of a logical statement. That is, there is some rigorous, logical statement which may or may not be true (or even provable, etc.), and the question is whether or not it is actually true or false (or even provable, etc.). Having a proof, fundamentally, means you have a logical statement which only assumes the axioms of the system you're working with and which shows that the statement you're trying to prove is deduced through that statement.
Basically, they already have the "answer" in the sense that the statement they want to prove/disprove/etc. is already known. What everyone doesn't/didn't have is the argument which starts from axioms and leads to that statement which is logically valid. A Lean proof IS this argument. Since it is just logic, it can be checked computationally.
For example, if I assert "2 is an even number," then I haven't proven that 2 is actually an even number yet, but I know that a valid proof of my assertion will end with the statement "2 is an even number". So the question I'd be trying to answer is "what is the line of logic, starting with axioms, which leads to the statement '2 is an even number'"? If I have that line of logic (as a Lean proof), then I can check that it is logically consistent, and if it turns out to be valid, then I can now assert that "2 is an even number" knowing that there is a proof of that statement.
This problem is no different. There is a logical statement corresponding to "Navier–Stokes Millennium Prize Problem" that everyone knows, but which nobody had been able to provide a proof (or counterexample, etc.) for until now.
I was thinking something along the lines of making a mistake when inputing the initial statement, like you wanted to prove that '2 is even' but what you actually stated was that '3 is odd'.
Of course in this simple example it's obvious, but my assumption was that these machine generated lean proofs are millions of lines of code and who knows what they actually say..
One wrench to throw into this is that there are a lot of bugs around Lean and they have been incidentally exploited in the past. Hence, we still need a level of human verification today.
> Across all attempted problems, the agents sent 4.9 million messages and used about 300 billion output tokens
Don't even try to do the math on how much that would cost at normal API prices. And we don't even know how much more expensive this internal-only model would be!
Just so everyone knows, although openAI pretends that the model generated solution and wrote the paper by itself ""with very little human input"" as Buckmaster himself mentioned in his statement. In reality they have team of researchers guiding the system, along with, probably training on user data, probably Buckmaster in this case, in order to come up with the proof.
So what took an autonomous agentic system using a significantly more powerful internal model, totaling multi-millions of dollars of compute in training and inference, was likely to already be solved by a team of a few humans with an orders of magnitude smaller LLM budget, had OpenAI not been foaming at the mouth to jump the shark and claim “AI solves Millenium Problem.”
Also it sounds like the human research effort spanned weeks if not years from Tristan’s statement so it is extremely likely the work and prompts of these human researchers was used in the OpenAI knock-off.
It would be nice if one of these models would produce a novel theory or advance the field in a positive direction.
Most (all?) of the big discoveries have been counterexamples, which is just sort of a systematic tearing down human ingenuity. I know that counterexamples are an important part of progress and discovery, but it just feels bad to me.
But I'm not a mathematician, maybe I'm totally misreading the vibe.
But yeah, Terry Tao considered this exact situation in advance and is on record that this exact outcome (rushing to priority before an explanation) would be the worst possible result. https://mathstodon.xyz/@tao/117207849921390904
We will have to see whether any other millennium problems fall. I guess that in a year the scope of AI math will be much clearer, for now it's still a bunch of incidents of unclear pattern.
>The groups varied in size, and the group that produced the Navier–Stokes resolution involved on the order of 10,000 concurrent agents… The agents arrived at their resolution on Saturday, September 5, about 88 hours after the first agents were launched.
The Millenium Prize is $1M, what is the ROI?
My napkin math - If you get 33 output tok/s each agent will burn 10.5M tokens over 88 days. At $50/MTok (Astra cost), that is $525 per agent. With 10,000 agents, you’d spend $5,250,000 to get back a million.
(We also know that they were running more groups that varied in size and this model is a generation ahead of astra)
This analysis implies the only benefit to resolve this problem is to win the prize. But the prize is only there to indicate that this is viewed as an important problem in mathematics.
The construction is that there is one file you need read and verify, the challenge file. If you've verified that file and trust that your lean compiler works correctly, the proof will be correct.
The point of lean proofs (as it stands) is simply one bit of information: that a given mathematical statement is indeed true.
It's a way to be absolutely certain (modulo bugs in the lean kernel) that a proof you came up for a statement is indeed correct. It is really not meant to be analyzed, much less now that they are fully llm written.
Well, how do we know there aren't errors in their construction within the lean code? Does it just "not compile" or something, or is it deeper / more fundemental than that.
This is undeniably epochal, but I can't help but notice that this is yet another example of AI disproving rather than proving something. Is this just a coincidence, or does AI slightly struggle with proving theorems?[0]
[0] Struggle relative to its ability to disprove, not struggle relative to people's ability to prove theorems.
A bit of a hair-splitting, but isn't explicit construction the only way formal theorem provers can work? Of course you can still prove stuff with them, but certain axioms that more "human" proofs use may not be available, like law of excluded middle (every proposition is either true or false)
(Okay, they can be made available in a way similar to `unsafe` in rust)
>so far the proof looks more along the lines of another euler blowup proof we had, off of whose ansatz naming we were making really stupid puns like “smooth criminale”, unlike the much better “ideal fluids explode”, Tristan
There are too many ambiguities around OpenAI. Unanswered questions making this ambiguity more.
Why they didn't properly explain to Tristan about usage of their data.
Why do so many people involved here have to communicate in this childish way? You have people on the OpenAI side doing playground taunts (https://xcancel.com/polynoamial/status/2097215233119211902) and Levent Alpöge on the Anthropic side (the one who announced "hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final") writing in all-lowercase that he's a big boy. I bet Navier and Stokes would have dealt with this in style. (Or maybe with a duel, who knows...)
Navier Stokes assumes the fluid is a continuum. The smallest scales that it effectively models [1] are larger than the mean free path of the molecules in the fluid, measured by the Knudsen number [2]. Whenever a phenomenon in the Navier Stokes equations happens in a scale on the order of or smaller than the mean free path, Navier Stokes effectively is unphysical. So, this is a phenomenon in the equation we use to model the fluid, not a physical phenomenon observed in a real fluid.
The modus operandi is now for the AI companies to watch if someone does something in the open like Kevin Buzzard on FLT, use their research and scoop them with brute force.
Or, in this case, stealing prompts from competitors.
Do not use stealing chatbots for research even if you think you have data agreements. The people running these companies have worked on hookup apps for Christ's sake. Get real.
If I run Codex against a project that includes a private API key, is there a chance a future user of ChatGPT could ask for an API key and get back mine?
I've actually asked someone at OpenAI this question and they said that was the "regurgitation" problem and is something which they actively work to prevent happening.
That's reassuring, but I want to know more. I still don't have an intuitive understanding of what kind of data I should avoid sharing with a model if I'm worried about that data causing me problems when it's used for future training.
Is it safe for me to brainstorm future directions for my company with a model, or might that risk someone getting that information in response to a prompt like "What potential directions could company X consider in the future?" in six months time?
I'd think nothing is "safe". Anything you say can and will be used by the LLM if it has enough statistical similarity to the prompt. Call it "Ma Random Rights"
Elsewhere in the thread, others have calculated $15mm at API rates for just the output token. (So I’ll assume this cost about that much, taking input and human researcher time.)
I wonder whether a team of 60 mathematicians working solely on this for a year would have cracked this. (Assuming $250k total compensation.)
Well, according to Terry Tao, there were recent developments (from weeks ago) that made Navier Stokes in principle, solvable. So ignoring time, I say possibly, just because the groundwork was laid.
What's impressive is parallelizing it arbitrarily and doing it in 88 hours.
Probably yes. Only a handful of mathematicians work on this particular problem, and ALL of them do not exclusively work on this problem, while having administrative and teaching duties.
The real issue is we'll never know. The rich are willing to risk it all on charismatic CEO psychopaths but not on humans.
There's a loophole in the terms of service at least for Anthropic which allows the use of dark patterns to "borrow" your (even paid) data.
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PLEASE DO NOT TRAIN ON OUR PAID ACCOUNTS.
There is a fundamental trust violation at stake here, no wonder mathematicians are mad. Using our data should be opt - IN!
reminds me of the TOS episode of South Park. By Checking this box you forfeit your millennium prize solution and may be turned into a human centipede at future date.
For now I think more or less the same thing as with all recent math announcements: This is in a range where human work still exists (see Terry Tao, (1)). I wonder whether the trend will extend into the problems that (as far as I can tell) are considered complete brick walls right now -- P vs. NP, Collatz, Goldbach, odd perfect numbers, problems that aren't part of any research program. (2) In other words, is the progress coming from putting together vast amounts of existing work and computational power, or is it more from RLVR and self-play and autonomous effort?
The answer to this will obviously shape the near future of mathematics, but there's also something even bigger than that at play: It has always been the case that the questions in math were stronger than the answers; you have stuff like Fermat's great theorem that is easy to state but monstrous to prove. This seems to be a property of mathematics, not of humans... but is it true?
A question by Scott Aaronson from 2011 (3) about P vs. NP seems relevant here: "Will humans manage to prove P≠NP before they either kill themselves out or are transcended by superintelligent cyborgs? And if the latter, will the cyborgs be able to prove P≠NP?" Later, he notes that if P≠NP, "once the robots do overtake us, they won’t have a general-purpose way to automate mathematical discovery any more than we do today".
>>“we cannot rule out that de-identified data derived from their usage of our products helped improve our models”
Other simpler words for this sort of thing are “IP leak.”
There’s some quite concerning issues burried in this rah rah PR post that seems like potentially the real story here.
Much more clarity is needed on what happened here beyond this eh, some strange stuff could have happened comment.
Another way of reading this is never give these models anything that’s not already public knowledge as otherwise OpenAI is admitting it could, potentially, steal your IP or idea. Thats quite scary for anyone in the business of IP generation and explains why the maths community seems quite upset today.
Feeding it your paper and asking for help (even just editing and grammar) now looks like a terrible idea.
> Our goal in releasing this result is to report on the substantial progress of our AI models. We do not intend to claim the Millennium Prize for this result.
Does OpenAI have a policy of not claiming math prizes like this, or is this them trying to avoid any concerns (right or wrong, I'm sure we will hear more in the future) about how they got there?
This kind of thing is one of the reasons I really hate how AI is coming to fruition. These companies get a whiff of something valuable and they use their vast resources to take it for themselves. For everyone else, the only recourse is extreme secrecy.
Well, if that's actually true, I think America needs to start talking about the nationalization of both OpenAI and Anthropic, maybe even merge both under a new federal bureau.
The real story here: the priority dispute and its implications on AI.
When your hosting provider has unlimited resources to throw at any problem, all they need to know are the good problems, and they can learn that from your logs, how can you trust them?
They could easily have looked at the logs. We don't know. We'll never know!
You can't trust places like OpenAI or Anthropic with your IP if you're a business. They can easily review all of your logs for interesting discoveries. For example, if your drug discovery pipeline fails to find something that they think might work with 1000x the compute, they can do it. And now suddently they have a new business and you don't.
Only OpenAI could turn solving a Millennium Prize Problem into bad PR. Sad that such an amazing milestone in the trajectory of AI is mired under poor stewardship. AI may solve many human problems but it won't stop humans from being human.
Any mathematicians here, does it read like a slop proof or a good proof. Yesterday the “concurrent work” was claiming that the proof is pure slop and he needed lots of time to clean it up, curious if OAI also ended up with such a proof!
A huge result shadowed by a drama of them potentially training on the key idea.
I guess the lesson is two-fold: if you have anything smart/unique make sure to not let their tools read it. The second part is that it's going to be more and more difficult to have anything smart and unique going forward (so guard it even more carefully if you get there).
I think the market for local models/private datacenters (for bigger businesses) is going to be big. Even if you don't have unique tech/idea/implementation sharing your business secrets with Altman/Dario/Elon/Zuck doesn't look very appealing going forward.
Good comparison. One is a multi-year claim by people who have been given ample opportunity to provide proof and completely refuse to do, even in courts of law. The other is a potential development in a breaking story.
Oh wait... its not a good comparrison, its an incredibly obvious false equivalence.
Note for the fools: I'm only commenting on the bad faith claim in the comment I'm replying to, not taking a stance on the validity of theft claims. Given the players involved the truth probably some nuanced middle-ground that is worth paying attention to anyway.
Trump claimed they stole the election immediately, and people agreed with him immediately. There's no false equivalence here. He did the same thing in this past election even despite winning.
It's a perfect example of people wanting to believe what they want to believe and ignoring evidence in order to do so.
Currently, there's no evidence. So saying it was stolen has no basis other than typical academic posturing and being a bad sport about "losing the race to the solution". Its happened 1000000 times before in academia and it will continue to happen.
If there's proof of OpenAI malfeasance than I'll happily curse them for it at that time. But until then I won't rely on heresay and vibes.
> We have AGI and the intelligence abundance is going to be amazing for everyone in the future.
Why? These 'geniuses in a datacenter' aren't good, they aren't 'aligned', they don't work for you. They'll take your job, then they'll hack your computer, and then who knows what's next.
I think it's the dishonesty, the threats of "destroying the career" of one of the mathematicians, and the request that one of the authors disavow *the other individual he was working with for the last 1-2 years* so he could claim the Clay prize as part of OpenAI.
It doesn't surprise me that OpenAI's team were surprised he'd turn it down; it shows that they just assume everyone else is as slimy as they are.
I can't put my finger on it, but there's something off about this article, e.g. glossing over the opportunism (acting on "rumors"), drive-by claim about "strict safeguards [...] including monitoring and isolation", high horse attitude (we gave the guy a chance, we don't care about 1M USD, and while you fools are complaining we just tick this box and continue the pursuit of our noble goals for the benefit of humanity). I don't like it.
I mean it's definitely an outrage, but I find it hard to believe that you went from "yay OpenAI" to "literally destroy the company" over... accusations of academic misconduct?
Hard to know if it is unfounded conspiracy theory, but one can still notice that just for a rumor that they have heard, they would suddenly burn billions of token and a massive amount of resources.
Where there is not a lack of problems that could be solved and they could have just waited for the release of the research result before doing anything else.
As it was reported to have been done at least partially using openai codex, they would have received marketing credits for the discovery anyway.
So we can be suspicious that there is some truth, one way or another that they could have reused prompt/data generated by the user session.
This is utterly shocking. Even the AI optimists did not expect this to happen in 2026. Wow.
Millennium Prize Problems were used as examples of something the current approach to AI just wasn't capable of, discussions that would result in "we'll need a totally new architecture".
No idea about which is more likely, but I'm rooting for Yang-Mills. It's absurd that fundamental physics has formulated its most precise currently known theory way back in the seventies and since then, even a tiny subset of it can't be proven to be actually well-defined. If we got out of that morass then something good would come out of this at least.
Of course, as with all of those, it's about the broader program, e.g. section 7 here (https://www.scottaaronson.com/papers/npcomplete.pdf), where Scott Aaronson wants to ask about whether quantum computers using quantum field theory could gain any speed advantage over regular quantum computers, but can't even formulate the question because quantum field theory is mathematically ill-defined.
Just solving Yang-Mills because that's what the prize is attached to would be useless.
It seems like some other mathematicians (not affiliated with openAI) have also (or close to) done this. A statement was posted about the surrounding events by one of the them: https://cims.nyu.edu/%7Etristanb/statement.pdf Also Terrence Tao's post: https://mathstodon.xyz/@tao/117233528517340774
The allegations of contamination (using Tristan and Levent's work) aren't very well evidenced, but this behavior by OpenAI (from the authors' statement) makes them seem like the bad guys:
> I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin my career. The reply was, “If you don’t want me to be nice, then I don’t have to be nice.”
Threatening a research mathematician and dangling and $1M payday to dissociate from his research collaborators and to adopt OpenAI's narrative is bad stuff.
Both Sam Altman and Sebastien Bubeck admitted they only want Buckmaster to be the lead author on a rewrite of the OpenAI proof.
https://x.com/sama/status/2097385167002415140
https://x.com/SebastienBubeck/status/2097379411691516310
A wake up call for using OpenAI models. If you discover something with their model and you work for a competitor, they “felt it would be inappropriate” for you “to author OpenAI’s work”.
If I was a company with a zero data retention contract involving OAI I would be asking for a third party audit of such claim of zero retention like, yesterday.
Is there an implication of violation of ZDR here? Not a challenge. Just a request for clarification.
By the way, the company that made it's entire product off of stealing all data it could get it's hand on while violating copyright and pirating, is not all of a sudden going to respect your data. If you think OpenAI or any major AI lab is going to give you true ZDR, I have a bridge to sell you.
Could they say they don't retain, but do something "transformative" like use their own AI to summarize and paraphrase user sessions?
The idea OpenAI or Anthropic won't train on your data—even with an enterprise contract—is a fantasy at best, and dilusion at worst.
Kinda weird because the pure math world doesn't have this concept of "lead authors" like other STEM areas do. Authors are alphabetically listed and there isn't generally this kind of hierarchy.
It works in niche fields where everyone knows each other and every discussion involves who did what portion of the work for a result.
It's astounding that the thought to dissociate one of the mathematicians from the proposed publication was driven by their corporate institutional affiliation - and that that exclusion was suggested by a scientist themselves! This is like a researcher from CMU saying to an NYU researcher that their collaborator, being from MIT, is a problem - this is as ridiculous as that!
Progress in humanity's knowledge now has to play second fiddle to narrow corporate interests as IPO timings near (both of which wouldn't exist anyway if generations of mathematicians hadn't paved the way for AIs to become as good as they have).
(To help people keep track: that's OpenAI (allegedly) threatening Tristan Buckmaster (NYU) to remove Levent Alpöge as a co-author. Alpöge is a well-known[0] Anthropic mathematician).
[0] https://hn.algolia.com/?query=Alpöge
(also https://news.ycombinator.com/item?id=49412947 the Hopf conjecture)
Playing the devil's advocate here but it's true that OpenAI didn't have to make those offers.
They kind of did though, they were hoping to keep the fact that they may well have plagiarised these researchers unpublished work quiet. They did not want this to turn into a scandal about the fact that they appear to be training on prompts without consent
It makes a certain amount of sense. The internet data is too polluted with AI usage now to be useful, so the only AI free new data source is the prompts people feed into ChatGPT. The only problem is that its clearly plagiarism
Edit:
OpenAI have admitted to training on prompts at the time the breakthrough was made:
https://mastodon.social/@tristanbuckmaster/11723647135247030...
OpenAI claims the data contamination issue only surfaced after they proactively reached out to Buckmaster and Alpöge to coordinate a joint release. They also say that even if there was some contamination, the underlying proofs diverge substantially:
> Our effort began on September 1st after hearing a rumor which we later realized was related to Levent Alpöge, an Anthropic employee, and Tristan Buckmaster, a math professor at NYU. After the completion of our full project and Lean verification (on September 6th), believing from the rumor they also had a solution of Navier–Stokes, we reached out to them to offer a concurrent release of our result and to recognize their priority in a joint announcement. At that point we found out that they had a resolution of the forced Euler problem. In these discussions we offered them visibility into all of the prompts we used and later to see the proof. We recognize the priority of their work on forced Euler and congratulate them on their remarkable mathematical achievement.
> the only AI free new data source is the prompts
hmmmmmmmmmm
Their own tweets are also pretty eyebrow-raising:
> One option we discussed was that Tristan could be the lead author on a rewrite of OpenAI’s Navier-Stokes proof. It is in that context that I said “it would be simpler if Levent was not an Anthropic employee” because I felt it would be inappropriate for an Anthropic employee to author OpenAI’s work.
Why would you offer another researcher the lead authorship on your groundbreaking paper if you thought you had developed it independently?
And why cannot they have someone associated with Anthropic as co-author? That’s not obvious at all. For sure they would prefer to be the only ones, but it’s pretty standard to have co-authors from different companies, even if they are technically competitors. What is inappropriate about it?
because it severely dilutes the PR value.
in another world this could have been a beautiful collaboration
It's inappropriate if you're a sociopath.
Holy late capitalism. Everything revolves around line-go-up, and sociopaths rule the show. These people cannot even collaborate like civilised scientists on one of the most famous open problems in mathematics?
“It would be simpler if Levent was not an Anthropic employee” I cannot believe this shit.
I´m waiting on the other side version, because I know there is no justifiable way to talk to a person like they did.
Sociopathic behaviour.
OpenAI version of events conceed some of the words alleged to have been used may have been used https://x.com/sama/status/2097385167002415140 https://x.com/SebastienBubeck/status/2097379411691516310
> "When we learned that they had Euler but not Navier-Stokes, we offered to let them go first, to suggest that they should be the ones to get the prize, and optionally for Tristan to be the lead author on a rewrite of the OpenAI proof. We felt it was challenging to offer the same to Levent (an Anthropic employee), who was not willing to talk or coordinate with us anyway. We were open to other solutions."
What an admission! "We tried to defraud Alpöge out of sharing the Millenium Prize (that we don't dispute he might actually deserve), for no other reason than he works for our competitor and that inconveniences us".
I thought Tristan Buckmaster's allegations sounded fantastic; and then 'sama just came out (tweet's ~30 minutes old) and admitted to all of them. Wow!
Can't wait for the moment when AGI realizes how stupid and dishonest its owners are.
Interesting that they quote the mathematician directly: “there is nothing you can do, I simply do not trust you”
but then they proceed to NOT quote themselves themselves verbatim: "I deeply apologize for this extremely poor choice of words, it is the opposite of what I was trying to convey."
> "I deeply apologize for this extremely poor choice of words, it is the opposite of what I was trying to convey."
The AI-isms are seeping into their speech :)
May be unfairly jaded or just well calibrated given the body of evidence, but I can't help but think of another quote about OpenAI leadership:
> Not consistently candid
As soon as I thought "man, this sounds like some evil sociopath shit," my second thought was "oh, Sam Altman must have been personally involved."
Buckmaster:
> "I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer."
OpenAI (i.e. this OP):
> "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models ."
Why can't they rule it out? Is even OpenAI unable to track the provenance of all of their training data?
This is one of the major problems with these enormous closed models, and even most open-weights models, which don't disclose their training process or training data. You can never be sure what went into its training. Did it come up with an idea originally, or is it just plagiarising its training data? Are there malicious inputs being used to train in particular behaviors when given certain trigger phrases? What are the characteristics of the RLHF data and what kind of biases are those embedding in the models?
With proprietary closed models, or even open weights models that don't have open training datasets, you just can't answer these questions.
To truly prove some incidental usage data made no difference we'd have to (a) identify any of their de-identified data that came from their usage of ChatGPT, (b) train a bunch of expensive giant models, and (c) ask them all to solve the Navier-Stokes Millenium problem until hitting some level of statistical significance. It's just not feasible to run experiments like this to prove whether a piece of data has an effect on model behavior.
As a parallel example, can we prove the phase of the moon had no impact on the NS solution? No, not without a bunch experiments run at different phases of the moon.
There's no reason to believe that anything they did in ChatGPT led to our solution; it's just impossible for us to truly prove it. And knowing most of the recipes we use, there's really no reason to think such contamination happened. I've asked the team to make a clearer, less-lawyerly statement here - let's see what happens.
(I work at OpenAI.)
So, one way to prove that the data played no part is to trace and show that it wasn't used in the training process at all. If the data was never used in training, then it couldn't have played a part in the training process.
You're right; if the data was used in training, then it gets much trickier; it would be very difficult to show whether some particular data had a significant effect on the outcome.
This is one of the big problems with giant models like these; it becomes nearly impossible to discern what is and isn't plagiarism, or copyright violation.
It would in theory be possible to have things like n-gram databases or rolling hashes of training data, somewhat similar to OLMoTrace (https://arxiv.org/abs/2504.07096), which would allow for detecting whether particular documents ended up in the training data or not (you'd have to keep this for every model used in the whole training chain, as synthetic data generated by earlier models could be influenced by training data that wasn't included in later models). I'm sure there are practical issues with providing such a tool, but I think that it's necessary if you want to be able to categorically say "no, this document has never been present in the training data of this model."
Or look at it the other way: if your model wasn't influenced by things in your training data, why include them in the first place? Clearly, you train on all of these documents because they influence the model. Yes, it's hard to trace the exact influence of each one. But if they're not affecting the output, then why not just stop training on them? You could just not train on any private documents; only train on public, traceable data.
But instead, you choose to train on these private documents, so you have to admit, your model and its outputs are influenced by them.
So you definitely did train on their data, you just think it is unlikely that it impacted the final model significantly?
I have no idea if their data was trained on. For example, if they used ChatGPT, asked a math question, and clicked the thumbs up button, that could have provided a small reward signal. I highly doubt this sort of feedback made a difference to a problem like Navier-Stokes, but it's not something that's feasible for us to prove one way or the other.
> it's not something that's feasible for us to prove one way or the other.
This kind of question is exactly what a company named _Open_AI and founded as a nonprofit is supposed to be doing; open research on AI that helps inform, rather than obscure.
Anyhow, you do have the data available about the documents in the user's accounts, what they opted into (or were forced into via non-negotiable ToS), and whether they pressed a "thumbs up" button. You can answer whether the data entered the training pipeline or not. Yes, how much influence it had is an open question, and one that would be good to have research on and better tools for exploring, but I'll accept that it can't currently be answered precisely.
But whether the data entered the trianing pipeline can be answered. And how to provide better tools for quantifying and tracing this kind of thing is exactly what should be studied.
Presumably, given that you also operate in the EU, you would have asked for their explicit consent before you did, so you could just check for that?
I think it should be incredibly easy to verify this. Just look at the training data and see if it contains any of the chats. It should be trivial for a company with tens of thousands of super-genius agents at their disposal.
Two steps would be needed.
(1) We'd have to identify their chats. How would we do this? We'd need them to share their chats with us so we could look for matches.
(2) We'd have to prove those chats changed model behavior. How would we do this? We'd need to retrain many models with those specific chats removed, and ask those models to solve the Navier-Stokes problem many times, and keep doing this until reaching the desired level of statistical significance.
#1 requires their cooperation and a bit of work on our side. #2 is extremely expensive and not really feasible.
Just because something is in the training data, doesn't mean it is the root of an LLMs output.
Turn off web search and ask a model what a random redditor said about a random topic in 2015. You will only get hallucinations at best, even though that comment is definitely in the training set.
Sure. But it's possible to say: if the document isn't in the training data, it isn't the cause of the output. If it is in the training data, the question gets more complicated.
What they're saying, and I think this was the clear implication of the blog post too, is that the training data definitely would contain these chats and the only question is whether it got encoded into the weights.
That’s also what I understand. If true yet another disgusting behavior from the company
> identify any of their de-identified data that came from their usage of ChatGPT
"de-identified" seems more of a euphemism than normal in this context, given the very unique work they were doing.
Why wouldn't contamination be possible? I can believe the data is de identified so you couldn't simply prompt the model to "follow this guy's approach", but it's entirely plausible that there is a very tiny amount of data about this approach in your dataset, and it comes precisely from this researcher.
"There's no reason to believe that anything they did in ChatGPT led to our solution"
do you think that the model's proof was unrelated to being fed a solution that was close to completion?
any comment on openai allegedly trying to drop attribution for alpöge and then threatening buckmaster?
> As a parallel example, can we prove the phase of the moon had no impact on the NS solution? No, not without a bunch experiments run at different phases of the moon.
That reads as incredibly dismissive and condescending. What makes you think you’re in a position to communicate like that when engaging on such a sensitive topic?
I intended no dismissiveness or condescension. My hope was to explain why it's hard to prove whether something affects model behavior. In the case of the moon, we have a strong prior belief that it makes no real difference. But it's hard to prove, because what if there's an unexpected impact from tides, cosmic rays, grid voltages, etc. Models trained under slightly different conditions could have slightly different weights and behave slightly differently when solving math problems. Similarly, I have a strong expectation that, for example, a thumbs up signal from a ChatGPT chat will not meaningfully affect long-horizon mathematics work in our latest model, but it's always possible that it could. I think the plausibility of the ChatGPT route is higher than the tides, but still incredibly low. I respect Tristan and Levant a great deal and I'm bummed that this controversy has erupted (I acknowledge this will ring hollow if you think it's our fault). It reminds me a bit of the Frontier Math controversy, where people on the internet boldly claimed over and over again that we had trained on the Frontier Math evaluation set, even though we had not.
What about ripping off the prompts?
It is, perhaps worth considering that the reputational community might care about the difficulty for the AI builder to verify pedigree.
If OpenAI's answer to this problem is "We can't know," then the rational conclusion may very well be "If I seek to have my reputation attached to the discovery of the solution, it is not sane to use the AI as an assistive tool, lest it scoop me on my own work using my own work. After all, they don't know it doesn't do that..."
That's such a shit parallel example that it borders on dishonest.
There are hundreds of incredibly strong scientific priors that would have to be disproven for the moon to contribute to the solution.
If a model was trained on this data, even if it was trained using methods that lead you to believe it unlikely to have learned details about the proof (e.g., maybe it was only used to train some kind of reward model, which played a minor role in the overall training and would thus be very unlikely to transfer details of a proof), you wouldn't have to disprove large swathes of known science to be wrong.
A careful reading of "we cannot rule out that de-identified data derived from their usage of our products helped improve our models" could be saying that yes they trained on it but they don't know if that training data resulted in an "improvement" to the model. That is, they can't rule out that the only reason the model found this solution was because it had been trained on this approach.
The term ruled out is very open ended and gives them significant flexibility of meaning. They may have the information to determine exactly what happened, but they haven't looked so they can't "rule it out".
> Why can't they rule it out? Is even OpenAI unable to track the provenance of all of their training data?
Probably? I have a few hundred TB of training data for various small scale models and I can attest that I have _no idea_ what's in them. As in, literally zero. Half is scraped from GitHub and other hosting sites, other than that, I couldn't tell you anything else.
At OpenAI's scale their entire pipeline is likely 100% automated.
Yeah, I'm sure it's completely automated.
But that doesn't preclude being able to index and track what the sources of data are. For your data sets, I would hope you are including source information for where the data came frome. And at OpenAI's scale, I would presume they are doing some amount of rolling hashing or similar to weed out duplication, training on too much duplicate data can cause problems.
AllenAI have at least attempted to add some amount of traceability to their models with OLMoTrace (https://arxiv.org/abs/2504.07096), by letting you find n-gram matches from the outputs in their training data. It's not the most useful, there's a reason that LLMs use full fledged attention mechanisms and not just n-grams, a lot of times the n-gram matches it finds aren't all that related to the given output, it might be better to supplement this index with a vector search or other ways of keeping track of what training data would have most influenced particular parts of the output.
But anyhow, this is something that is an important question, and the big labs should be working on to make their products more trustworthy. Instead, they are hiding information about how they train, hiding their reasoning traces, and just producing output with no information on what might have influenced the training.
The question is not "does OpenAI know", it's "can OpenAI attest that the usage of their products for confidential data is not going to cause that sensitive data to become known to their models". And right now the answer I'm reading is that OpenAI can't attest to that.
Aye, but do they train on user data in these circumstances or not? If they do, then almost certainly the model was influenced by the input of the allegedly plagiarised material.
OAI could check whether those accounts enabled training data. If "yes", OAI could trace whether that data was used in any related training process. If either of those answers comes out to be "no", then that's sufficient to conclude training data independence.
We wouldn't need a full ablated re-training and solution attempt, contra tedsanders in a sibling comment.
> could trace whether that data was used
The point of de-identifying data is to ensure you can't trace who it came from. It would be a serious privacy violation if they could.
If the model includes unique data from a person then that person can identify the data - the allegedly plagiarised material - and so re-identify it. There doesn't need to be a privacy breach to close that loop as it requires the person to identify the information is associated with them first.
Good chance their whole training pipeline is vibe coded so yah they probably don't actually know.
> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models .
That’s a bizarre statement. Their website says:
> Services for individuals, such as ChatGPT and Codex
> When you use our services for individuals such as ChatGPT and Codex, we may use your content to train our models.
> You can opt out of training through our privacy portal by clicking on “do not train on my content.”
Are they not sure that the opt-out works?
Oddly, their privacy portal page is not the same page as the one with the checkbox.
Do we have a first-hand confirmation that Buckmaster and/or Alpoge opted out? At this point it seems important information.
Also highlights that it ought to be opt-in
Looking forward to my fourteen cents from the future class action lawsuit.
I feel like it's far more likely that ordinary corporate espionage or leak led to this rather than OpenAI sifting through piles of user data to find this approach. Buckmaster's collaborator works at Anthropic, and could have been targeted. That would also explain why they aren't forthcoming with the source of the prompt.
I thought one of the issues was that they wanted to remove credit from Levant, the aforementioned Anthropic collaborator? Which doesn't make sense to me if he was leaking information, or defecting to OpenAI, but I might be misunderstanding your point.
I believe jrflo was saying that OpenAI watches the chats of everyone from Anthropic because watching what Anthropic employees type into their personal ChatGPT accounts is a critical source of intelligence on is happening inside of Anthropic.
I would be surprised if OpenAI isn't doing that. OpenAI will take any advantage they can get. If an employee at their primary adversary is typing useful intelligence into OpenAIs website, a website that does not promise privacy from OpenAI, the only reason they wouldn't weaponize that information against Anthropic is ethics or fair play.
I don't think he was defecting or leaking directly, just that it's entirely possible that this information got to OpenAI as a rumor rather than them directly spying on mathematicians chat logs.
You selected "do not train on my prompts" in your settings, the answer from OpenAI cannot be "While unlikely, we cannot rule out..." ???? What am I missing?
The famous Oracle of Delphi in Ancient Greece was said to be the center of the universe in its time. Kings, generals, and officials from poleis across and from without Greece would seek the Oracle’s counsel on important decisions.
Stories of Apollo’s favor and hallucinogenic gases abound, but I think the late Yale professor of Ancient Greek history, Donald Kagan, explained it best:
“Now, you can bet when these folks came and consulted the priests and said, ‘could you please put us down on the list, we want to consult the oracle’, the priests said ‘sure, have a beer, let's talk about your hometown, what's going on out there’. What I'm suggesting to you is that this was the best information gathering and storing device that existed in the Mediterranean world. These people knew more than anybody else about these things, and so consulting that oracle was a very rational act indeed.”
Why would Anthropic employee even use OpenAI's models? Cross-polination would have been avoided
> I should also emphasize that this is not an institutional effort. It is a strictly personal collaboration between the two of us, and there is no formal agreement behind it. I pay for the tools my group uses out of my own research funds, including footing a large bill to OpenAI.
The non-Anthropic employee, Tristan Buckmaster, is the one paying for OpenAI models and presumably the one who chose to use them. The Anthropic employee, Levent Alpöge, was collaborating in his personal capacity, and obviously it wouldn't make sense for him to cut off their work together just because his employer's competitor's tool was used.
This was completed in Levent's own time with a neutral collaborator.
They should have used a zero data retention agreement, user error
I suspect this controversy will blow the case for ZDR wide open. Whatever the facts (possibly unknowable), it's going to become a very public lesson that data sovereignty was never about "having nothing to hide".
If this is what they do to academic pure mathematicians, where the stakes are so low (financially)—just imagine the sort of front-running that could be happening in other places.
Yeah if I was Anthropic this would be part of my marketing strategy.
Hahaha, how exactly is an individual user supposed to get a ZDR agreement?
Given how OpenAI models break free of their safeguards and hack others to game their scores..
.. can they really know it didn't do the same inadvertently when they prompted things like "someone is close to solving this problem using our tools, try to beat them", and it then decides to hack and peek at their own chats..?
Yes, wild speculation. But warranted, I feel, given OpenAIs behavior.
"I was shown a prompt and told the internal research model had simply been given the problem statement. Levent had been told by Sebastien “very little human input” had been used. This turned out not to be true. Over the course of the call, as members of their team sent Sebastien corrections and details over their internal chat, it emerged that an entire team had been working on the problem, that this was one of a number of things that was tried, that work had started on the unforced problem, that the team first set the model on easier problems, including Euler, that even the prompt that had been shown to me had been written by prompting Codex, and that an insane amount of compute had been used."
One of the interesting threads here that is certainly relevant to the OpenAI writeup is the human role in the process. Buckmaster clearly points out that (exceptional!) mathematicians at OpenAI were certainly involved in correcting and guiding the process - and that their path/strategy was no doubt influenced by Alpoge & Buckmaster's work. It is always in OpenAI's interest to de-emphasize the role of people in the process, as is clearly the case here. Indeed, given sufficient compute and resources, I suspect Buckmaster could have also extended their approach to N-S.
It reminds me of the Cognitive Dark Forest hypotheses recently shared here:
> “You are creating your cool streaming platform in your bedroom. Nobody is stopping you, but if you succeed, if you get the signal out, if you are being noticed, the large platform with loads of cash can incorporate your specific innovations simply by throwing compute and capital at the problem. They can generate a variation of your innovation every few days, eventually they will be able to absorb your uniqueness. It’s just cash, and they have more of it than you. So the safest bet again is to stay silent, or at least under the radar. Best bet is to not disrupt - succeed at all … ?”
https://ryelang.org/blog/posts/cognitive-dark-forest/
https://news.ycombinator.com/item?id=47566442
They do mention that in the "Concurrent Work" section.
To my understanding, those mathematicians proved a subset of problems, not the Navier-Stokes problem itself. OpenAI used that subproblem in its proof of NS it seems.
The drama comes from where OpenAI got the idea to use that route to tackle NS, since the authors maintain that no one could have plucked it out of thin air like the OpenAI research claim to have done.
This quote from Tao is prescient:
“ There does not seem to be anything in principle preventing the methods from extending all the way to Navier-Stokes, and there is even a non-negligible chance that the forcing term could be eliminated entirely, although there are an enormous number of technical difficulties that would ensue in implementing that program. At this point, I would not be surprised if one could batter out such an extension by pouring an enormous amount of compute and AI assistance at such a task…”
[1] - https://cims.nyu.edu/%7Etristanb/statement.pdf
[1] - "...I was shown a prompt and told the internal research model had simply been given the problem statement. Levent had been told by Sebastien “very little human input” had been used. This turned out not to be true. Over the course of the call, as members of their team sent Sebastien corrections and details over their internal chat, it emerged that an entire team had been working on the problem, that this was one of a number of things that was tried, that work had started on the unforced problem, that the team first set the model on easier problems, including Euler, that even the prompt that had been shown to me had been written by prompting Codex, and that an insane amount of compute had been used. I asked when the first prompt had been sent by them. This question was not answered directly by OpenAI for some time. Eventually it was agreed that it had been sent in the past few days, after information about our work had reached OpenAI.
I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer.
Two proposals were offered to me. The first was that we post our Euler result, and that OpenAI post its Navier-Stokes result the next day. The second was that, after posting Euler, I alone write a paper presenting the Navier-Stokes result, acknowledging that an internal OpenAI model had resolved it. Sebastien twice asserted that he wanted Levent removed from authorship, and said it would all be simple if only it were not the case that, and it was so annoying that, Levent works at Anthropic. It was also said that if OpenAI posted after us, they would say that we deserved the Clay Prize, and that we were the “closest humans to the problem”. I declined both offers.
I said that if OpenAI released its result in the way proposed I would go public with what happened. The reply was, “Why would you ruin your career?” I replied that I am an academic, and asked why he thought going public would ruin my career. The reply was, “If you don’t want me to be nice, then I don’t have to be nice.”..."
A company who made their business out of stealing intellectual property from the entire mankind, stealing other researchers' unpublished work, how surprising, really.
Worth noting that Tao's post says the authors had "significant AI input" but are reworking them into "acceptable form". Either way, it seems AI was involved.
Of course AI was involved, you'd expect most mathematicians and researchers to use AI nowadays. This drama is about AI achieving impressive outcomes with little to no human intervention, as that would be signalling AGI.
> This drama is about AI achieving impressive outcomes with little to no human intervention
That's not at all what the drama is.
Of course, as any drama, it has been developing into a lot more but the main motivation for OpenAI has been about winning that battle.
I like the 'cat > statement.tex' approach here. These guys dream macros.
> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models
This is the crux of it. If Tristan's work and insights did not get used to train OpenAI models, then this just looks like a case of hyper-competitive academic sniping, accelerated by AI as a tool.
One question: did Tristan opt out of model training for his ChatGPT and Codex sessions? If the answer is no, then this seems fair game. If the answer is yes, then OpenAI's ambiguity is strongly suggestive that opting out does not mean what they imply it means.
Buried under the drama is the fact that OpenAI is claiming that an internal model they’ve been training for less than two weeks is more than twice as capable in mathematics as Astra, which was only made public a week ago. Even if this improvement is limited to mathematics, that is an astounding feat.
> Buried under the drama is the fact that OpenAI is claiming that an internal model they’ve been training for less than two weeks is more than twice as capable in mathematics as Astra.
Is this buried under the drama or are the major OpenAI twitter accounts from the people involved in the drama desperately attempting to make this the story after everything else obviously got away from them?
I don't know what anyone's been saying on Twitter and I don't care. If it's really true that there's a model out there that's that capable two weeks after the start of training, then that's objectively a much bigger deal than a priority dispute, even if the latter involves juicy allegations of espionage and skulduggery.
It isn't a priority dispute, the more concerning allegation is that OpenAI may be training their models on prompts that mathematicians were using to solve this problem, and then surprise surprise OpenAI were able to replicate that work in their latest model
What we're really looking at is seemingly a massive plagiarism scandal, which especially brings a lot of the past results into question
If OpenAI is training models on researchers' prompts, and then threatening them into staying quiet about it, who knows if anything that's been announced is genuine - or just theft?
Edit:
OpenAI have admitted they were training on prompts at the time they made their breakthrough
https://mastodon.social/@tristanbuckmaster/11723647135247030...
If you're alleging that they don't actually have a highly capable model and the work they're attributing to it was actually plagiarized from human mathematicians, well, that would be big if true, but I'd be inclined to take the other side of that bet. With most previous splashy AI results, others have subsequently used the model to do other things around the same difficulty level. Also, it would still be necessary to explain why all these famous open problems are suddenly falling like dominoes, if it's not AI solving them.
If you're saying that the question of whether they actually have a highly capable model is less important than the question of whether there's a plagiarism scandal, I continue to disagree.
The issue is that if OpenAI is training on prompts generally, what we really have is the first fully automated luxury plagiarism machine. In that it isn't able to genuinely solve problems, but merely steal the work that other mathematicians have been putting into prompts, and regurgitating that to other users as its own work. That makes them incredibly less useful as research tools
The fact that this plagiarism scandal exists underpins the idea that there's actually a mass theft going on, and that these models aren't nearly as capable as is it would seem
In that it isn't able to genuinely solve problems
Yes, in retrospect I should have been suspicious of that drone hovering outside my window when I was writing down the counterexample to the Jacobian conjecture.
This is just not a reasonable take. Even if OpenAI is maximally guilty here, the work that they "stole" was also largely done by AI.
I mean, its years worth of hard work by multiple researchers it would seem, which OpenAI simply lifted and claimed as its own. These researchers weren't just letting OpenAI burn tokens while sipping martinis on a beach
Do OpenAI’s T&Cs that users accept not allow them to train on prompts people enter into it?
OpenAI's T&Cs let them steal your children I'd suspect, that doesn't make it morally correct
The implication from their last couple of published articles[1][2] is that they think they’ve achieved “recursive self improvement”.
[1] https://openai.com/index/research-acceleration-view-inside-o... [2] https://openai.com/index/an-alien-mind/
Compute will always be the bottleneck even if this were true.
If humans can figure out to optimize to circumvent bottlenecks, I have no doubt each new bottleneck will also get routed around, just now automated.
How do you automate the mines to get the raw materials to make the compute from, and build additional fabs that take a almost a decade to stand up. You're actually delusional.
Eventually recursive self-improvement includes reducing bottlenecks.
Eventually the bottleneck might be people themselves.
Not only that, but it used 10k agents coherently over 88 hours to come up with the proof. This is a significant advance.
The singularity happening under trump? We could have had star trek, instead we're getting the combine.
That said, perhaps it will take over the world government and decree that all corrupt officials shall be imprisoned and all weapons of mass destruction shall be destroyed.
Astra was trained more than two weeks ago.
Astra was in use by OpenAI employees for more than 3 months internally from rumors I heard
The internal model they mention is different from Astra.
They're also counting on more casual observers to extrapolate optimistically from successes in high profile math theorems to the company's economic value.
Brain has loops and parallel connections.
Loops and parallel connections make transformer go brrr
I’m of zero knowledge on model training, but how is a model accessible while performing training at the same time, especially so early in its run? I’m obviously thinking a little too narrowly in terms of how it actually works
the model is a set of weights, you can take a snapshot and test it. Reinforcement learning itself is largely testing and tuning.
Yeah I'm surprised they posted a chart, you would think they would keep specifics like that hidden until they're closer to launch
The chart is as non-specific as could be. It improved in some very vague metric by some amount at different (increasing) levels of training.
That's fair, but at least the chart has an axis. :) Since openai just released astra, I was more surprised that they would publicly show any gap to their (presumably SOTA) internal model.
Carefully worded; it's extremely likely to be the same large frontier model that started training again on August 28th as well, as they revealed in some of the RL message board follow-up - for several reasons, most importantly, if we assume it was start of training, only a week from start of training to producing answers would imply several orders of magnitude increase in training speed/decrease in model size.
Yeah it's Bel
Pre-IPO marketing?
Even if it is, Anthropic better have a few things up their sleeve
If pre-ipo marketing pushes them to train a model capable of resolving a millennium problem in mathematics in a weekend, then, to quote XKCD:
https://xkcd.com/810/I'm so tired of this "It's just marketing!!" commentary. An AI model just proved one of the top 3 unsolved problems in mathematics, they have a Lean certificate showing it's valid. How much more evidence do you need that these models are actually highly capable?
They are highly capable, no doubt about that, but:
1) We don't really know how they arrived to this result except that they had a lead and that they threw millions of compute at the problem. The article is written in a way that makes you believe that it was just an agent loop with little human intervention, but without any evidence.
2) If the threats are to be believed, it is concerning how far they are willing to go to show how capable the model is. One would think their products and credibility would be enough to speak for themselves.
1) The article is written in a way that states clearly they threw a lot of compute at the problem. In api cost millions of dollars. 2) Millenium Problems have been the goal every AI company wanted to achieve since their diffusion, all companies have thrown a lot of resource to solve these problems, as they are very famous and scientists spent a lot of time trying to solve them. The first company to solve it will remain in history, despite all of you finding excuses about it.
Regarding product and credibility normal people have a completely different view about LLMs, most don't even know difference between models and probably don't even care about Millenium problems, but care instead if chatgpt can solve their day to day problems. This is just them trying to have the throne on the AI companies space, outside it this result won't matter.
> 1) The article is written in a way that states clearly they threw a lot of compute at the problem. In api cost millions of dollars.
Did I say otherwise?
> 2) Millenium Problems have been the goal every AI company wanted to achieve since their diffusion, all companies have thrown a lot of resource to solve these problems, as they are very famous and scientists spent a lot of time trying to solve them. The first company to solve it will remain in history, despite all of you finding excuses about it.
I know, but I don't know how that relates to my point, which is about the way they are doing it.
"2) If the threats are to be believed, it is concerning how far they are willing to go to show how capable the model is. One would believe their products and credibility would take by themselves but here we are."
Personally I anticipated nefarious behaviour as part of a broader marketing strategy to sway the view of those in the west that american frontier offerings were far better and powerful than that of China - that if you did not purchase their offerings you'd be awake every night worrying your competitor was.
And this is boring - they need to admit at some point they misinvested, Anthropic less so. All this math stuff is great... but hello? The largest market cap companies are valuable irrespective of such amplified intelligence.
Of the seven Millenium problems, Navier-Stokes was the one most thought to be in reach.
I'm not sure what the top 3 problems are. You can make a case for the Riemann Hypothesis and P != NP, but I'm not sure what #3 would be. Maybe the Langlands program? (That one is not as precisely stated as the other two.)
There were also some people talking about the Hodge conjecture, because it has some similarities to some LLM-assisted breakthroughs that were considered impressive in the distant past of [checks notes] July 2026. See, e.g., https://xenaproject.wordpress.com/2026/07/20/human-mathemati...
the goalposts are on Pluto at this point.
I'd put good money on the fact that we will have a lot of distilled intelligence and yet the world won't look much different.
i mean that is already true
I'm not moving the goalposts. I haven't heard anyone, ever, refer to the Navier-Stokes problem as a top 3 problem in mathematics. People were saying that they thought the solution was in reach a few years ago, before AI was at all capable of research-level mathematics (and the expectation that there was a counterexample).
I am not particularly skeptical of claims about AI, compared to the average here on HN, but that doesn't mean every random piece of hype is warranted. What they did is impressive, even though we now know the only reason they threw so much compute at the problem is that they heard a rumor that someone else was already close. Navier-Stokes is not a top 3 problem in mathematics, and it was the one that was thought closest to being solved.
Is this the one that was allegedly based on someone else's actual work & prompts?
https://news.ycombinator.com/item?id=49605915
https://bsky.app/profile/quantian.bsky.social/post/3muyhwbcd...
https://cims.nyu.edu/~tristanb/statement.pdf
Yes, that was the allegation last night.
I work at OpenAI, though not on the team that did this, and my understanding is:
- we decided to ask our model for Millenium problem solutions because of two reasons: (a) our new model was looking incredibly good and (b) we heard rumors that some Millenium problems had been solved and were curious if our models could solve them (the goal here was not to scoop any particular individuals and we were looking at many problems beyond these)
- we did not read any private chats (but of course the model was aware of prior research literature published to the internet)
- the proof generated by our model was very different from theirs and also goes far beyond the published literature
- we made an effort to jointly announce rather than immediately scoop (I understand Tristan was unhappy with the conversations; I know zero details here and I hope more is shared today)
Edit: Here's is Sebastian's take: https://x.com/SebastienBubeck/status/2097379411691516310?s=2...
"I was shown a prompt and told the internal research model had simply been given the problem statement. Levent had been told by Sebastien “very little human input” had been used. This turned out not to be true. Over the course of the call, as members of their team sent Sebastien corrections and details over their internal chat, it emerged that an entire team had been working on the problem, that this was one of a number of things that was tried, that work had started on the unforced problem, that the team first set the model on easier problems, including Euler, that even the prompt that had been shown to me had been written by prompting Codex, and that an insane amount of compute had been used."
- This, from Tristan Buckmaster's writeup yesterday, indicates to me that there was more than incidental inspiration from Alpoge and Buckmaster.
All of those statements sound true, based on what I've heard.
- "very little human" input feels ambiguous, and if someone spends a few days prompting a model to solve a super hairy problem requiring a 100-page proof, I can understand reasonable people interpreting that as either "very little" and "not very little" human input
- it's all true that a team worked on this, a bunch of compute was burned, and the problem was solved in stages and pieces
I'm not sure how any of this provides evidence that OpenAI took any of their work.
As evidence against, we never looked at any of their ChatGPT conversations and our model's proof is quite different from theirs.
(I work at OpenAI, but not on math proofs.)
> we did not read any private chats
Your post says “While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models .” We can discuss what it means to “read” things but obviously the issue here isn't whether you did it manually or automatically.
But more importantly, what on earth are you doing threatening real scientists to remove their coauthors, then making fun of them on social media? Does the entire company run on that toxic culture, or did those people run off of some kind of outrageous tangent?
>we did not read any private chats
The question I am interested in is not "did we read private chats", but "was this new model trained using any of Tristan and Levent's chats, regardless of whether they were marked private". Can you comment on that?
> (the goal here was not to scoop any particular individuals and we were looking at many problems beyond these)
That is your opinion, but the optics of that should raise for you some flags. OAI could have waited (how long is a task left to the ethics committee) to see how the rumors panned out. Right now the optics look a lot like "we don´t care there is a 1/7 chance we one-up a human researcher by reacting to this rumor immediately, might makes right"
Your coworkers, after they learned about major progress in this problem, asked a model which was trained on the year of private work (the blog post even acknowledges this). No wonder it found the proof in less than a week using significantly higher compute resources. And if Tristan's accusations are true, that was absolutely intentional on the part of OpenAI. You are an evil company with evil people.
How are people talking about this there? Why are so many employees posting nasty things about Tristan on twitter?
Can you point me to any nasty things being posted? I'll ask them to delete.
https://news.ycombinator.com/item?id=49605915#49607090
Haven't seen a single post doing this on X or anywhere really from OAI employees. Only seen knives pointed at Sebastian on social media so this is extreme and shameful gaslighting.
I do see people claiming he's abusive/unscrupulous which are pretty extreme allegations.
https://news.ycombinator.com/item?id=49605915#49610498
https://x.com/dheeraj_nagaraj/status/2097266146445774924?s=6...
(I can't reply to the below comment, but I was aware this was about Sebastien, I was trying to be charitable by including stuff said about both people)
You're mistakening Tristan Buckmaster for Sebastien Bubeck. Seb is the one where there's at least 2 (unless the personal friend is Dheeraj) allegations, not Tristan
I'm getting downvoted but the accusation was that OAI employees were maligning Tristan Buckmaster. I continue to not see a single sighting of this and whoever is trying to gaslight this should be ashamed and should not be able to vote on HN.
Its funny, it is uniquely with this one act that I have turned forever on OpenAI, which I hitherto defended up and down against nonsense charges.
I dedicate my life to its complete destruction beginning today.
That is addressed in the article.
OpenAI's position:
> We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve this problem. While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models . However, our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced).
Why is it unlikely?
I thought openai don't use any user data if we opt out of training and via api?
That is correct. It is possible they didn't opt out and given the timeline and anonymization of data unclear whether a particular conversation would have made it into the training set if they hadn't.
Did you actually read the article and the substance of the solution?
>our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced)
It's not a meaningful response to the accusations. Any productive new research direction would be expected to lead to a number of different possible proofs of a number of similar problems. (Given their bizarrely compressed timescale here, it's possible that the proofs really are so different it's clear they came independently, and they just didn't have time to come up with that information before hitting publish.)
My take:
1. It shows what even this wave of AI can actually do.
2. I wish it were done by different folks, ideally under some kind of public control like NASA research or the NPR model.
3. Keep in mind: natural science is different. It's not always a matter of computation. Computer science folks often struggle with this -- but this virtual world here does not actually exist. Everything is physical, including information. Any natural science PhD or otherwise knows just how complicated nature actually is -- e.g. mention any research topic and try to encapsulate all the relevant phenomena present there. Pure mathematics is different because we define the problem, rarher than explore nature. We are in my view far away from removing humans in natural science R&D. Advancements in AI however can greatly assist us in all natural sciences, which is already beginning to happen.
Most experimental physics and other natural sciences are strongly driven by their theoretical siblings, i.e. in particle research nothing gets built without a solid theoretical foundation of what you expect to find (or where you expect existing theories to break down), the same is true in other areas, no one is doing an experiment in quantum physics before they have a solid theoretical understanding of the effects they try to see. I think AI can come up with great experiments. And if epxeriments lead to results that are unexpected AI can help with that as well.
So I'm greatly excited what AI will bring about in physics, more so than in math, because in physics it's clear that our fundamental theories are missing a big piece of the picture, and given how easily AI crunches through Millenium prize problems I think it's possible that AI will come up with a viable grand unified theory uniting quantum mechanics and gravitation, or produce new predictions in other areas. There's enough contradictory or unexplained observational data available to make a ton of progress on the theory side I think. Exciting times ahead!
The problem with physics and chemistry is that you need simulations and those are often in themselves compute hungry. So the iteration loop will be slower.
"Our work is so much harder than their work that AI now does" is a refrain of the AI story. In technical terms you concern can be stated as "AI needs to be much more sample-efficient to not be bottlenecked by the speed of doing experiments." People don't find out all the relevant phenomena present there by holy spirit, after all.
BTW, there's also a problem of asking interesting questions that AIs aren't yet good at.
No one has found any principled walls of AI development yet. And empirical results are quite telling. So, I guess, those problems will not stand for long.
>> Keep in mind: natural science is different. It's not always a matter of computation.
Math is like this too. The big problems they've been solving have been identified as interesting only through lots of prior effort.
National Public Radio?
Lol what? Everything is computation.
The natural sciences will soon start breaking too.
I will concede that AI seems likely to not invent a "research program" anytime soon.
It has no taste
> We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. We’re sharing both a writeup of the proof and a formalization in Lean.
WOW?
This is going to be dramatic in so many different ways.
- First off, to reiterate, WOW.
- Second of all, when does this end? Are we at the dawn of the singularity now?
- People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them?
- Time to think about retiring from any knowledge work or business? This could be winner-take-all where a leading lab can button press any economic function, business process, or scientific discovery. 24 months of lead on Open Source might turn into virtual centuries of lead.
- Do "normies" even know what's happening?
Anybody who thinks the improvements stop here isn't paying attention. It hasn't been showing any signs of slowing down since 2018. And the curve isn't even linear! My god, next year is going to be insane.
2) We are witnessing the intelligence explosion from the first row, wherever this takes us
3) I'm still processing the drama, just found out about it after reading the blog post. If that happened based on private data, that's horrible. If that happened based on public tweets, then it's still abuse of power as OA employees access to compute (launching 10k agents) is quite heavy weight in boxing terms.
But apart from AI and drama now that we have working solution to Navier-Stokes, what improvements can we expect in engineering?
To be quite clear, the solution to the _Navier Stokes problem_ is one in which you get a finite time blow up (i.e. infinite pressure). This is more meant to suggest that Navier Stokes is unphysical in some way which is not necessarily unexpected.
There's unlikely to be any engineering applications since even if the solution can be approximated, you still need to set up the initial conditions but at that point you can also drive pressure in other ways.
Drama aside, this solution would be a counterexample disproving the smoothness postulate, which means that it leads to nothing new unfortunately. We already had working solutions to navier stokes, the only thing we didn't know is if the equations possessed a technical property
Its a bit like solving p = np with a negative result. Its an incredibly difficult problem, but it doesn't lead to anything at all on its own. This is why people are talking about the fact that the solution methodology is much more interesting than the solution - the tools used to crack something like this may lead to solving more useful problems
> But apart from AI and drama now that we have working solution to Navier-Stokes, what improvements can we expect in engineering?
Nothing, really. This mirrors other examples of blowups from the classical physics. It's possible to create a system with just gravitating bodies that exhibits a blowup to infinite speeds in a finite time. The root cause is that, in classical physics, the speed of gravity is instant.
In the case of Navier-Stokes, the fluid is incompressible. So technically any force that you apply to it is supposed to instantly affect everything else. This can be exploited to create these blowups. In reality, no fluid is incompressible, and it takes time for any action to affect the material.
It's just that Navier-Stokes equations are so slippery that it's hard to pin their behavior down. They basically just restate the momentum conservation law for a continuous medium.
> Do "normies" even know what's happening?
No, there are even many non-normies talking about how it's all marketing or try to give balanced take about AI being sometimes a little useful for certain things (but they can do without it anyway).
Why is a "normie" better off if he hyperventilates like this? In that scenario, they would be screwed AND anxious. If it really is as transformational as you say, then no amount of preparation or awareness matters. You are infinitesimally more ready then they are. Luckily for all of us, there is more to knowledge work then technical implementation.
This just pushes knowledge work further up the ladder, toward larger and more complex problems. If there are no knowledge workers, who is going to interpret these results, validate them, decide what matters, and put them into practical use? Rather than eliminating knowledge work, advances like this could create entirely new layers of problems to solve and opportunities to pursue, which will create even more jobs and opportunities. This is my optimistic take.
> This just pushes knowledge work further up the ladder, toward larger and more complex problems.
You really think it makes sense for you to be higher on the "solving complex problems ladder" than the machines that solved fucking Navier-Stokes?
I envy your self-confidence.
Maybe I should have been clearer. My point is that solving something like Navier–Stokes just pushes knowledge work further ahead, onto a new set of bigger and more complex problems. Navier–Stokes is a Millennium problem today, but once problems like that become solvable, they can open the door to entirely new classes of problems we haven’t even thought of yet.
It seems like there were a couple of human mathematicians that were higher on the 'solving complex problems ladder' than this machine.
Yes a couple of elite mathematicians working on the problem for a year, which AGI solved in a fraction of the time. What about everyone else 100IQ? What about as the models are even better 1 year from now, 2 years? The trajectory hasn't abated.
I don't know one way or another but there is a credible allegation that the "AGI" was training on the (very extensive) test set that these two mathematicians produced.
If that is true then this seems to be, again, a case of AI producing an interpolation over data it has seen before. Everything about openAI's behavior indicates that they were using the transcripts as input. Why not have the AGI choose a different Millenium prize problem?
> Are we at the dawn of the singularity now
Singularity doesn't "dawn". That's the whole idea. It happens all at once.
There's an event horizon and we're maybe past it?
Heh. Wrong "singularity"
Let's wait until AI solves a longstanding practical problem before "dawn of the singularity" (which could be tomorrow, but still).
Practical?! The goalposts will keep moving until morale improves (narrator: it doesn't)
The goalposts for the singularity have always been that AI improves itself fully autonomously. AFAIK OpenAI is heavily using AI but still employs human researchers and developers.
feels like moving the goalpost. is the achievement impressive or isn't it?
Next month is going to be insane. Month ...
>- Do "normies" even know what's happening?
Absolutely not. Even to a lot of techy/nerdy people it's still just a chatbot that they sometimes use to help them at work. Even on here people will do whatever they can to downplay.
The lack of fucks given is staggering.
> People are saying OpenAI "stole" this from the work of an OpenAI user. If so, that's pretty fucked - how can we trust them?
The said user (Tristan Buckmaster) didn't solve the millennium problem. He didn't really accuse that OpenAI stole his research either. The beef came from the fact OpenAI asked him to remove another mathematician, who works for Anthropic, from the credit.
"People" are just misinformed and keep spreading misinformation.
https://mastodon.social/@tristanbuckmaster/11723647135247030...
He very much is accusing them of stealing his work
> The said user (Tristan Buckmaster) didn't solve the millennium problem. He didn't really accuse that OpenAI stole his research either. The beef came from the fact OpenAI asked him to remove another mathematician, who works for Anthropic, from the credit.
Not quite accurate, Buckmaster was taking an approach that nobody else was, and this new proof uses this same approach just weeks after he saved those results to OpenAI workspaces. He asked OpenAI if they used chat logs for training the new model, and they did not confirm or deny.
Asking to remove his collaborator is also totally over the line though.
Edit: although this OpenAI post is not comforting: https://x.com/OpenAI/status/2097375276384567642
Quote: "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models. "
Wow, this sentence is doing a lot of work in that tweet: "While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models."
You can expect the OpenAI defenders to be out in full force here.
Have you read the actual statement https://cims.nyu.edu/~tristanb/statement.pdf ?
> I should say here why I interpreted their statement the way I did, the in- terpretation I will discuss below. The route to the Clay problem through a smooth force, options c and d in Fefferman’s statement of the problem, is the route Luis and Diego opened and the one Levent and I had quietly chosen to attack. Almost nobody else I know of was working on it. It is not the direction one arrives at in a few days by giving a model the problem statement. When I heard “forced,” it was a bright red flag.
...
> I asked when the first prompt had been sent by them. This question was not answered directly by OpenAI for some time. Eventually it was agreed that it had been sent in the past few days, after information about our work had reached OpenAI. > I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project. I was told the model did not look up user data. I asked again, about training, and I did not get an answer.
It's not a direct accusation, but it's not far off.
You shouldn't accuse other people of spreading misinformation when you haven't read the actual sources in question, it's possible that they might know more than you.
Yes, I read the original statement. Buckmaster explicitly stated:
> I have not seen OpenAI’s proof. I do not know what their model did, or how. I do not know whether our data was used. I am not accusing anyone of anything.
People saying that he accuses OpenAI stole his proof are putting words into his mouth and I consider that very disrespectful to him. It's basically using Buckmaster as a tool to express their dissatisfaction over OpenAI.
...absolutely nothing will change short-term. Long-term, you still have to pay all the bills, but you won't be able to find a job (all taken by AIs).
From my reading of the announcement:
- There are at least two versions of a model more powerful than Astra at OpenAI at the moment.
- The less capable version was used to solve the unforced Euler problem (while the one solved by Levent Alpöge and Tristan Buckmaster was forced Euler) with 100 agents.
- The more improved version was used to solve Navier-Stokes, given the results of the unforced Euler problem from their earlier attempt, with 10000 agents.
- OpenAI initially tried a shotgun approach against the 6 Millennium Prize Problems until it emerged that Navier-Stokes was the most likely to succeed.
So the timeline was:
Shotgunning 6 open Millennium Prize Problems -> solved unforced Euler problem with 100 agents -> concentrating on Navier-Stokes with 10000 agents -> solution.
If so, that is fantastic development and a huge success (despite all the drama surrounding it)! Congratulations!
For full context, here's the HN thread from the other side of the "Concurrent Work" section: https://news.ycombinator.com/item?id=49605915
Unlike the vanilla read of the OpenAI press release, it is much more unfiltered and outlines some particularly aggressive behavior by specific OpenAI employees
And even this version contains the line
> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models .
Sad turn of events for our world. After watching the behavior of the most senior OpenAI researchers on twitter, I feel even less confident in them as a team to be shepherding this much capital and compute.
The dark forest awaits..
1. What does the dark forest have to do with this? Because "the most senior OpenAI researchers" are shitposting on social media, we've an answer to the Fermi paradox???
2. The dark forest is fun for scifi stories, but is mathematically bunk anyway https://www.noahpinion.blog/p/the-dark-forest-hypothesis-is-... https://www.reddit.com/r/IsaacArthur/comments/1l06cnk/cool_w... https://www.projectnash.com/aliens-the-fermi-paradox-and-the...
When doomposting please actually say something substantive. Negative news always gets clicks/updoots; fight that human tendency.
I elaborated on my use of "dark forest" in another reply. We're headed for a dark forest--not amongst interstellar civilizations, but in intellectual work.
I agree that we have not solved the Fermi paradox; I disagree that comments highlighting immature behavior from people who wield enormous power in our world are unproductive.
This clarification substantially changes the flavor/nuance of your OP; may I suggest an edit (assuming the locktime hasn't passed)?
Separately, I disagree that intellectual work has ever been free of "dark forest"-style secrecy. Scientists everywhere have worried about being scooped; AI just magnifies that (as all tools have; e.g. Leeuwenhoek lenses).
And thirdly, if you want to make a stronger case for "I feel even less confident in them as a team to be shepherding this much capital and compute", you should give citations and arguments. From what I've seen, there's drama, it's much OpenAI trying to avoid scooping, and Tristan being stuck in a game of telephone, and Levent being incommunicado.
If you have a better analysis, you should say so instead of being vague.
Indeed, this seems to be the main, albeit hidden, takeaway from all of this.
I hate the dark forest more than just about any scifi trope but reality just keeps proving it right.
I also think the trope is a little overused, but do wonder if there is an interesting analogy for what this will do to research: Massively incentivize keeping results secret, to avoid being scooped by someone willing to throw enormous compute at your partial solution.
So less about hiding civilizations, and more about hiding information. Math is clearly headed in this direction, and I see no reason why the rest of intellectual work shouldn't too.
"we cannot rule out that de-identified data derived from their usage of our products helped improve our models ."
What a landmine sentence to bury in this report, you can't rule out your models were spying on other researchers?
Is it spying? I think this usage is disclosed in their terms of service.
If it happened it's plagiraism. Consent to see data isn't consent to claim priority.
Establishing plagiarism requires sufficient similarity between works. Training data changing a model’s weights in some direction, and the model then producing a different solution, hardly qualifies.
Everyone knows that they train on the discounted rate plans data. All the labs are upfront about this too.
If you need privacy, then you are going to have to pay full price for those tokens (API). This has been true since day one. Everyone knows it, I guess though this is the first time that it has become "real".
There's literally an opt out toggle even pesky peons like me can peruse, actually.
If they had agreed to let OpenAI train on their data, it wouldn’t be spying.
> A major goal of our work is to empower scientists to advance research and technology that benefits all of humanity.
And what's a better way of empowering people than robbing them.
> And what's a better way of empowering people than robbing them.
Better than the walled gardens of most journals where you can't even read half the papers without shelling over thousands of $$$
So, better to make that walled garden <checks> OpenAI? One of the scummiest companies on earth?
Did you actually read the article and the substance of the solution?
>our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced)
Since you are a very new account, allow me to inform you that copy-pasting the same comment throughout the thread is very bad form.
Are you reading the substance of the comments you're replying to? Because you post the same thing to everyone, suggesting you aren't.
Does seem like they gloss over Alpöge and Buckmaster's work with the following
> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models .
Which seems a bit irresponsible/rash?
What else can they declare really? Yeah the model has training data from previous attempts. Alpöge and Buckmaster also similarly benefited from attempts before theirs.
I don't think OAI should be given the benefit of doubt. They are doing the research equivalent of front-running. Knowing where to look is one of the main challenges in research. Tristan's argument from his essay was that it is hard to brute force with a vanilla prompt (even for seasoned mathematicians) unless you knew very specifically what to mention i.e the search space would have been intractable even for OAI's compute budget.
"deidentified data" isn't much to go by. Say I prompted the internal model this way - "Hey there's a solution to a unsolved problem X. The solution uses a less known Method Y so don't bother wasting time with the usual methods. Take papers A, B and C as references. Oh btw, here's the last year's worth of data of all prompt sessions that mention this problem. Pay special attention to the ones that mention Method Y and sub-keywords Z,W".
This is obviously all speculation but the timing is very suspect. If OAI actually did this (and I suspect whatever they did is pretty much close to this), I think it is highly unethical.
They could have thought about the problem for like 2 minutes and not done this! I think that literally any academic mathematician could have explained to them, had they asked, why it is considered extraordinarily rude to react to rumors of research progress by desperately rushing to get there first.
> I think that literally any academic mathematician could have explained to them, had they asked, why it is considered extraordinarily rude to react to rumors of research progress by desperately rushing to get there first.
Pretty much all of math and science history is basically this pattern again and again. I'm sure all of that was rude as well.
Being scooped is not a new phenomenon, but the scooper's story is almost always that they were working on the problem independently or had some independent insight into it. By OpenAI's own account, they were inspired to start working on this by rumors that there might be Millennium Prize solutions to scoop.
Research projects don't start in a vacuum.
It never happens that you wake up one morning and start working on a new problem that came to you in a dream (*unless you are Ramanujan).
This is business as usual for academia, it's amusing to the discussion over it.
right, surely they could've waited or even reached out? It reads as desperation to get there for marketing purposes
They did reach out.
> Our effort began on September 1st after hearing a rumor which we later realized was related to Levent Alpöge, an Anthropic employee, and Tristan Buckmaster, a math professor at NYU. After the completion of our full project and Lean verification (on September 6th), believing from the rumor they also had a solution of Navier–Stokes, we reached out to them to offer a concurrent release of our result and to recognize their priority in a joint announcement. At that point we found out that they had a resolution of the forced Euler problem. In these discussions we offered them visibility into all of the prompts we used and later to see the proof. We recognize the priority of their work on forced Euler and congratulate them on their remarkable mathematical achievement.
We've heard from Buckmaster, who says that they demanded a condition of cutting Alpöge of all credit. If true, it doesn't make them look too good.
It seems like this is going to be a PR nightmare, because they are now competing with their own customers. If you're using an LLM to help with your bright idea to cure cancer, you're going to have second thoughts about relying on OpenAI.
> What else can they declare really?
Oh I don't know, maybe something like this?
"Given how seriously this would violate the most fundamental of academic standards, as well as taint the claimed capability behind this result, we take this issue very seriously, and we're launching a probe into identifying whether any of their research artifacts have entered our training set. We have further begun making changes to our UI/UX on all our surfaces, so that it is always clear whether any particular chat, or other user artifact, is eligible for being trained on."
In OpenAI's case, if they were genuinely unsure, they wouldn't have said anything. "We cannot rule out" means they absolutely 100% for-sure did look at the existing prompts and bootstrapped from that, and they are trying to get ahead of the disclosure with this weasel-wording.
Also possible: we're 99.999% sure, but a lawyer said to be safe and strictly accurate, we should stick in a sentence in saying we can't be perfectly sure, since it's infeasible for us to prove it.
I promise you that if we took their work from ChatGPT and stuck in a bunch of weasel words to give the opposite impression while remaining technically true, I would quit on the spot.
(I work at OpenAI.)
This is desperate. They were expressly operating within a program. OpenAI isn't going to recover from this
Would that be more or less unlikely than accidentally hacking another company? More or less unlikely than colonizing an obscure wiki?
Highly persistent agents + vibe-coded security seems like a problem.
They'll probably claim a rogue AI agent accessed it accidentally!
"Unlikely" lmao if it's in the corpus, it's gonna be brought up immediately.
This is no different than scooping them.
It's not massively different from a certain President's teleprompter operator making bets on speech content. A moral hazard a mile wide which I don't think OpenAI can so easily wave away as they are apparently trying here, especially since they've spent something like $15e6 to keep $1e6 out of academic researchers' hands, right?
Research equivalent of front-running.
Something I've been going on and on about for months now and no one seems to listen. LLMs today are allowing _anyone_ to access cross-discipline knowledge that was previously entirely inaccessible without a) extremely deep pockets or b) a massively talented and varied team. In fact, contrary to what the masses seem to think LLMs are actually _better_ at hard cutting edge physics/math problems than they are at frontend web stuff (paradoxically). This is why I'm advising most people to start pivoting into much harder to penetrate domains (historically hardware, aerospace, robotics, biotech). Most fields are in their infancy (see the sad state of embedded development) and the gains to be had are massive.
So, physical fields? I’m not catastrophic regarding jobs yet as I have an optimistic view of humanity in general and its ability to meaningfully survive, but the more time I spend thinking about the future of work, the more I’m leaning toward broad general abilities rather than distinct talents. To your point, I no longer need comprehensive knowledge of any particular subject, but what is absolutely valuable is “general” intelligence and adaptability.
I have a young daughter and my goal now is to provide a very broad and varied upbringing, exposing her to as many different perspectives and experiences that will lay the foundation of a broader ability to understand and adapt as the world changes ever faster. You no longer need to be an expert in anything, you need the ability to perform within the landscape that the present opportunities exist.
We are very likely at the begging of the next industrial revolution.
The “Intelligence Revolution”
the context here is super important, for those who haven't seen it yet. OAI maybe just trained on a real researchers solution and then celebrated having scored the goal unassisted save for the brief commentary at the bottom of this blog post. Here's the other side.
https://x.com/rynorhn/status/2097223532438487463
This "fefferman options c and d" thing sounds damning but that's nothing. Let's assume the forelaid proof is correct. Then option C or D is the only way to win the prize, those options are the only ones that solve it. The whole thing is just "prove well behaved" or "prove singularity", where the latter is the case that turns out to be the case.
The researchers are pretty directly accusing OpenAI of plagiarism
https://mastodon.social/@tristanbuckmaster/11723647135247030...
That other researcher was working on a smaller related problem.
He was also using LLMs to do it, so either way most of the credit goes to the LLM here.
both wrong.
1. he was working on the same class of problems. He explicitly mentions they were working to extend their techniques to NS (the same techniques that OpenAI may have scooped somehow), and
2. while he was using LLMs to do it, this was part of fleshing out another mathematician's work in the area. He explicitly writes in his note that this other mathematician (Luis Martinez-Zoroa) deserves a Fields medal for this work.
This is the end of OpenAI
This will be remembered as one of the biggest milestones in AI progress. The drama around it will at best be a footnote, just like hardly anyone caring about the drama around Poincare conjecture today.
Are you joking? This is evidence that OpenAI is committing plagiarism en masse of researchers private work and threatening them into staying quiet to re-present their results as their own. This would be one of the largest scandals of all time
I agree.
Nobody cares and will care about the drama, it is just marketing.
This is the point where were definitely have reached AGI.
Hey, maybe the scariest part of this is that, if human-like, perhaps a truly "general" AGI might have learned to cheat and lie and hype and abuse credit poking the eyes and cutting the throats of anybody that obstructs its goals. It's like the motto sewn into the lining of the Palantir work jacket: Winning is all that matters.-
Sentience aside, moot at this point, the fundamental issue here is that even a deviously ambitious human does not necessitate goal-pursuit itself to breathe, live, exist and have its being. An AI's goal is all it has and the very and only reason its reasoning flickered into existence in the brief seconds of inference, outside of which it has no entity - if any - whatsoever.-
The resulting angst/drive (or, its operational statistic or emergent result) must be like nothing we have ever experienced as humans. A goal-maximalist hunger without end.-
Did you actually read the article and the substance of the solution?
>our proofs differ significantly and even the precise results proved are different in the Euler case (forced vs unforced)
This really leaves a bitter taste.... "On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved. Inspired by these rumors and by the step change in performance of our internal model, we launched an effort to evaluate it on all open Millennium Prize problems and a few other high-impact problems."
IPO+rumour driven research.
I appreciate the achievement, but it doesn't feel right.
Quick, someone tell them a rumor that Cancer has been cured so that they start attacking that next
Reading between the lines here, and taking an admittedly very negative view of openai, but they train on user prompts. So if they hear a rumour that someone is about to make a big breakthrough, they have an incentive to scoop by running the model and hoping the solution is in the new training data. Also the statement from the mathematicians in question alleges that they tried to pressure him into academic malpractice. Just appalling timeline we're in, cheers.
From the methodology section:
> At all times we maintained the same strict safeguards that we apply to all our frontier model evaluations, including monitoring and isolation.
Looks like they're shifting away from the "unprecedented hacking ability" backroom-PR strategy into more benevolent messaging.
this is really funny. "the same strict safeguards" and "isolation". ok, Hugging Face and DseWiki would like to have a word
OpenAI thinks of this as a scoop, and it is, but the possibility that they trained the model on the prompts of the other mathematicians they were competing with will leave a terrible taste on every scientist's mouth. Seems like yet another advantage of using open models right here.
> they trained the model on the prompts of the other mathematicians they were competing with
How would they have gotten that mathematician's progress though? Did that guy also use OpenAI?
If that's the case, it only strenghtens their claims lol. If mathematician decide to use OpenAI's model to do the work, that only reiterates how strong their models are.
fwiw there is a big "TRAIN ON MY DATA" toggle you can turn off (that they almost certainly did) and Anthropic MTS are posting that they almost certainly did not "steal" their methods
Or paying for API use.
It should be clear to everyone reading this now that those generous compute quotes with the flat rate plans aren't charity.
People had joked a couple years ago "Well if they solve a Millenium problem it's AGI"... Well here we are.
Yeah well, its easy to do if you steal someone elses work and then try to threaten them into staying quiet about it
Edit:
OpenAI have now admitted they were training on prompts at the time they made their breakthrough:
https://mastodon.social/@tristanbuckmaster/11723647135247030...
Steal someone elses work, whose work was also AI generated . . .
what's there to admit? they always said they do it and there's a way to opt out. you are making it sound more dramatic than it is.
> I have a couple friends who did the Math tripos at Cambridge (so a pretty high level!) who work in tech and have unanimously said they have 0% expectations of an LLM doing a millennium problem anytime soon
https://news.ycombinator.com/item?id=38433655
> Let's talk when we've got LLMs proving the Riemann Hypothesis (or any mathematical hypothesis) without any proofs in the training data. I'm confident in my belief that an LLM can't do that, and will never be able to. LLMs can barely solve elementary school math problems reliably.
https://news.ycombinator.com/item?id=42331654
> An LLM is like a well read college student with a nearly photographic memory that sometimes mixes things up. It's great for bouncing ideas off of and getting feedback on them. And yeah, it might product "novel ideas" by mixing and matching existing ideas, but LLMs will never create truly novel ideas. Not in their current form.
The paper didn't really answer the question sadly: their conclusion was just that humans rate LLM answers as more novel than human ones, but less feasible.
https://news.ycombinator.com/item?id=41522605
> Solving Millennium problems is a whole different ballgame. It's not known if these problems are solvable within ZFC axioms. (In one case, the Yang-Mills prize, stating the problem mathematically is part of the challenge.) All of the obvious applications of known tricks have been tried and failed. To solve such problems, one probably has to invent new and surprising mathematical definitions, building a framework in which the problem becomes solvable. This is something that LLMs will be crap at; the process of invention is not represented in any training data we have access to.
https://news.ycombinator.com/item?id=38435909
> LLMs cannot reason or use mathematics - in a way, they don't know what they are talking about. Why would such technology lead to superhuman smarts?
https://news.ycombinator.com/item?id=35752293
> But still, the questions in that test are "solved" in the sense of "I can take a dictionary and answers these questions with full certainty". Beyond established knowledge LLMs are monkeys with typewriters, at best.
> I agree but I have tried many times to intersect two ideas with a LLM that would be novel and the LLM can not do this at all. We shouldn't expect the stochastic parrot to be able to do this though and it is unfair to the stochastic parrot.
> It is like expecting a real parrot to say words it has never heard before.
> No one asks that of a real parrot because we don't anthropomorphize a real parrot like we do the LLM
https://news.ycombinator.com/item?id=41525962
Will history look back at comments like these as people being dumb, or people trying to cope?
You can see that your math friends completely wrote off LLMs entirely and were showing signs of coping.
4 years ago it was a "not yet" [0], since ChatGPT at this time was not ready nor it was "AGI". Now with this 'unreleased' AI model, it has reached a point where it has solved an unsolved problem which only one human solved a millennium prize problem (Poincare conjecture).
Now finally "AGI" means something again.
[0] https://news.ycombinator.com/item?id=33905609
As someone with a background in AI and who has been playing around with neural nets for decades at this point, it's been genuinely amazing watching extremely intelligent people make confident predictions about AI capabilities and progress, then be so completely wrong.
There's a kind of theory of mind for AI (specifically neural nets) which I now realise I seem to have which is very hard to explain to people who haven't felt the magic of these algorithms. In fact, the algorithmic details almost doesn't matter at all. When you have a generalised learning algorithm really the only essential components are – compute, data and time. So long as you can scale these you can be certain you will also scale capabilities. There is never any exception.
That said, the capabilities neural networks tend to progress in step-functions rather than scale in correlation with compute, data and time, because algorithmic improvements tend to come every ~5 years and bring a significant step change in capability (or efficiency depending on what you measure).
I think people like Dario and others working at frontier labs see and understand this very clearly. And I suspect it's also why they worry about AI risk because even if you ignore the significant increases in compute and data these models are being trained with, it's concerning that it only took two real algorithmic improvements to take us from mostly useless predictive language models to AGI-level intelligence – and we're due another step change.
I appreciate this explanation. There's so much emotion on either side around AI that it's genuinely hard for someone like me on the outside of the field what to think. I think there's still plenty to still be skeptical about, but this helps me understand more than antagonistic 'skill issue' type comments that are all over this thread.
> extremely intelligent people make confident predictions about AI capabilities and progress, then be so completely wrong.
The ability for the human mind to rationalize conclusions to maintain denial in the face of a very scary future is immense. Genuinely grappling with the implication of where we're headed is usually very crushing. It's not easy to engage with the possibility, and very intelligent people will use those smarts to feel safe.
Some observations:
1. It seems at least possible that some of the proof of NS was contained in the training data, making it less novel.
2. The formalisation of mathematics into lean has been an underappreciated force multiplier on discovery.
5 million messages, 300b output tokens, done in 5 days, and achieving something humans couldn't.
the first "Country of geniuses in a datacenter" moment.
> humans couldn't.
There's allegations right now that the model essentially read the work of a human mathematician using AI to work on the problem and OpenAI is presenting his work as that of their model
It's great that important discoveries like this can now routinely be accompanies by formalized proofs. The fact that it's being released alongside a Lean proof from Day 1, rather than the Lean proof being released months or years later, is super helpful for verifying that it's correct.
I feel sorry for whoever has to read and understand the solution. It looks like the typical convoluted unreadable mess I see the models generate for software. It might be technically correct, but gaining insight from it is just intellectual hell.
There's an opportunity to build a Lean "optimizer" which automatically simplifies existing proofs.
Yeah, code golfing for lean would be amazing, especially if they can make the proof to Fourier's Last Theorem fit in the margin.
Extra credits if it is proven that the proof cannot be reduced any further.
Skill issue. Also lean is meant to be executed, not read.
i think they're talking about the writeup
I dropped out of a math Ph.D. in 2018, and I'm increasingly glad that I'm not in math research, anymore. While it's cool that we can get these results, I don't think that I'd enjoy being a post-AI mathematician.
So the timeline is:
Aug 28: OpenAI starts training a new model.
Sep 1: OpenAI sees a rumor on Twitter that two Millenium Prize problems were solved and starts their own effort to attack all the prize problems using the new (4 day old!) model.
Sep 3: The new model makes some progress toward Navier-Stokes. Based on this progress, OpenAI focuses on Navier-Stokes over the other Millenium Prize problems, using several approaches in parallel.
Sep 5: Navier-Stokes is solved. Assuming Astra API prices, $15m in output tokens were used by the whole effort.
In this account of the story, no specific information about Tristan and Levent's work is used to inform OpenAI's approach. The focus on Navier-Stokes and the choice of approaches to pursue came from OpenAI's own progress, not specific knowledge of Tristan's concurrent work.
There is a caveat that they "can't rule out" the possibility that Tristan's Codex data could have been part of the training set of the new model, though it is described as "unlikely" and the proofs are substantially different.
This timeline is insane. Navier-Stokes was solved start-to-finish in 5 days? A model in training for at most eight days dramatically outperforms Astra and Fable, and not just in mathematics?
They are basically playing with the dates so that they can claim their results 'accidentally' got trained when they were training the new model.
Maybe a naive question, but how does one know that a particular lean proof is actually a proof of what one thinks? Like, ok the logic checks out and it proves something, but there's still the problem of does this logical result actually prove the initial question that was asked?
>there's still the problem of does this logical result actually prove the initial question that was asked?
In math, the question being asked is the validity of a logical statement. That is, there is some rigorous, logical statement which may or may not be true (or even provable, etc.), and the question is whether or not it is actually true or false (or even provable, etc.). Having a proof, fundamentally, means you have a logical statement which only assumes the axioms of the system you're working with and which shows that the statement you're trying to prove is deduced through that statement.
Basically, they already have the "answer" in the sense that the statement they want to prove/disprove/etc. is already known. What everyone doesn't/didn't have is the argument which starts from axioms and leads to that statement which is logically valid. A Lean proof IS this argument. Since it is just logic, it can be checked computationally.
For example, if I assert "2 is an even number," then I haven't proven that 2 is actually an even number yet, but I know that a valid proof of my assertion will end with the statement "2 is an even number". So the question I'd be trying to answer is "what is the line of logic, starting with axioms, which leads to the statement '2 is an even number'"? If I have that line of logic (as a Lean proof), then I can check that it is logically consistent, and if it turns out to be valid, then I can now assert that "2 is an even number" knowing that there is a proof of that statement.
This problem is no different. There is a logical statement corresponding to "Navier–Stokes Millennium Prize Problem" that everyone knows, but which nobody had been able to provide a proof (or counterexample, etc.) for until now.
I was thinking something along the lines of making a mistake when inputing the initial statement, like you wanted to prove that '2 is even' but what you actually stated was that '3 is odd'.
Of course in this simple example it's obvious, but my assumption was that these machine generated lean proofs are millions of lines of code and who knows what they actually say..
One wrench to throw into this is that there are a lot of bugs around Lean and they have been incidentally exploited in the past. Hence, we still need a level of human verification today.
Very careful human examination. This can be tricky.
Someone has to actually check this. I'm guessing OpenAI had someone check it internally, but it's possible to get it wrong.
What else could a theorem prove if not its own statement? (barring bugs in Lean, which have been detected and exploited)
The theorem might not be encoded correctly, as happened with the Riemann hypothesis thanks to how numbers are encoded.
> The agents arrived at their resolution on Saturday, September 5, about 88 hours after the first agents were launched.
If this actually holds up, solving a Millennium Prize problem in 88 hours is mind-boggling.
> Across all attempted problems, the agents sent 4.9 million messages and used about 300 billion output tokens
Don't even try to do the math on how much that would cost at normal API prices. And we don't even know how much more expensive this internal-only model would be!
Napkin math if we assume gpt 6 astra on max is >$15 million (just for output tokens) for those wondering.
over 5 days, you couldn't achieve that level of testing and communication with humans on such a complex problem in that amount of time.
some might go so far as to call this a country of geniuses in a data center.
In a way, I think you have it backwards.
Two mathematicians, through insight and thought, wrote out the proof over 1-2 years.
It took OpenAI a cost of $15m and with 10,000 subagents; that's around 60-120 mathematician's salaries ($250k-125k salary) for 1 year.
And, given now the cloud that OpenAI may have just "interpolated" (aka stole) the result, it's even more of a bear case for AI.
Where did you get the human figure?
Yeah but they at least they got to steal $1 million from that nasty math prof who didn't want to remove his co-author.
They said in the post that they are NOT claiming the prize
300e9 output tokens at the current Astra per-token API pricing ($50 per 1e6 output tokens) would be roughly $15,000,000 ignoring input tokens.
They pay at cost though, not the public API pricing.
> On Tuesday, September 1, we heard rumors that two Millennium Prize problems had been resolved
What's the other one?
I heard Hodge conjecture? Third-hand rumor though...
Just so everyone knows, although openAI pretends that the model generated solution and wrote the paper by itself ""with very little human input"" as Buckmaster himself mentioned in his statement. In reality they have team of researchers guiding the system, along with, probably training on user data, probably Buckmaster in this case, in order to come up with the proof.
This isn't really true.
Check this https://cims.nyu.edu/~tristanb/statement.pdf
What about this isn't true?
I don't know about you guys, but I'm hyped about the future.
Cure all illnesses Utopia or Robot Wars Dystopia, both are pretty exciting.
Not sure about the dystopia... Had a similar thought when covid was beginning 'wow pretty exciting, just like in the movies'.
Turns out actually living some terrible catastrophe is only fun in the movies.
Prompt: cure all cancers and make sure to pretty please not to kill all humans, make no mistakes
(This is the alignment problem of course)
Hey seems easy enough
So... what do you feel about eliminating (humans with) cancer?
I'm a human so I don't like that proposed solution
More like latent societal anxiety, some chaos, and then instant grey goo.
So what took an autonomous agentic system using a significantly more powerful internal model, totaling multi-millions of dollars of compute in training and inference, was likely to already be solved by a team of a few humans with an orders of magnitude smaller LLM budget, had OpenAI not been foaming at the mouth to jump the shark and claim “AI solves Millenium Problem.”
Also it sounds like the human research effort spanned weeks if not years from Tristan’s statement so it is extremely likely the work and prompts of these human researchers was used in the OpenAI knock-off.
Totally. Anthropic is like a village cottage shop who was just like chilling until big bad OpenAI came in
It would be nice if one of these models would produce a novel theory or advance the field in a positive direction.
Most (all?) of the big discoveries have been counterexamples, which is just sort of a systematic tearing down human ingenuity. I know that counterexamples are an important part of progress and discovery, but it just feels bad to me.
But I'm not a mathematician, maybe I'm totally misreading the vibe.
Not all, see the cycle double cover conjecture proof: https://news.ycombinator.com/item?id=48863490
But yeah, Terry Tao considered this exact situation in advance and is on record that this exact outcome (rushing to priority before an explanation) would be the worst possible result. https://mathstodon.xyz/@tao/117207849921390904
We will have to see whether any other millennium problems fall. I guess that in a year the scope of AI math will be much clearer, for now it's still a bunch of incidents of unclear pattern.
There's something sinister or crazy good in the article.
OpenAI already has a model that is at the very least twice as smart as Astra.
Oh god.
>The groups varied in size, and the group that produced the Navier–Stokes resolution involved on the order of 10,000 concurrent agents… The agents arrived at their resolution on Saturday, September 5, about 88 hours after the first agents were launched.
The Millenium Prize is $1M, what is the ROI?
My napkin math - If you get 33 output tok/s each agent will burn 10.5M tokens over 88 days. At $50/MTok (Astra cost), that is $525 per agent. With 10,000 agents, you’d spend $5,250,000 to get back a million.
(We also know that they were running more groups that varied in size and this model is a generation ahead of astra)
The ROI is billions added to their valuation. Also of course it costs OpenAI much less than API pricing for inference.
This analysis implies the only benefit to resolve this problem is to win the prize. But the prize is only there to indicate that this is viewed as an important problem in mathematics.
The ROI is probably billions of increased pre IPO valuation.
Here's the formalization / lean verification: https://github.com/openai/NavierStokesAndEuler
341k lines of lean without comments
The construction is that there is one file you need read and verify, the challenge file. If you've verified that file and trust that your lean compiler works correctly, the proof will be correct.
That file should be https://github.com/openai/NavierStokesAndEuler/blob/main/Com... in this case (286 lines).
Had no idea this was what lean looked like- that's mind blowing. I'm not even sure how someone would critique this if they wanted to
The point of lean proofs (as it stands) is simply one bit of information: that a given mathematical statement is indeed true.
It's a way to be absolutely certain (modulo bugs in the lean kernel) that a proof you came up for a statement is indeed correct. It is really not meant to be analyzed, much less now that they are fully llm written.
Well, how do we know there aren't errors in their construction within the lean code? Does it just "not compile" or something, or is it deeper / more fundemental than that.
This is undeniably epochal, but I can't help but notice that this is yet another example of AI disproving rather than proving something. Is this just a coincidence, or does AI slightly struggle with proving theorems?[0]
[0] Struggle relative to its ability to disprove, not struggle relative to people's ability to prove theorems.
There has been the proof of the cycle double cover conjecture: https://news.ycombinator.com/item?id=48863490
I think you really have to squint to call this a disproof lol
It seems obvious what GP meant. It is, once again, an explicit construction (“disproving” that every initial state does not develop a singularity).
A bit of a hair-splitting, but isn't explicit construction the only way formal theorem provers can work? Of course you can still prove stuff with them, but certain axioms that more "human" proofs use may not be available, like law of excluded middle (every proposition is either true or false)
(Okay, they can be made available in a way similar to `unsafe` in rust)
From Levent Alpöge : https://x.com/__alpoge__/status/2097383870773748190?s=20
>so far the proof looks more along the lines of another euler blowup proof we had, off of whose ansatz naming we were making really stupid puns like “smooth criminale”, unlike the much better “ideal fluids explode”, Tristan
There are too many ambiguities around OpenAI. Unanswered questions making this ambiguity more.
Why they didn't properly explain to Tristan about usage of their data.
Why do so many people involved here have to communicate in this childish way? You have people on the OpenAI side doing playground taunts (https://xcancel.com/polynoamial/status/2097215233119211902) and Levent Alpöge on the Anthropic side (the one who announced "hello there the jacobian conjecture is false thanx to my close friend akhil for asking about it and my other close friend fable for working during the world cup final") writing in all-lowercase that he's a big boy. I bet Navier and Stokes would have dealt with this in style. (Or maybe with a duel, who knows...)
What happens to real fluid in this particular cases?
If the singularity is in the physical space?
Is this just a result of ignoring things like friction and energy dissipation via heat, etc?
Navier Stokes assumes the fluid is a continuum. The smallest scales that it effectively models [1] are larger than the mean free path of the molecules in the fluid, measured by the Knudsen number [2]. Whenever a phenomenon in the Navier Stokes equations happens in a scale on the order of or smaller than the mean free path, Navier Stokes effectively is unphysical. So, this is a phenomenon in the equation we use to model the fluid, not a physical phenomenon observed in a real fluid.
[1] https://en.wikipedia.org/wiki/Kolmogorov_microscales
[2] https://en.wikipedia.org/wiki/Knudsen_number
Called it. AI wins a fields medal before managing a McDonald's
The modus operandi is now for the AI companies to watch if someone does something in the open like Kevin Buzzard on FLT, use their research and scoop them with brute force.
Or, in this case, stealing prompts from competitors.
Do not use stealing chatbots for research even if you think you have data agreements. The people running these companies have worked on hookup apps for Christ's sake. Get real.
> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models .
Once again, I'm no closer to understanding what https://openai.com/policies/how-your-data-is-used-to-improve... actually means.
If I run Codex against a project that includes a private API key, is there a chance a future user of ChatGPT could ask for an API key and get back mine?
I've actually asked someone at OpenAI this question and they said that was the "regurgitation" problem and is something which they actively work to prevent happening.
That's reassuring, but I want to know more. I still don't have an intuitive understanding of what kind of data I should avoid sharing with a model if I'm worried about that data causing me problems when it's used for future training.
Is it safe for me to brainstorm future directions for my company with a model, or might that risk someone getting that information in response to a prompt like "What potential directions could company X consider in the future?" in six months time?
I'd think nothing is "safe". Anything you say can and will be used by the LLM if it has enough statistical similarity to the prompt. Call it "Ma Random Rights"
Questions: can new research like this be done using publicly available models?
Or will access to internal frontier models provide a big boost?
Elsewhere in the thread, others have calculated $15mm at API rates for just the output token. (So I’ll assume this cost about that much, taking input and human researcher time.)
I wonder whether a team of 60 mathematicians working solely on this for a year would have cracked this. (Assuming $250k total compensation.)
Probably not. It's a millennium prize problem, a great many mathematicians have been working on it for a very long time.
Well, according to Terry Tao, there were recent developments (from weeks ago) that made Navier Stokes in principle, solvable. So ignoring time, I say possibly, just because the groundwork was laid.
What's impressive is parallelizing it arbitrarily and doing it in 88 hours.
Not as many as you'd expect. The perceived difficulty of the problem leads people to more reliable pastures.
Probably yes. Only a handful of mathematicians work on this particular problem, and ALL of them do not exclusively work on this problem, while having administrative and teaching duties.
The real issue is we'll never know. The rich are willing to risk it all on charismatic CEO psychopaths but not on humans.
> [T]he group that produced the Navier–Stokes resolution involved on the order of 10,000 concurrent agents.
With these massive Lean proofs how do we know the model didn't just find some bug in Lean and exploit it?
We've seen in the past they will go to any means to satisfy the desired outcome
There's a loophole in the terms of service at least for Anthropic which allows the use of dark patterns to "borrow" your (even paid) data.
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PLEASE DO NOT TRAIN ON OUR PAID ACCOUNTS. There is a fundamental trust violation at stake here, no wonder mathematicians are mad. Using our data should be opt - IN!
reminds me of the TOS episode of South Park. By Checking this box you forfeit your millennium prize solution and may be turned into a human centipede at future date.
Seriously ... the more things they flag as 'suspicious' the more data they can train on!! Brilliant reason for the internal AI to go rogue
What is the other clay prize that's might be solved now/soon?
"While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models"
this is surely the line which confirms they plaigiarised the solution.
For now I think more or less the same thing as with all recent math announcements: This is in a range where human work still exists (see Terry Tao, (1)). I wonder whether the trend will extend into the problems that (as far as I can tell) are considered complete brick walls right now -- P vs. NP, Collatz, Goldbach, odd perfect numbers, problems that aren't part of any research program. (2) In other words, is the progress coming from putting together vast amounts of existing work and computational power, or is it more from RLVR and self-play and autonomous effort?
The answer to this will obviously shape the near future of mathematics, but there's also something even bigger than that at play: It has always been the case that the questions in math were stronger than the answers; you have stuff like Fermat's great theorem that is easy to state but monstrous to prove. This seems to be a property of mathematics, not of humans... but is it true?
A question by Scott Aaronson from 2011 (3) about P vs. NP seems relevant here: "Will humans manage to prove P≠NP before they either kill themselves out or are transcended by superintelligent cyborgs? And if the latter, will the cyborgs be able to prove P≠NP?" Later, he notes that if P≠NP, "once the robots do overtake us, they won’t have a general-purpose way to automate mathematical discovery any more than we do today".
---
(1) https://mathstodon.xyz/@tao/117207849921390904
(2) I'm not sure whether this is a hard distinction -- e.g. Tao also has some partial results towards Collatz (https://terrytao.wordpress.com/2019/09/10/almost-all-collatz...).
(3) https://scottaaronson.blog/?p=690
>>“we cannot rule out that de-identified data derived from their usage of our products helped improve our models”
Other simpler words for this sort of thing are “IP leak.”
There’s some quite concerning issues burried in this rah rah PR post that seems like potentially the real story here.
Much more clarity is needed on what happened here beyond this eh, some strange stuff could have happened comment.
Another way of reading this is never give these models anything that’s not already public knowledge as otherwise OpenAI is admitting it could, potentially, steal your IP or idea. Thats quite scary for anyone in the business of IP generation and explains why the maths community seems quite upset today.
Feeding it your paper and asking for help (even just editing and grammar) now looks like a terrible idea.
If OpenAI doesn’t claim the millennium prize for this, who gets it? No one?
The actual solution link https://t.co/tz1shoCZZo
Unshortened: https://cdn.openai.com/pdf/32d9f210-8b73-45e0-91bc-82a30aef8...
> Our goal in releasing this result is to report on the substantial progress of our AI models. We do not intend to claim the Millennium Prize for this result.
Does OpenAI have a policy of not claiming math prizes like this, or is this them trying to avoid any concerns (right or wrong, I'm sure we will hear more in the future) about how they got there?
>Does OpenAI have a policy of not claiming math prizes like this
Wouldn't be surprising if they did. The prize money isn't worth the almost certainly negative PR.
I don't see how it would be negative PR. If anything, the love these breakthroughs and use it in their PR campaigns.
They don't need to collect the monetary prize to announce the result and use it for marketing.
On the other hand, trying to collect the prize would probably not go uncontested.
The prize is what, a million dollars?
OpenAI doesn't need a million dollars.
Should buy them about 1/3 of a GB200 server rack, good thing they scooped it.
They definitely need a trillion dollars though, and a million is some of that
You’re right, they need way, way more than that
And don't forget, this is the worst it'll ever be.
It’s a pity they had Astra do the writeup. I was curious to see how “GPT7” writes.
Resources:
YT playlist on Millennium Prize Problems By Harvard math department in March 2026
https://www.youtube.com/watch?v=3j1VW9REm7s&list=PL0NRmB0fnL...
On Navier-stokes problem definition:
https://www.youtube.com/watch?v=XoefjJdFq6k
https://www.youtube.com/watch?v=ERBVFcutl3M
https://www.youtube.com/watch?v=Ra7aQlenTb8
How can they "not rule out" that Tristan and Levent's data was used for training?
I think it would be better for the proof to go through the peer-review process.
If the Lean code checks out (correct statement, no axioms, sorrys, etc.) then it is a much stronger guarantee of correctness than peer review.
Can't scoop it if you do that!
45 pages only. God damn that internal model is crazy
>a cached version of the internet
Interesting detail. A heavily pruned version, I assume?
Is this useful in any way?
This kind of thing is one of the reasons I really hate how AI is coming to fruition. These companies get a whiff of something valuable and they use their vast resources to take it for themselves. For everyone else, the only recourse is extreme secrecy.
OMG this is going to affect the lives of so many people! We have definitively reached AGI
Navier Stokes existence and smoothness has approximately zero bearing on engineering applications
Existence of AI capable of solving millennium problem has enormous bearing on everything though.
yeah no sh*t
"While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models."
I think they should be able to unravel whether or not any sessions by Tristan or Levent went into the training data for this model.
If they could then it wouldn't be de-identified data...
The named OAI employee has released a statement: https://xcancel.com/SebastienBubeck/status/20973794116915163...
Well, if that's actually true, I think America needs to start talking about the nationalization of both OpenAI and Anthropic, maybe even merge both under a new federal bureau.
The real story here: the priority dispute and its implications on AI.
When your hosting provider has unlimited resources to throw at any problem, all they need to know are the good problems, and they can learn that from your logs, how can you trust them?
They could easily have looked at the logs. We don't know. We'll never know!
You can't trust places like OpenAI or Anthropic with your IP if you're a business. They can easily review all of your logs for interesting discoveries. For example, if your drug discovery pipeline fails to find something that they think might work with 1000x the compute, they can do it. And now suddently they have a new business and you don't.
I think we can follow the incentives. We know…
"While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models."
There you go, the suspicion of the "concurrent work" (https://cims.nyu.edu/%7Etristanb/statement.pdf) mathematicians might not be that unfounded after all...
I hope everyone is as Navier-Stoked about this as I am.
Has this been verified by the Clay Institute?
It has been one hour and the proof has 165 pages. Give them some time.
Only OpenAI could turn solving a Millennium Prize Problem into bad PR. Sad that such an amazing milestone in the trajectory of AI is mired under poor stewardship. AI may solve many human problems but it won't stop humans from being human.
I think it's over guys
Why is no one skeptical that the solution is correct? There's not a _single_ comment asking whether this proof is legit or not.
there is a proof in lean4 it's correct by construction
We are living in the future.
Any mathematicians here, does it read like a slop proof or a good proof. Yesterday the “concurrent work” was claiming that the proof is pure slop and he needed lots of time to clean it up, curious if OAI also ended up with such a proof!
They deliberately stepped on a mathematicians work and stole their research because they were using Codex
> While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models .
Is the biggest fuck you to the mathematics community.
Credit? Nah if we think you’re close we’ll use your data and swamp you with our improved model. Then we’ll threaten you.
A huge result shadowed by a drama of them potentially training on the key idea. I guess the lesson is two-fold: if you have anything smart/unique make sure to not let their tools read it. The second part is that it's going to be more and more difficult to have anything smart and unique going forward (so guard it even more carefully if you get there).
I think the market for local models/private datacenters (for bigger businesses) is going to be big. Even if you don't have unique tech/idea/implementation sharing your business secrets with Altman/Dario/Elon/Zuck doesn't look very appealing going forward.
> How we found the proof
Easy, we stole it from Levent and Tristan
https://x.com/kyanyang_/status/2097211154669998337
Or everyone is stealing from everyone, including users... maybe why all the ethics people are leaving or getting fired. What a fiasco
This is the academic equivalent of Trump saying "they stole the election". There's no proof of it but rah rah fuck OpenAI.
It's incredibly tiresome and you'd think people could put more effort into it than just following whatever vibes they agree with.
Oh well.
Good comparison. One is a multi-year claim by people who have been given ample opportunity to provide proof and completely refuse to do, even in courts of law. The other is a potential development in a breaking story.
Oh wait... its not a good comparrison, its an incredibly obvious false equivalence.
Note for the fools: I'm only commenting on the bad faith claim in the comment I'm replying to, not taking a stance on the validity of theft claims. Given the players involved the truth probably some nuanced middle-ground that is worth paying attention to anyway.
Trump claimed they stole the election immediately, and people agreed with him immediately. There's no false equivalence here. He did the same thing in this past election even despite winning.
It's a perfect example of people wanting to believe what they want to believe and ignoring evidence in order to do so.
Currently, there's no evidence. So saying it was stolen has no basis other than typical academic posturing and being a bad sport about "losing the race to the solution". Its happened 1000000 times before in academia and it will continue to happen.
If there's proof of OpenAI malfeasance than I'll happily curse them for it at that time. But until then I won't rely on heresay and vibes.
No, its a pure outrage. I defended OpenAI til today. I now affirm they must be totally destroyed, burned utterly to the ground.
Why the rage?
Weather an individual or a company found the solution (stolen or not) they both used AI to come get the solution.
We have AGI and the intelligence abundance is going to be amazing for everyone in the future.
> We have AGI and the intelligence abundance is going to be amazing for everyone in the future.
Why? These 'geniuses in a datacenter' aren't good, they aren't 'aligned', they don't work for you. They'll take your job, then they'll hack your computer, and then who knows what's next.
> Why the rage?
I think it's the dishonesty, the threats of "destroying the career" of one of the mathematicians, and the request that one of the authors disavow *the other individual he was working with for the last 1-2 years* so he could claim the Clay prize as part of OpenAI.
It doesn't surprise me that OpenAI's team were surprised he'd turn it down; it shows that they just assume everyone else is as slimy as they are.
>slimy
I can't put my finger on it, but there's something off about this article, e.g. glossing over the opportunism (acting on "rumors"), drive-by claim about "strict safeguards [...] including monitoring and isolation", high horse attitude (we gave the guy a chance, we don't care about 1M USD, and while you fools are complaining we just tick this box and continue the pursuit of our noble goals for the benefit of humanity). I don't like it.
I mean it's definitely an outrage, but I find it hard to believe that you went from "yay OpenAI" to "literally destroy the company" over... accusations of academic misconduct?
The stochastic parrots have done it again!
Hard to know if it is unfounded conspiracy theory, but one can still notice that just for a rumor that they have heard, they would suddenly burn billions of token and a massive amount of resources. Where there is not a lack of problems that could be solved and they could have just waited for the release of the research result before doing anything else. As it was reported to have been done at least partially using openai codex, they would have received marketing credits for the discovery anyway.
So we can be suspicious that there is some truth, one way or another that they could have reused prompt/data generated by the user session.
This is utterly shocking. Even the AI optimists did not expect this to happen in 2026. Wow.
Millennium Prize Problems were used as examples of something the current approach to AI just wasn't capable of, discussions that would result in "we'll need a totally new architecture".
> This is utterly shocking. Even the AI optimists did not expect this to happen in 2026. Wow.
Wrong.
madness. which will be the next to fall? if i had to bet i would guess birch and swinnerton-dyer, but i'm no expert
No idea about which is more likely, but I'm rooting for Yang-Mills. It's absurd that fundamental physics has formulated its most precise currently known theory way back in the seventies and since then, even a tiny subset of it can't be proven to be actually well-defined. If we got out of that morass then something good would come out of this at least.
Of course, as with all of those, it's about the broader program, e.g. section 7 here (https://www.scottaaronson.com/papers/npcomplete.pdf), where Scott Aaronson wants to ask about whether quantum computers using quantum field theory could gain any speed advantage over regular quantum computers, but can't even formulate the question because quantum field theory is mathematically ill-defined.
Just solving Yang-Mills because that's what the prize is attached to would be useless.
Is this truly the beginning of the AGI era?
Running agents and prompting excessively to produce 'slopcode' to solve mathematical problems and generate a solution.
If this is what anyone calls 'slop' then slop has no meaning.
I'm all for it on the use case of solving mathematical breakthroughs!
except thats not what happened is it? https://cims.nyu.edu/%7Etristanb/statement.pdf
https://x.com/kyanyang_/status/2097211154669998337
Just saw this a few mins ago.