When OpenAI posted about their 10 breakthroughs, I saw lots of career research mathematicians say things mostly along the lines of “I don’t understand any of this it’s way over my head”.
Are we missing the forest for the trees here? If a math problem falls in the forest but nobody is around to understand it does it make a sound?
How can we possibly make use of these breakthroughs if we don’t understand them? How could we ever make anything useful with them?
Are we ready to just let go of our intellectual faculties and give them to a giant supercomputer nobody understands? How do we tell truth from fiction?
I get the impression that the value of unproven conjectures is more in the new math and techniques that may be discovered - by humans - trying to prove/disprove them, rather than much utility in any eventual result itself.
Take something like Fermat's last theorem - I'd be curious to hear of any use of the result itself, but there was a massive amount of new mathematics generated by those working on it, whether ultimately successful or not.
These AI math proofs are interesting testament to the power of reinforcement learning applied to math, obviously reflecting the axiomatic self-consistent nature of math itself, but it doesn't seem they have the same value as a humans working on these problems since they are using known math to solve them rather than inventing anything new.
However, it would still be interesting to analyze the LLM lines of reasoning that lead to any of these results, since there may be value there even if no new math, just as human Go players have found value in analyzing computer Go.
Still, as Demis Hassabis has himself said, the real goal with AI is discovery and creativity - you want to create the thing that could design the game of Go in the first place, not just play it. Similarly with math, while there is interest in seeing an AI "play math" using the rules of the game, what would be of much more interest is the AI that can create new math, in the same way as Andrew Wiles did while proving Fermat's last theorem.
> When OpenAI posted about their 10 breakthroughs, I saw lots of career research mathematicians say things mostly along the lines of “I don’t understand any of this it’s way over my head”.
Math is an incredibly broad field. I mean, you don't expect a traffic engineer to understand anything about nuclear reactors, do you? Yet, they are all 'career engineers'.
I would expect anyone calling themselves an engineer of any field to understand basics of fission power generation. Come on, it's 7th (school) grade material.
This seems like an extreme exaggeration from a few people claiming to not understand a very recent result. This cycle of a new result being discovered, and reaearchers needing some time to truly digest and disassemble it, is normal.
I think it's the scientist version of "I vibecoded ten apps this weekend (at one point I'll have real users too)".
Because it's math, it's all mysterious and genuinely impressive, but in the end, if no human cares about it (apart from attention grabbing "it's so over" tweets and articles), does it really matter?
Nah, people are vibe coding lots of apps that no one cares about, but this is more like going through Stack Overflow and answering the most upvoted issues that don't have answers. These are published problems that have prior interest, for decades usually, and a few snarky internet comments don't undo that.
Mathematics is an unusually dense (if not the most dense...by a few large steps) field. So lots of areas of mathematics are extremely deep and narrow without any real shortcuts, even for seasoned mathematicians.
So a good fraction of famous old math puzzles with no practical use are famous because they are in some way similar to problems people actually care about. If you can solve the toy problem that is in some way simpler, maybe you can use the same methods to solve the "real" problem.
One open question is whether these machine solutions to these problems will act as springboards to future research, either when given to human mathematicians, or when used to train future machine models.
One of the most famous mathematicians of all time studied number theory. He wrote an apology to humanity for all of the very smart and capable people wasting time studying number theory, since these things are clearly unless old puzzles with no practical use whatsoever. Now, 100 years later, these results underpin all of modern public key cryptography.
It's just really hard to affirm that something has "no practical use whatsoever". Maybe it doesn't have use "now", maybe it doesn't have "direct" use but can be used for another finding that is useful, Math has a long story of finding out stuff that turns useful later on.
Maybe the "beautiful, elegant" math is really just accidentally that way, just the tiny cross section our dumb human brains can understand. The vast majority of it could be inscrutable, ugly, chaotic and seemingly meaningless.
> When OpenAI posted about their 10 breakthroughs, I saw lots of career research mathematicians say things mostly along the lines of “I don’t understand any of this it’s way over my head”.
Huh?
Mathematics is an extremely wide subject, it's perfectly normal even for two professional mathematicians not to understand each other's work. Have you considered that maybe they just don't work in that area?
Are you implying OpenAI's paper (which was, by the way, edited by humans and provided Lean certificates for most of the proofs) is actually gibberish? That's flat-earth levels of conspiracy.
I have the same questions about human mathematicians!
I can't tell if xkcd #435 is still true, or if math is just as mushy as everything else seems to be. When a math proof can only be understood by a handful of people, what does that mean about that proof? I think the LLMs are pushing a problem that existed already and pushing it further.
The mathematics are above my intellectual capacities, but I still find the man and his lifestyle fascinating. Though I admit his heart attack probably wasn't a coincidence, sadly.
I wonder if national, institutional, or otherwise "eccentric" sponsorships (encouraging a similar migrant-madman approach to academic cultivation) of some of the folks on HN wouldn't lead to meaningful discoveries in CS.
I often see comments that some of the users here long to "make a computer do neat tricks all day", and I can't help but think meager sponsorship could go a long way in this area. Existing grant structures, being much more traditional, are constrained by their cost.
> I wonder if national, institutional, or otherwise "eccentric" sponsorships (encouraging a similar migrant-madman approach to academic cultivation) of some of the folks on HN wouldn't lead to meaningful discoveries in CS.
The problem is that Paul Erdos was eccentric but he was also Paul Erdos. I'm not saying you're implying that, but I feel it's a similar line of thinking to how popular culture often romanticizes autism and Asperger's because some very smart people are (allegedly) affected. The same group includes people who need 24/7 care.
Computer science at the frontier is as specialized and hard as mathematics, you need years of study to truly understand a field well enough to make meaningful contributions. You can try sponsoring me if you really want, but I don't think you'd be spending your money wisely in expectation.
FWIW I've worked in two different academic labs, both of which would have benefited from a runaway worker barreling down random paths, as long as they were being productive in some capacity.
The AIs seem to have some combination of very broad familiarity with math (enabling relevant things from other subfields to be brought in to the proof) as well as patience and "sitzfleisch" (stamina in working through details even if they aren't immediately obviously promising.)
An obvious area for improvement would be automated generation of new conjectures and attempts to prove (or disprove) them, with the discovered arguments then being used as training for refined models. This will require autoformalization to check the results as there will be too many for manual verification.
something i've just realized : today long-standing maths problems are falling. It's great intellectually but won't probably have an immediate impact on our lives.
Now, what will happen once long-standing physics ( and chemistry and biology) problems will start to fall and at the same rate ?
Then we're going to enter a totally different world.
Not really. These same techniques fall flat on their face when applied to most physics and chemistry problems. All of academia has already been doing ML4Science for the last 8 years. God knows how many billions have been spent.
The only two major highlights are weather modeling and folded protein backbone prediction.
Mostly everything else, either lacks enough data, or there are contraits on the size of the foundational models that render them impractical or they just fail to generalize.
Disappointing lack of "Why" in an article that starts with it.
Are they actually doing something new and novel, or are they just absorbing that "a=b as was proven in transcendental hyper-circular group theory; and b=c was proven in universal quantum superposition"; and they're the first to find the connection that a=c? And several of the problems are counterexamples, not novel proofs of correctness?
Its fascinating either way, but it'd be nice to actually understand more of what is happening.
One of the recent problems was actually proven with elementary results. It did use a technique not usually applied to the problem space, but it wasn’t a hyper specialized result.
There is no such thing as the Renaissance Fund. Quanta receives funds from the Simons Foundation... I also don't know where you get it from that Renaissance Technologies is heavily invested in AI. Any sources to back up your claims because I suspect you made all that up?
We have now passed the point where the AI bots were annoying. Now it is the reactionary “everything even possibly slightly remotely tangentially connected to AI must be deplatformed” rants everywhere that are even worse.
It would be tempting to assume the commenter here has no idea what Renaissance is or how they made so much money.
> The company is widely considered one of the most profitable hedge funds in history, generating an estimated $7 billion to $8 billion in annual revenue solely from management and performance fees
When OpenAI posted about their 10 breakthroughs, I saw lots of career research mathematicians say things mostly along the lines of “I don’t understand any of this it’s way over my head”.
Are we missing the forest for the trees here? If a math problem falls in the forest but nobody is around to understand it does it make a sound?
How can we possibly make use of these breakthroughs if we don’t understand them? How could we ever make anything useful with them?
Are we ready to just let go of our intellectual faculties and give them to a giant supercomputer nobody understands? How do we tell truth from fiction?
I get the impression that the value of unproven conjectures is more in the new math and techniques that may be discovered - by humans - trying to prove/disprove them, rather than much utility in any eventual result itself.
Take something like Fermat's last theorem - I'd be curious to hear of any use of the result itself, but there was a massive amount of new mathematics generated by those working on it, whether ultimately successful or not.
These AI math proofs are interesting testament to the power of reinforcement learning applied to math, obviously reflecting the axiomatic self-consistent nature of math itself, but it doesn't seem they have the same value as a humans working on these problems since they are using known math to solve them rather than inventing anything new.
However, it would still be interesting to analyze the LLM lines of reasoning that lead to any of these results, since there may be value there even if no new math, just as human Go players have found value in analyzing computer Go.
Still, as Demis Hassabis has himself said, the real goal with AI is discovery and creativity - you want to create the thing that could design the game of Go in the first place, not just play it. Similarly with math, while there is interest in seeing an AI "play math" using the rules of the game, what would be of much more interest is the AI that can create new math, in the same way as Andrew Wiles did while proving Fermat's last theorem.
> When OpenAI posted about their 10 breakthroughs, I saw lots of career research mathematicians say things mostly along the lines of “I don’t understand any of this it’s way over my head”.
Math is an incredibly broad field. I mean, you don't expect a traffic engineer to understand anything about nuclear reactors, do you? Yet, they are all 'career engineers'.
I would expect anyone calling themselves an engineer of any field to understand basics of fission power generation. Come on, it's 7th (school) grade material.
This seems like an extreme exaggeration from a few people claiming to not understand a very recent result. This cycle of a new result being discovered, and reaearchers needing some time to truly digest and disassemble it, is normal.
I think it's the scientist version of "I vibecoded ten apps this weekend (at one point I'll have real users too)".
Because it's math, it's all mysterious and genuinely impressive, but in the end, if no human cares about it (apart from attention grabbing "it's so over" tweets and articles), does it really matter?
Nah, people are vibe coding lots of apps that no one cares about, but this is more like going through Stack Overflow and answering the most upvoted issues that don't have answers. These are published problems that have prior interest, for decades usually, and a few snarky internet comments don't undo that.
Latest presentation of Terence Tao on what current advancements in AI mean for math discusses (among other things) those issues: https://teorth.github.io/tao-web/slides/age-of-ai-icm-2026.p...
Mathematics is an unusually dense (if not the most dense...by a few large steps) field. So lots of areas of mathematics are extremely deep and narrow without any real shortcuts, even for seasoned mathematicians.
Awesome observation. What would you consider denser?
Physics possibly.
QWEN-3.6-27B
P.S. Couldn't resist :p
I don't mean to be dismissive, are these just old puzzles with no practical use whatsoever?
So a good fraction of famous old math puzzles with no practical use are famous because they are in some way similar to problems people actually care about. If you can solve the toy problem that is in some way simpler, maybe you can use the same methods to solve the "real" problem.
One open question is whether these machine solutions to these problems will act as springboards to future research, either when given to human mathematicians, or when used to train future machine models.
Isn't most of math this way? Occasionally, we find a practical use for it, but that's usually not the point.
One of the most famous mathematicians of all time studied number theory. He wrote an apology to humanity for all of the very smart and capable people wasting time studying number theory, since these things are clearly unless old puzzles with no practical use whatsoever. Now, 100 years later, these results underpin all of modern public key cryptography.
It's just really hard to affirm that something has "no practical use whatsoever". Maybe it doesn't have use "now", maybe it doesn't have "direct" use but can be used for another finding that is useful, Math has a long story of finding out stuff that turns useful later on.
True. Though ~99% is still useless in the end.
This has been an ongoing debate since the computerized proof of the four color theorem fifty years ago.
Maybe the "beautiful, elegant" math is really just accidentally that way, just the tiny cross section our dumb human brains can understand. The vast majority of it could be inscrutable, ugly, chaotic and seemingly meaningless.
> When OpenAI posted about their 10 breakthroughs, I saw lots of career research mathematicians say things mostly along the lines of “I don’t understand any of this it’s way over my head”.
Huh?
Mathematics is an extremely wide subject, it's perfectly normal even for two professional mathematicians not to understand each other's work. Have you considered that maybe they just don't work in that area?
Are you implying OpenAI's paper (which was, by the way, edited by humans and provided Lean certificates for most of the proofs) is actually gibberish? That's flat-earth levels of conspiracy.
I have the same questions about human mathematicians!
I can't tell if xkcd #435 is still true, or if math is just as mushy as everything else seems to be. When a math proof can only be understood by a handful of people, what does that mean about that proof? I think the LLMs are pushing a problem that existed already and pushing it further.
[0] https://xkcd.com/435/
That's why OpenAI also published machine-checkable proofs.
The process is very, very faintly similar to running a typechecker over your software sources.
The mathematics are above my intellectual capacities, but I still find the man and his lifestyle fascinating. Though I admit his heart attack probably wasn't a coincidence, sadly.
I wonder if national, institutional, or otherwise "eccentric" sponsorships (encouraging a similar migrant-madman approach to academic cultivation) of some of the folks on HN wouldn't lead to meaningful discoveries in CS.
I often see comments that some of the users here long to "make a computer do neat tricks all day", and I can't help but think meager sponsorship could go a long way in this area. Existing grant structures, being much more traditional, are constrained by their cost.
> I wonder if national, institutional, or otherwise "eccentric" sponsorships (encouraging a similar migrant-madman approach to academic cultivation) of some of the folks on HN wouldn't lead to meaningful discoveries in CS.
The problem is that Paul Erdos was eccentric but he was also Paul Erdos. I'm not saying you're implying that, but I feel it's a similar line of thinking to how popular culture often romanticizes autism and Asperger's because some very smart people are (allegedly) affected. The same group includes people who need 24/7 care.
Computer science at the frontier is as specialized and hard as mathematics, you need years of study to truly understand a field well enough to make meaningful contributions. You can try sponsoring me if you really want, but I don't think you'd be spending your money wisely in expectation.
FWIW I've worked in two different academic labs, both of which would have benefited from a runaway worker barreling down random paths, as long as they were being productive in some capacity.
> [...] as long as they were being productive in some capacity.
I'm afraid you only know that after the fact.
You might also like TempleOS, or at least the context and history behind it.
I guess that's the crux of the issue
> Though I admit his heart attack probably wasn't a coincidence, sadly.
He died aged 83...
I didn't know that. A poor assumption I made that his amohetamine use shortened his life significantly.
Non-Erdős problems are also falling.
The AIs seem to have some combination of very broad familiarity with math (enabling relevant things from other subfields to be brought in to the proof) as well as patience and "sitzfleisch" (stamina in working through details even if they aren't immediately obviously promising.)
An obvious area for improvement would be automated generation of new conjectures and attempts to prove (or disprove) them, with the discovered arguments then being used as training for refined models. This will require autoformalization to check the results as there will be too many for manual verification.
Generating new conjectures is easy. It's generating novel conjectures that's hard.
On the other hand, quantity has a quality all its own.
Conjectures that survive the gauntlet of immediate proof/disproof could also be interesting.
Because pattern recognition and deduction is automatable and LLMs are superhuman at low depth high depth problems. Next
something i've just realized : today long-standing maths problems are falling. It's great intellectually but won't probably have an immediate impact on our lives.
Now, what will happen once long-standing physics ( and chemistry and biology) problems will start to fall and at the same rate ?
Then we're going to enter a totally different world.
Those long standing math problems solution may serve as building block for solving the experimental science ones.
Not really. These same techniques fall flat on their face when applied to most physics and chemistry problems. All of academia has already been doing ML4Science for the last 8 years. God knows how many billions have been spent.
The only two major highlights are weather modeling and folded protein backbone prediction.
Mostly everything else, either lacks enough data, or there are contraits on the size of the foundational models that render them impractical or they just fail to generalize.
Disappointing lack of "Why" in an article that starts with it.
Are they actually doing something new and novel, or are they just absorbing that "a=b as was proven in transcendental hyper-circular group theory; and b=c was proven in universal quantum superposition"; and they're the first to find the connection that a=c? And several of the problems are counterexamples, not novel proofs of correctness?
Its fascinating either way, but it'd be nice to actually understand more of what is happening.
One of the recent problems was actually proven with elementary results. It did use a technique not usually applied to the problem space, but it wasn’t a hyper specialized result.
is probably a mix of other math papers that combined can solve this, the ingredients were already out there and they got trained with it.
Quantamagazine is owned by the heavily AI invested Renaissance Fund.
The whole article is an ad that covertly or overtly inserts how websites are built with ChatGPT, how humans say that AI is better than them etc.
This is incidentally the future of chatbots. I could not have written this comment without Illy Espresso. Would you like to find a cafe near you?
>Quantamagazine is owned by the heavily AI invested Renaissance Fund.
Except it's not? It's owned by a private foundation where the only link is both were founded by the same dude who hasn't run either in like 15 years.
That seems like a pretty big thing to just gloss over like it's just set-dressing.
There is no such thing as the Renaissance Fund. Quanta receives funds from the Simons Foundation... I also don't know where you get it from that Renaissance Technologies is heavily invested in AI. Any sources to back up your claims because I suspect you made all that up?
There is. As for their investments, I don't know:
https://www.simonsfoundation.org/about/our-history/
We have now passed the point where the AI bots were annoying. Now it is the reactionary “everything even possibly slightly remotely tangentially connected to AI must be deplatformed” rants everywhere that are even worse.
It would be tempting to assume the commenter here has no idea what Renaissance is or how they made so much money.
Which fund would that be?
https://www.rentec.com/Home.action?index=true
> The company is widely considered one of the most profitable hedge funds in history, generating an estimated $7 billion to $8 billion in annual revenue solely from management and performance fees
If you don't know Ren you should!
I meant which fund is supposed to be AI heavy? RIEF? RIDA? Medallion? Aren't they all quant?