I'm reading this paragraph with the precedent of AlphaGo in mind, where none of the Go players would have expected that databases of human games would be valuable training material for machines instead of humans:
> I learned mathematics because others gave their time and knowledge freely, and I wanted to do the same for the next generation. The possibility that a student would go on to do something I could not do was part of the point. But I had imagined this as a continuation of a human activity. [...] I could not imagine treating this knowledge as something to be guarded.
But soon after, AlphaZero was trained purposefully without human games in the training data. The "extractive" training was sufficient to show that a certain machine learning model worked, but unnecessary to produce a machine that performs beyond the level of humans.
For coding agents I imagine it is similar: humans introduce so many subtle bugs, and they're only subtle relative to human cognitive capacity. I'm sure subtle mistakes pass peer review in mathematics too, even if it's generally more rigorous.
What I'm getting at is that labs have demonstrated that a certain model architecture is capable of producing mathematics at a (super)human level, and their extractive methodology was sufficient, but possibly not necessary. You can fight in court whether their methodology is against the law, but it would be naive not to look beyond that, which is my main gripe with the AHM statement the author refers to [1]
Fortunately the author of this article has a more nuanced view:
> I can understand the anger, but I am not sure that withdrawing from AI is the answer
AlphaZero isn’t a precedent for mathematics. Go is a game with a predetermined goal and a closed list of rules. Mathematics has neither. You can’t deduce the axioms of geometry from those of set theory because there’s nothing inherently interesting about geometry. Humans are interested in geometry because we’re interested in building things in the real world.
> Humans are interested in geometry because we’re interested in building things in the real world.
To clarify and be fair, the people who actually invented geometry, or at least worked on the majority, were never interested in building things. Or at least that wasn't their primary concern.
It's more accurate to say that mathematicians were just interested in intellectual exploration, everyone else was interested in building things, and there's an uneasy alliance between the two that is about to be shattered.
One thing I don't yet understand and would appreciate an opinion from a professional mathematician is: are we okay with mathematicians that outsource the discovery of new theorems to AI while providing verification services themselves?
For instance, imagine a mathematical institute that hires reasonably competent mathematicians who are amazing AI prompters but lack mathematical creativity or "genius". All they produce are mathematical papers with clear proofs and explanations. Very human readable stuff. But the catch is that they are not discovering any of it. All they are doing is "translating" full AI discoveries into a format others can understand.
Former pro mathematician here. There's a big divide amongst mathematicians right now. Some like the idea of going full steam ahead with ideas like this, and others are dead-set against it. There's even "The Association for Human Mathematics" [1] which believes in human mathematics and not using AI at all.
The central problem is that the majority of people go into math because they love discovering mathematics and want to participate in the process. That itself is a huge part of the reward. That creates the community. Simply have huge numbers of people outputting math as if it were an industrial factory kills the joy in the process and so in itself destroys the community.
So in short we're seeing a dichotomy between the "problem miners" who are simply hooked on producing results and mining them and "explorers" for lack of a better term.
There's one thing you've got to keep in mind - mathematics, in reality, is mostly useless in the sense that most discoveries these days will always be useless. What is useful generally is teaching, and applying mathematical abstraction to more realistic problems, a skill that you mainly get from dicovering generally useless stuff. (Math for art's sake.) That's how math works, or at least worked before AI. Once you put AI in the mix, it messes up all the incentives....
Personally, I'm 100% anti-AI because I think there's not much point in simply discovering new things if it's not primarily a human journey. It's revolting to have solutions generated by machines like that.
That's insightful, thank you. The follow up, then, is: will most "explorers" survive in a world where "problem miners" exist? I can see that the very best explorer could do that, but if things like tenure and prestige are decided by how many publications you have and which journals accept you, it will be next to impossible to compete against the miners.
To be clear, I empathize with your sentiment and revolt, despite being more of a "builder" myself in the software world. I just can't see how the explorer mindset can survive the onslaught of AI-augmented output.
> So in short we're seeing a dichotomy between the "problem miners" who are simply hooked on producing results and mining them and "explorers" for lack of a better term.
Interesting, thanks for the insight. Very similar to the 'builders' vs 'coders' dichotomy that seems to crop up amongst programmers now.
So do you care more about the way someone solves a problem or about result(the fact that it solves it)? For a student I think the answer is obvious because he has to understand the basics but for a researcher we don’t ask bio researcher to do research with pen and paper alone, do we or just using some deep thinking. AI is a tool. Get over it. Math is not an art.
Is it simply a bias in the sampling or are the people in math (the discipline) as shaken as the stuff that shows up on HN makes it look like?
FWIW, it reads very similar to the woes of the SWEs previously, in the sense that it kinda appears like people assigned value to the wrong part of the work within the discipline?
The take-away of it being it being imperative to have open weights models accessible to all, instead of cloud-hosted models owned by few is of course true regardless of those specifics, but it gets a bit muddied by that, which is a shame, as that will be weaponized to dismiss it.
> Is it simply a bias in the sampling or are the people in math (the discipline) as shaken as the stuff that shows up on HN makes it look like?
My local community is in a mixture of denial and despair. Especially for the PhD students and postdocs, and faculty in terms of hiring (how do we hire?).
An author who only posted very terse notes until 2025 and then started writing long-form essays about AI, illustrated by AI, all in the same mold (e.g., "How Machines Learn to Write", "How AI Generates: From Noise to Form", "What is Intelligence? From Reflection to Suffering"). Numerous LLMism. And a Pangram flag.
If you read any classic mathematics or computer science textbook, you get the sense that the author wants to impart the idea that this subject leads to an interesting and meaningful life. There are many famous quotes about being the architect or designer of an idea rather than just a technician holding a power tool following instructions someone else wrote. Now all of those adages have become effectively meaningless because so many involved in these careers are cool with the industry dying for some vague notion of progress due to a machine god. It’s a pathetic state of affairs that the elders aren’t speaking out more to protect the next generation of human thinking.
I say this as someone who uses LLMs in the physical sciences (one of the only areas where I would say it is ethical to use them).
What exactly to protect? I really don’t get what this fuss is all about.
We still need math research just like we still coding or software or cpu research regardless of how many problems the AI solves.
To me it feels like a bio researcher complaining that his field has no future because AI started to cure diseases so now instead to spend 100 years to run experiments someone can do it in a day with AI(obviously it’s not the case yet).
Are they guys upset that people can “run math” without hiring a math guy?
The main problem is that without safeguards it becomes impossible to adjudicate new work in math or CS, meaning grad students who care about originality in work will have little sense of accomplishment if the AI gives them all the answers and will decide to study something else. Not to mention that AI users in math/CS are often ignoring standards in publishing, including issues with plagiarism and scooping of work. These are pretty serious problems that will end up causing a lot of people to move to other subjects.
But that’s not something specific to mathematics, is it? I am bit against “safeguards”. That reads more like censorship to me from some kind of high priests.
I'm reading this paragraph with the precedent of AlphaGo in mind, where none of the Go players would have expected that databases of human games would be valuable training material for machines instead of humans:
> I learned mathematics because others gave their time and knowledge freely, and I wanted to do the same for the next generation. The possibility that a student would go on to do something I could not do was part of the point. But I had imagined this as a continuation of a human activity. [...] I could not imagine treating this knowledge as something to be guarded.
But soon after, AlphaZero was trained purposefully without human games in the training data. The "extractive" training was sufficient to show that a certain machine learning model worked, but unnecessary to produce a machine that performs beyond the level of humans.
For coding agents I imagine it is similar: humans introduce so many subtle bugs, and they're only subtle relative to human cognitive capacity. I'm sure subtle mistakes pass peer review in mathematics too, even if it's generally more rigorous.
What I'm getting at is that labs have demonstrated that a certain model architecture is capable of producing mathematics at a (super)human level, and their extractive methodology was sufficient, but possibly not necessary. You can fight in court whether their methodology is against the law, but it would be naive not to look beyond that, which is my main gripe with the AHM statement the author refers to [1]
Fortunately the author of this article has a more nuanced view:
> I can understand the anger, but I am not sure that withdrawing from AI is the answer
[1] https://www.ahmath.org/statements
AlphaZero isn’t a precedent for mathematics. Go is a game with a predetermined goal and a closed list of rules. Mathematics has neither. You can’t deduce the axioms of geometry from those of set theory because there’s nothing inherently interesting about geometry. Humans are interested in geometry because we’re interested in building things in the real world.
> Humans are interested in geometry because we’re interested in building things in the real world.
To clarify and be fair, the people who actually invented geometry, or at least worked on the majority, were never interested in building things. Or at least that wasn't their primary concern.
It's more accurate to say that mathematicians were just interested in intellectual exploration, everyone else was interested in building things, and there's an uneasy alliance between the two that is about to be shattered.
Sure, but you can deduce a proof of e.g. Navier Stokes given its statement and some axioms
One thing I don't yet understand and would appreciate an opinion from a professional mathematician is: are we okay with mathematicians that outsource the discovery of new theorems to AI while providing verification services themselves?
For instance, imagine a mathematical institute that hires reasonably competent mathematicians who are amazing AI prompters but lack mathematical creativity or "genius". All they produce are mathematical papers with clear proofs and explanations. Very human readable stuff. But the catch is that they are not discovering any of it. All they are doing is "translating" full AI discoveries into a format others can understand.
Is that acceptable?
Former pro mathematician here. There's a big divide amongst mathematicians right now. Some like the idea of going full steam ahead with ideas like this, and others are dead-set against it. There's even "The Association for Human Mathematics" [1] which believes in human mathematics and not using AI at all.
The central problem is that the majority of people go into math because they love discovering mathematics and want to participate in the process. That itself is a huge part of the reward. That creates the community. Simply have huge numbers of people outputting math as if it were an industrial factory kills the joy in the process and so in itself destroys the community.
So in short we're seeing a dichotomy between the "problem miners" who are simply hooked on producing results and mining them and "explorers" for lack of a better term.
There's one thing you've got to keep in mind - mathematics, in reality, is mostly useless in the sense that most discoveries these days will always be useless. What is useful generally is teaching, and applying mathematical abstraction to more realistic problems, a skill that you mainly get from dicovering generally useless stuff. (Math for art's sake.) That's how math works, or at least worked before AI. Once you put AI in the mix, it messes up all the incentives....
Personally, I'm 100% anti-AI because I think there's not much point in simply discovering new things if it's not primarily a human journey. It's revolting to have solutions generated by machines like that.
1. https://www.ahmath.org/
That's insightful, thank you. The follow up, then, is: will most "explorers" survive in a world where "problem miners" exist? I can see that the very best explorer could do that, but if things like tenure and prestige are decided by how many publications you have and which journals accept you, it will be next to impossible to compete against the miners.
To be clear, I empathize with your sentiment and revolt, despite being more of a "builder" myself in the software world. I just can't see how the explorer mindset can survive the onslaught of AI-augmented output.
> So in short we're seeing a dichotomy between the "problem miners" who are simply hooked on producing results and mining them and "explorers" for lack of a better term.
Interesting, thanks for the insight. Very similar to the 'builders' vs 'coders' dichotomy that seems to crop up amongst programmers now.
So do you care more about the way someone solves a problem or about result(the fact that it solves it)? For a student I think the answer is obvious because he has to understand the basics but for a researcher we don’t ask bio researcher to do research with pen and paper alone, do we or just using some deep thinking. AI is a tool. Get over it. Math is not an art.
Is it simply a bias in the sampling or are the people in math (the discipline) as shaken as the stuff that shows up on HN makes it look like?
FWIW, it reads very similar to the woes of the SWEs previously, in the sense that it kinda appears like people assigned value to the wrong part of the work within the discipline?
The take-away of it being it being imperative to have open weights models accessible to all, instead of cloud-hosted models owned by few is of course true regardless of those specifics, but it gets a bit muddied by that, which is a shame, as that will be weaponized to dismiss it.
> Is it simply a bias in the sampling or are the people in math (the discipline) as shaken as the stuff that shows up on HN makes it look like?
My local community is in a mixture of denial and despair. Especially for the PhD students and postdocs, and faculty in terms of hiring (how do we hire?).
> Is it simply a bias in the sampling or are the people in math (the discipline) as shaken as the stuff that shows up on HN makes it look like?
Given that this appears to be a largely AI-written article, I guess it's AI being shaken by AI.
What gave you the impression?
An author who only posted very terse notes until 2025 and then started writing long-form essays about AI, illustrated by AI, all in the same mold (e.g., "How Machines Learn to Write", "How AI Generates: From Noise to Form", "What is Intelligence? From Reflection to Suffering"). Numerous LLMism. And a Pangram flag.
If you read any classic mathematics or computer science textbook, you get the sense that the author wants to impart the idea that this subject leads to an interesting and meaningful life. There are many famous quotes about being the architect or designer of an idea rather than just a technician holding a power tool following instructions someone else wrote. Now all of those adages have become effectively meaningless because so many involved in these careers are cool with the industry dying for some vague notion of progress due to a machine god. It’s a pathetic state of affairs that the elders aren’t speaking out more to protect the next generation of human thinking.
I say this as someone who uses LLMs in the physical sciences (one of the only areas where I would say it is ethical to use them).
What exactly to protect? I really don’t get what this fuss is all about.
We still need math research just like we still coding or software or cpu research regardless of how many problems the AI solves.
To me it feels like a bio researcher complaining that his field has no future because AI started to cure diseases so now instead to spend 100 years to run experiments someone can do it in a day with AI(obviously it’s not the case yet).
Are they guys upset that people can “run math” without hiring a math guy?
The main problem is that without safeguards it becomes impossible to adjudicate new work in math or CS, meaning grad students who care about originality in work will have little sense of accomplishment if the AI gives them all the answers and will decide to study something else. Not to mention that AI users in math/CS are often ignoring standards in publishing, including issues with plagiarism and scooping of work. These are pretty serious problems that will end up causing a lot of people to move to other subjects.
But that’s not something specific to mathematics, is it? I am bit against “safeguards”. That reads more like censorship to me from some kind of high priests.