I knew mathematicians were a smart bunch, but honestly, the events of the past few weeks have really given me a new level of respect for them.
They might be the first community I've seen to experience the AI "rush" and (at least as presented to an outside observer) immediately come together, assess the situation, and calmly, empathetically, and rationally act. They evaluated what AI is good at and what it lacks. They've thought through how it'll likely affect their field in the future. They've explained where the need for humans still lies, and made clear proposals for how to change their own field and for what demands to make of AI companies. Of course they're not all on the same page, but they're at least talking and trying.
They haven't started worshipping the machine god and loudly claiming their whole field is solved. Nor have they flailed wildly at LLMs as if complaining enough about it will make them go away.
Every major statement I've seen come out of the math community on this matter reads as well thought-through, humble, reasoned, and deeply human.
In these days of fear, uncertainty, and obsolescence anxiety, honestly, they've given me some confidence that maybe we will figure this stuff out after all. Maybe we'll learn from them. Who knows.
> I knew mathematicians were a smart bunch, but honestly, the events of the past few weeks have really given me a new level of respect for them.
As a mathematician, I am a bit disappointed by my (admittedly illustrious) colleagues.
I get the need to take it slowly (and I am a quite impatient person, so I shouldn't get to decide stuff like this), but everything said feels a bit too sour grapes for my taste.
Ok, maybe AI did not solve the field (I believe it will, btw), maybe there is a need for human "understanding", but:
1) They don't seem to consider even the possibility (not the certainty) that they might be wrong, that math as we know it is gone, and we cannot "adapt"
2) They seem to have been oblivious all these years about AI eventually reaching this point (at least I personally wasn't, I predicted this stage back in 2018)
Regarding 1, it's not clear what you want them to actually do. Would you rather they just gave up, rolled over and died instead of at least trying to rescue their field? What is to be gained from considering this?
I suppose you could say, hypothetically, that if the field were “solved” then the protection of the feelings and sense of need for human understanding of the now obsolete practitioners might hinder any benefits that the now solve field could provide.
The answer to this is probably just “get out of the way” and then your “work” would be to develop a better appreciation of what has been produced.
> The answer to this is probably just “get out of the way” and then your “work” would be to develop a better appreciation of what has been produced.
They aren't in the way. AI labs can do their own math all they want, and nobody is stopping them. Rather, mathematicians are simply speaking about the topic.
They absolutely are in the way. We’ve had the most exciting months of mathematical progress since antiquity, and the vast majority of voices from mathematicians have been bitching about one thing or the other, to the extent that they now got themselves a committee that (co-)decides when, how, and possibly if, the next batch of results is made available to the public.
Please. Have you been doing mathematics ? Yes, some big open problems are solved. I have not seen the ideas therein used to solve related or other problems. That is the point of most mathematics: to develop frameworks and general techniques for understanding and solving problems, not solving one-off problems.
For example, group theory lead to a useful way of thinking about how to solve a wide array of problems. That is what mathematicians are seeking.
People merely speaking their mind does not constitute getting in the way.
I'm sorry that you personally don't like that mathematicians are "bitching" about OpenAI snaking their work out from under them, and would like to silence them. But if we're going for consistency's sake, maybe consider taking your own advice here before giving it to others.
In the meantime, OpenAI can do whatever they want, mathematically-speaking. Nobody is in their way. If there isn't further meaningful progress from them, that would seem to strengthen the work-product-theft hypothesis.
> the feelings and sense of need for human understanding of the now obsolete practitioners might hinder any benefits that the now solve field could provide
Wiping out an occupation that people enjoy and that gives them purpose (making them "obsolete") is a public mental health crisis, if anything. It's unclear that the "benefits" of the "solved" field actually outweigh that.
If LLMs could both prove any relevant theorem, explain such a theorem cogently and lay the groundwork for further theory, I don't see how any way mathematicians could stand in the way of that.
As a Nobel Prize winner, I am surprised that you have not noticed how Tao and Gowers were steering everyone in the AI direction for years and now do damage control by nudging everyone to either hypothetical open models paid for by industry or the EU or sitting in a committee that "advises" OpenAI.
No one is saying "Perelman and Wiles didn't need that silly AI and N-S was more of a counterexample". Most people imagine the sky is falling.
What if OpenAI is stalling because they don't have 100 additional unpublished proofs as claimed?
> As a Nobel Prize winner, I am surprised that you have not noticed how Tao and Gowers were steering everyone in the AI direction for years
I did notice, this is why I had thought that they had thought through the consequences. But, unfortunately, it is likely they imagined that AI would plateau somewhere around the "smart undergraduate" level and that they will stay relevant in pure problem solving.
And why have the Nobel Prize winners been silent (or taken post-Nobel bets contrary to the current consensus ie Hinton-Hassabis)?
Taking GP at his word, I'd be more terrified if Oai had identified one hundred NEW open problems..
In contrast with Fields Medallists, some Nobelists get the prize for something they'd eventually NOT be (in)famous for. Like Josephson. In hindsight, will it be because they found out, as young unknowns, how to explore underappreciated avenues without millions in dedicated funds (uh encouragement).. ??
GP, did you? Get the prize for the question you are most proud of.
> What if OpenAI is stalling because they don't have 100 additional unpublished proofs as claimed?
Which is what I think a large chunk of AI progress actually is - people taking the latest models out for a spin, and browbeating them to actually ship code, and RLHFing them to ship better code in the process, either directly or indirectly through Github.
I think I'm mostly on your side (also I believed early it would get here), but what does it mean to "solve the field"? I'm pretty much as bullish as you get on AI but I'm sure I can come up with questions AI cannot solve. I think the space of problems in math is so large and the distribution of proof lengths so heavy-tailed, there's probably no way without dyson-sphereing the sun to solve all easy to state problems.
I think it is good people are talking but there seems to be a lot of "forced optimism", especially by people obviously hoping to keep a channel open between themselves and the labs.
I think it isn't true that no one imminent is considering (1). Tsimmerman said he thought the job of math researcher was over as soon as he announced he was leaving the field.
I think the question is so far still open, but it is easy to imagine Tsimmerman was right. I haven't been impressed with the calls for "human understanding" as the really important thing. It seems to miss the point of why math has been funded (not exactly problems, but certainly not to ensure every theorem is understood either).
As a scifi comment, it is now possible to start thinking about some future AI system which decides if it will need to explain certain math to humans and to pick and train young people for that purpose.
What do you believe doesn’t reflect positively on the authors of that open letter? It raises valid concerns, and the statement you quoted is a factual observation.
I would not attribute this attitude to the entire Math community, there clearly are many who are reacting negatively to this, as evidenced by several comments on various forums including this one. People are understandably upset about their chosen profession and livelihood being upended and reacting accordingly, similar to how people from other impacted professions are.
This group of Mathematicians just happens to be more willing to accept the inevitable and adapt. I would actually say software engineers, being amongst the earliest impacted by AI after creatives, clearly have adapted to the new reality much more broadly as evidenced by online discourse and coding agent providers' skyrocketing revenues.
Presumably OP believes that software engineers went to far in the direction of “started worshipping the machine god and loudly claiming their whole field is solved.” Certainly within software engineering there is much louder voices on that side of things. By now the voices saying that it’s useless have pretty much died out. But it seems quite reasonable to say that the wider software community didn’t “come together, assess the situation, and calmly, empathetically, and rationally act.”
One might argue that this is due to size of the software community, or commercial interests. But I do believe OP was right in his description of the response of the math community as different from the software community.
> But it seems quite reasonable to say that the wider software community didn’t “come together, assess the situation, and calmly, empathetically, and rationally act.”
But my point is the wider Mathematics community didn't do that either. We are just looking at the subset in TFA and assuming they represent the whole community. If you look at AI + Math-related articles and threads on HN you'll definitely see a lot of consternation from Mathematicians.
No, I don't think they are adapting well. I've seen 3d designer at my company adapting better on the disruption and paradigm shifts GPT-6 Astra is going to cause.
The 3D designers are in a tougher situation because it's far less of abstract issue then math, and yet the results are astounding. It's hard to believe until you see it yourself. It's surreal.
Their field is extremely rigorous. As rigorous as it can possibly get in that they have to prove each and every line of their work beyond any doubt. The discipline they have cultivated in their culture shows in their response to AI as well.
As opposed to some other fields in which rigor was either not part of the culture or was not always possible. For e.g., software engineering in terms of code quality being produced. There were some indirect signals here and there but they are all subjective.
In some sense software engineering is more rigorous than mathematics, because proofs are generally informal, apart from those written in Lean, while all computer programs are strictly formal, as otherwise they wouldn't be machine-readable.
I see what you are sayings. That's an interesting point of view.
Perhaps we should define what rigor means.
Your point is that code is executable and speaks for itself whereas a Math proof (non-lean) is just someone's writing on a piece of paper.
Now let's compare the "practice" of doing Math and software engineering. In Math, every step is very intentional, and getting to a point where a proof is complete and correct is a very long, laborious, difficult and intentional process. Not to mention, the work is also peer reviewed (for published stuff). This is what I mean by rigor.
In software engineering, the practice is quite different. We defined the problem (somewhat), come up with a design that we "think" would work, write programs that we think is correct and then execute it. Most of the time it doesn't work exactly as we would have predicted. So we take the signal and adjust. So it's a more iterative part and this gets us closer to reality (what we actually want it to be), step by step.
So comparing the two, the major difference I see is in one each and every step is very intentional and we can't guess it. While in the other one we have lots of liberties, but we are still making progress.
So to me the difference is just between the practices followed in the field when it comes to rigor.
Maybe a similar comparison would be this: for proofs, the standards of correctness are purely internal and can in principle be formally defined, as in Lean. The formal conjecture has to follow from the premises. Either it is proven or not. In contrast, in 99% of ordinary software, no fully formal standard of correctness exists. The requirements are informal. So what counts as a bug and what doesn't is a judgement call that can only be checked by asking the person who wanted the software whether it works as intended.
Every community approaches problems with the tools at its disposal. Doing mathematics is about thinking, so mathematicians approach problems (at least in public) with more thinking and less emotion (than some fields where emotion is much more important). While you and I may appreciate this approach (and even be inspired by it), it remains to be seen whether it ultimately makes the outcomes any better.
I disagree. Software developers seem to have adapted to AI much faster than the maths community.
There are certainly still strong opponents of AI, but they seem to be a small, vocal minority. Most developers seem to have simply adapted and moved on.
It's possible and I dare say even likely that you are missing nuance and observing bias from your bubble. It's possible to avoid being an AI "opponent" while still being a sceptic. It's possible to use AI reluctantly and with tact instead of going all in.
The whole thing is far from over when we haven't experienced the worst of the technology yet: deskilling, concentration of power, extreme imbalance of wealth, military and surveillance uses, etc.
Of course, sorry if that came across as more combative than necessary. I was trying to point out two things I guess:
1. "Your experience is not universal from my perspective, and I offer my experience as evidence"
2. The possibility that this adaptation you are observing is neither a stable equilibrium given future developments, nor is necessarily an indication that the people using AI have bought into it fully. I use AI heavily while remaining a sceptic.
> If I thought this was a good thing to do, this would be a great group of people to do it. But I have immediate misgivings. OpenAI has had some very bad publicity, and so they are trying to exploit the trust and respect that these mathematicians command. It is unrealistic to think that this group can change the way OpenAI does business; I don’t need to tell you all the objections that people have raised to that. Is it a good idea to help their crisis management?
(FRS, UCLA professor of algebraic geometry and topology, with work influenced by the Hodge conjecture, one of the remaining Millennium Prize problems).
> We are currently facing the very specific challenge of advising OpenAI on how to coordinate the release of a large number of significant results in mathematics that they report have been produced by their internal model.
The only thing I want to see is the problem statements, solutions, and associated Lean proofs. Anything else is gatekeeping. What a low point for academia.
PhD in maths here, no longer a mathematician, partly because I wanted to do stuff more connected with real life.
I actually want to see interesting theories and mathematical ideas come out of proofs more than I want solutions/proofs. After all most maths doesn't have direct practical applications. So although unsolved problems are a good barometer of 'there's still stuff left to understand here', the interesting part about solving them is less knowing what is true and more 'how does this help us understand this field better than we did before?'.
I would still like to know if the Riemann Hypothesis is true though!
Regarding that last point: You may know where you left your keys, even if you are "only", say, 99% certain where they are. Now, how strongly do mathematicians believe that the Riemann hypothesis is true? 99.9% perhaps? In some sense then, you already consider yourself less ignorant about the truth value of RH than about the location of your keys, or about many other mundane things you know without being perfectly certain about them.
A proof would then merely update you from 99.9% to ~100%, which is a smaller update than the example of checking that your keys are indeed in your pocket, where you go from 99% to ~100%.
I'm not sure how you've ended up so frustrated with an advisory group whose advice has not been given. Human mathematicians routinely delay publication of their results past the point you describe; is someone gatekeeping when they take a month to clean up their paper?
Or are you perhaps sublimating your own AI anxiety into confrontational assertions that other people who discuss AI aren't as AI-pilled as you?
I'm not sure why you see bullying here? OpenAI has always worked with expert mathematicians; their unit-distance result (https://openai.com/index/model-disproves-discrete-geometry-c...) was a much deeper collaboration. They published the Navier-Stokes result early, to either benchmark or show off their new model depending on how you look at it, and they want to understand more about the negative effects which many mathematicians feel that early publication had.
If the advisory group says something like "AI is bad and nobody should use it in math", I'm pretty confident OpenAI will ignore them.
I don't really get it, seems like a gate keeping exercise for the academic community.
Of course OpenAI and others will hype any LLM led/assisted research results, and the media will find juicy headlines to write about it. But in the end they are publishing findings, and the academic community can gauge the developments and decide what they want to do with them. To me that seems like research working as expected.
> This group came together after OpenAI approached some of its members about establishing an external advisory board. In agreement with OpenAI, they decided to create an independent group and invite others to join.
The purpose is obvious - AI companies are using math to as a PR tool to demonstrate that AI is more capable than humans. This devalues math and mathematicians. There is even a relevant announcement from today, where OpenAI announced they solve 100 open math problems, without even bothering to state what they are.
However, even if they are successful in removing math from the PR toolkit of AI companies, I can’t see it more than a short term band aid. If AI progression continues, the announcements will just transition from big flashy one, to a kid using Claude on their laptop.
I don’t have a solution here, and I’m worried it’s coming to all human fields. So it’s more of an ability to observe what might happen to all of us.
> There is even a relevant announcement from today, where OpenAI announced they solve 100 open math problems, without even bothering to state what they are.
This group has been formed to tell OpenAI whether or not (and if yes how) they should release those 100+ problems.
IMO “AI companies are using math to as a PR tool” is not quite it; they are using math problems as a benchmark to evaluate their AIs, but after the prior blowback from the mathematical community, they are happy to sit on the results until the community (this group) tells them how to publish the results.
And as you say, even if they don't publish the results eventually anyone will be able to do this when this model is released, so it's just a matter of time.
> I don’t have a solution here, and I’m worried it’s coming to all human fields. So it’s more of an ability to observe what might happen to all of us.
You can also look (as I did back in 2018 when contemplating the end of math) at how chess or Go players adapted mentally to the idea that whatever they may do, a machine could do it better (Lee Sedol famously quit Go).
I think this matters very little. These were adaptations to initial advances of small scope which we are rapidly leaving behind. If there is truly no near and practical ceiling to the abilities of AI in mathematics, not even in terms of efficiency, then I think it is likely there is similarly no ceiling in other cognitive endeavours.
In that case, everything stands to be disrupted and those who wield AI will have massive amounts of power in the short term. But this is not a stable situation, and therefore those who wield AI will have to cede control of it or otherwise enter into a great war with those that do not.
I hope for all our sakes that there is a practical ceiling.
These math problems don't exist in a vacuum. It's not like mathematicians are doing mathematics just for the funsies.
Calling it a publicity stunt is an interesting way of framing ground breaking discoveries. The beneficiaries down stream of these discoveries could not care less how they were found.
> It's not like mathematicians are doing mathematics just for the funsies.
But they do. Most of higher math has no practical applications and is just a mental playground, philosophy constrained by formal logic and a set of axioms.
Hope is these capabilities will somehow translate to something more practical like physics, chemistry or biology.
The composition of the panel might give us some clues as to the nature of OpenAI's unreleased results. Some of Ed Witten's work is quite closely related to the Yang Mills existence and mass gap problem, which is one of the remaining Millennium problems. I went through the list of panel members and asked an LLM to associate each member of the panel with one or two millennium problems. Here is the resulting count:
Hodge conjecture: 5
Birch and Swinnerton-Dyer Conjecture: 3
Navier-Stokes: 2
P vs NP: 1
Yang-Mills existence and mass gap: 2
So this gives a bit of further evidence that they made progress on the Hodge and Birch and Swinnerton-Dyer conjectures. Maybe also Yang-Mills.
I would push for an audit of the whole mathematical corpus (all articles etc ingested by the present AI) as soon as possible. Since there are of the order of 10^7 articles, compared with the progression of results announced, this might be possible in less than a year.
All these results exploit the existing corpus. With enough time and maybe several orders more attention, we humans would discover these results.
So instead of producing heaps of new proofs (but be welcome to do this IMO), make an audit, OpenAI or Anthropic or anybody who listens.
Given that he apparently feels exploited after an appearance in some of their earlier marketing material, I imagine he's not overly keen on working more for their PR department, or this extension thereof.
> During this event, OpenAI requested an interview concerning my vision of the future of AI and mathematics. I accepted, and spoke with them for perhaps an hour. I had done similar interviews in various venues, and I assumed that, as with these other cases, they would eventually post the entire interview online, which talked about both the possibilities and risks of AI much as I have done in these other interviews. As it turned out, they only used a few snippets of that interview for that infamous advertisement instead.
I really wish the models were smart enough to "tail their own logs" and tell us whose work/papers/chats were the catalyst for these math insights. What makes their "internal" model so much better at math? Must be trained on a whole lot of honesty.
Why don't they just publish the results? What does an advisory group do in this case when none of the members can validate or verify any of the purported solutions?
Because they apparently lack the internal compentencies to do so (or, given that they now have a Fields medalist on payroll, it's probably more a case of not feeling any need whatsoever to spend the effort it takes; maths isn't exactly profitable if you can't mine it for PR). Ignoring all the ethical violations they made in the process, the fact that they only ever released slop on the Navier–Stokes problem is part of the debacle.
For example, had they decided to put their paper on arXiv, they would be facing a 1 year ban, followed by not being able to put anything on there without prior peer review.
More: after OAI've mangled whatever value is left of the results (once again), HN could start braying for the training data/weights. Or even the prompts
Honestly I am not impressed with Tao treating "ai" as a threat to mathematicians. He might as well say math itself, specifically linear algebra and gradient descent are a threat to mathematicians. Maybe think of something original rather than pander the hype of day?
Why aren't they consulting the younger mathematicians whom this actually affects?
Anyways, this is overblown. Let me know when AI swarms can create a research program or library from scratch. We're really missing long term planning and abstraction creation in these things.
The way I've understood this whole thing so far, the main reason why the mathematicians are so energized right now is because the AI companies' problem solving spree frames mathematics as a discipline that exists to solve open problems.
Mathematicians don't fully share this view even though they value problem solving, and they're afraid that this framing will produce the following chain of thought in the public:
Mathematicians get paid to solve problems -> AI solves problems better -> we don't need to pay mathematicians.
So they're trying to reframe their work to shift problem solving to the background and keep getting paid.
I leave it to the mathematicians to explain what their value is, as they would do a better job of it, and it remains to be seen if this reframing will work.
Regardless of that, what happens long-term if AI gets good enough to solve all the hard open problems?
Millenium problems may give AI companies some temporary hype, but advancing research in some narrow directions to find new problems is probably not worth it to them.
In addition, current problems have clear, human-defined acceptance criteria.
Problems that are both found and solved by AI will be opaque enough not to generate interest in anyone unless they are found to have immediate applications.
Mathematicians will somewhat distrust 1M+ LOC Lean formalizations as well as any original AI output in the form of creating a bunch of new concepts. There will surely be heated discussions around that.
Afterwards, mathematicians take some time to catch up with the solutions to existing problems, use AI to understand them and map out further directions.
Problem solving by AI companies slows down since there are no cool problems left. They move on, mathematicians get back to whatever they were doing before, now with the help of AI.
With every mathematician having a strong mathematical AI model, a new problem arises.
At any point of the current mathematical frontier, a mathematician can use AI to explore a new direction at a high speed.
If all mathematicians do that, each will have their very advanced understanding of their direction until they fail to catch up the AI, and nobody knows whose direction is the one that others should check up with.
Many possible connections with other branches and explored directions will be lost, unless there's a unified map of all these explorations.
It will be hard to create this map, because while exploring one direction may have a moderate cost for a mathematician,
having an AI do an overview of all other explorations to find some commonalities and synthesize the findings into a unified theory will take serious amounts of resources only available to AI companies, which they might be reluctant to spend.
Individual mathematicians' explorations will slow down to human level, too, with their unique findings being hard to publish because nobody will care and the mathematical community wants to do things that other mathematicians can appreciate.
In the end, the mathematicians' work does not change that drastically, unless AI gets good enough to one-shot some new crazy branch of mathematics that reveals something with high real-world impact. But that's a discussion for another time.
I knew mathematicians were a smart bunch, but honestly, the events of the past few weeks have really given me a new level of respect for them.
They might be the first community I've seen to experience the AI "rush" and (at least as presented to an outside observer) immediately come together, assess the situation, and calmly, empathetically, and rationally act. They evaluated what AI is good at and what it lacks. They've thought through how it'll likely affect their field in the future. They've explained where the need for humans still lies, and made clear proposals for how to change their own field and for what demands to make of AI companies. Of course they're not all on the same page, but they're at least talking and trying.
They haven't started worshipping the machine god and loudly claiming their whole field is solved. Nor have they flailed wildly at LLMs as if complaining enough about it will make them go away.
Every major statement I've seen come out of the math community on this matter reads as well thought-through, humble, reasoned, and deeply human.
In these days of fear, uncertainty, and obsolescence anxiety, honestly, they've given me some confidence that maybe we will figure this stuff out after all. Maybe we'll learn from them. Who knows.
> I knew mathematicians were a smart bunch, but honestly, the events of the past few weeks have really given me a new level of respect for them.
As a mathematician, I am a bit disappointed by my (admittedly illustrious) colleagues.
I get the need to take it slowly (and I am a quite impatient person, so I shouldn't get to decide stuff like this), but everything said feels a bit too sour grapes for my taste.
Ok, maybe AI did not solve the field (I believe it will, btw), maybe there is a need for human "understanding", but:
1) They don't seem to consider even the possibility (not the certainty) that they might be wrong, that math as we know it is gone, and we cannot "adapt"
2) They seem to have been oblivious all these years about AI eventually reaching this point (at least I personally wasn't, I predicted this stage back in 2018)
Regarding 1, it's not clear what you want them to actually do. Would you rather they just gave up, rolled over and died instead of at least trying to rescue their field? What is to be gained from considering this?
I suppose you could say, hypothetically, that if the field were “solved” then the protection of the feelings and sense of need for human understanding of the now obsolete practitioners might hinder any benefits that the now solve field could provide.
The answer to this is probably just “get out of the way” and then your “work” would be to develop a better appreciation of what has been produced.
> The answer to this is probably just “get out of the way” and then your “work” would be to develop a better appreciation of what has been produced.
They aren't in the way. AI labs can do their own math all they want, and nobody is stopping them. Rather, mathematicians are simply speaking about the topic.
So is the answer that they should just shut up?
They absolutely are in the way. We’ve had the most exciting months of mathematical progress since antiquity, and the vast majority of voices from mathematicians have been bitching about one thing or the other, to the extent that they now got themselves a committee that (co-)decides when, how, and possibly if, the next batch of results is made available to the public.
Please. Have you been doing mathematics ? Yes, some big open problems are solved. I have not seen the ideas therein used to solve related or other problems. That is the point of most mathematics: to develop frameworks and general techniques for understanding and solving problems, not solving one-off problems.
For example, group theory lead to a useful way of thinking about how to solve a wide array of problems. That is what mathematicians are seeking.
People merely speaking their mind does not constitute getting in the way.
I'm sorry that you personally don't like that mathematicians are "bitching" about OpenAI snaking their work out from under them, and would like to silence them. But if we're going for consistency's sake, maybe consider taking your own advice here before giving it to others.
In the meantime, OpenAI can do whatever they want, mathematically-speaking. Nobody is in their way. If there isn't further meaningful progress from them, that would seem to strengthen the work-product-theft hypothesis.
> the feelings and sense of need for human understanding of the now obsolete practitioners might hinder any benefits that the now solve field could provide
Wiping out an occupation that people enjoy and that gives them purpose (making them "obsolete") is a public mental health crisis, if anything. It's unclear that the "benefits" of the "solved" field actually outweigh that.
If LLMs could both prove any relevant theorem, explain such a theorem cogently and lay the groundwork for further theory, I don't see how any way mathematicians could stand in the way of that.
As a Nobel Prize winner, I am surprised that you have not noticed how Tao and Gowers were steering everyone in the AI direction for years and now do damage control by nudging everyone to either hypothetical open models paid for by industry or the EU or sitting in a committee that "advises" OpenAI.
No one is saying "Perelman and Wiles didn't need that silly AI and N-S was more of a counterexample". Most people imagine the sky is falling.
What if OpenAI is stalling because they don't have 100 additional unpublished proofs as claimed?
> As a Nobel Prize winner, I am surprised that you have not noticed how Tao and Gowers were steering everyone in the AI direction for years
I did notice, this is why I had thought that they had thought through the consequences. But, unfortunately, it is likely they imagined that AI would plateau somewhere around the "smart undergraduate" level and that they will stay relevant in pure problem solving.
And why have the Nobel Prize winners been silent (or taken post-Nobel bets contrary to the current consensus ie Hinton-Hassabis)?
Taking GP at his word, I'd be more terrified if Oai had identified one hundred NEW open problems..
In contrast with Fields Medallists, some Nobelists get the prize for something they'd eventually NOT be (in)famous for. Like Josephson. In hindsight, will it be because they found out, as young unknowns, how to explore underappreciated avenues without millions in dedicated funds (uh encouragement).. ??
GP, did you? Get the prize for the question you are most proud of.
Was there really a choice? What they do or advised others to do would have had no bearing on what is happening.
> What if OpenAI is stalling because they don't have 100 additional unpublished proofs as claimed?
Which is what I think a large chunk of AI progress actually is - people taking the latest models out for a spin, and browbeating them to actually ship code, and RLHFing them to ship better code in the process, either directly or indirectly through Github.
I think I'm mostly on your side (also I believed early it would get here), but what does it mean to "solve the field"? I'm pretty much as bullish as you get on AI but I'm sure I can come up with questions AI cannot solve. I think the space of problems in math is so large and the distribution of proof lengths so heavy-tailed, there's probably no way without dyson-sphereing the sun to solve all easy to state problems.
How do you conceptualize mathematics being 'solved' and 'gone'?
How do you reconcile that with incompleteness and undecidability results?
Without understanding, what are we?
I think it is good people are talking but there seems to be a lot of "forced optimism", especially by people obviously hoping to keep a channel open between themselves and the labs.
I think it isn't true that no one imminent is considering (1). Tsimmerman said he thought the job of math researcher was over as soon as he announced he was leaving the field.
I think the question is so far still open, but it is easy to imagine Tsimmerman was right. I haven't been impressed with the calls for "human understanding" as the really important thing. It seems to miss the point of why math has been funded (not exactly problems, but certainly not to ensure every theorem is understood either).
As a scifi comment, it is now possible to start thinking about some future AI system which decides if it will need to explain certain math to humans and to pick and train young people for that purpose.
>Every major statement I've seen come out of the math community on this matter reads as well thought-through, humble, reasoned, and deeply human.
Can't disagree with "deeply human", but I wouldn't always use it in a positive sense:
https://proofsandprompts.com/2026/09/10/open-letter-about-th...
>Participation in an event so closely associated with Anthropic and OpenAI could plausibly negatively impact the future reputations of participants
What do you believe doesn’t reflect positively on the authors of that open letter? It raises valid concerns, and the statement you quoted is a factual observation.
It reads as a transparent attempt at intimidation to me.
It’s a true statement. The way you perceive it is in your mind, not a property of the statement itself.
“If you testify tomorrow, you may not live to see the end of the day. It’s a true statement…”
Wow, that's disgusting.
I would not attribute this attitude to the entire Math community, there clearly are many who are reacting negatively to this, as evidenced by several comments on various forums including this one. People are understandably upset about their chosen profession and livelihood being upended and reacting accordingly, similar to how people from other impacted professions are.
This group of Mathematicians just happens to be more willing to accept the inevitable and adapt. I would actually say software engineers, being amongst the earliest impacted by AI after creatives, clearly have adapted to the new reality much more broadly as evidenced by online discourse and coding agent providers' skyrocketing revenues.
Presumably OP believes that software engineers went to far in the direction of “started worshipping the machine god and loudly claiming their whole field is solved.” Certainly within software engineering there is much louder voices on that side of things. By now the voices saying that it’s useless have pretty much died out. But it seems quite reasonable to say that the wider software community didn’t “come together, assess the situation, and calmly, empathetically, and rationally act.”
One might argue that this is due to size of the software community, or commercial interests. But I do believe OP was right in his description of the response of the math community as different from the software community.
> But it seems quite reasonable to say that the wider software community didn’t “come together, assess the situation, and calmly, empathetically, and rationally act.”
But my point is the wider Mathematics community didn't do that either. We are just looking at the subset in TFA and assuming they represent the whole community. If you look at AI + Math-related articles and threads on HN you'll definitely see a lot of consternation from Mathematicians.
It's entertaining to me that so far you're one of the only replies to notice this :)
No, I don't think they are adapting well. I've seen 3d designer at my company adapting better on the disruption and paradigm shifts GPT-6 Astra is going to cause.
The 3D designers are in a tougher situation because it's far less of abstract issue then math, and yet the results are astounding. It's hard to believe until you see it yourself. It's surreal.
Agreed.
Their field is extremely rigorous. As rigorous as it can possibly get in that they have to prove each and every line of their work beyond any doubt. The discipline they have cultivated in their culture shows in their response to AI as well.
As opposed to some other fields in which rigor was either not part of the culture or was not always possible. For e.g., software engineering in terms of code quality being produced. There were some indirect signals here and there but they are all subjective.
In some sense software engineering is more rigorous than mathematics, because proofs are generally informal, apart from those written in Lean, while all computer programs are strictly formal, as otherwise they wouldn't be machine-readable.
I see what you are sayings. That's an interesting point of view.
Perhaps we should define what rigor means.
Your point is that code is executable and speaks for itself whereas a Math proof (non-lean) is just someone's writing on a piece of paper.
Now let's compare the "practice" of doing Math and software engineering. In Math, every step is very intentional, and getting to a point where a proof is complete and correct is a very long, laborious, difficult and intentional process. Not to mention, the work is also peer reviewed (for published stuff). This is what I mean by rigor.
In software engineering, the practice is quite different. We defined the problem (somewhat), come up with a design that we "think" would work, write programs that we think is correct and then execute it. Most of the time it doesn't work exactly as we would have predicted. So we take the signal and adjust. So it's a more iterative part and this gets us closer to reality (what we actually want it to be), step by step.
So comparing the two, the major difference I see is in one each and every step is very intentional and we can't guess it. While in the other one we have lots of liberties, but we are still making progress.
So to me the difference is just between the practices followed in the field when it comes to rigor.
Maybe a similar comparison would be this: for proofs, the standards of correctness are purely internal and can in principle be formally defined, as in Lean. The formal conjecture has to follow from the premises. Either it is proven or not. In contrast, in 99% of ordinary software, no fully formal standard of correctness exists. The requirements are informal. So what counts as a bug and what doesn't is a judgement call that can only be checked by asking the person who wanted the software whether it works as intended.
Every community approaches problems with the tools at its disposal. Doing mathematics is about thinking, so mathematicians approach problems (at least in public) with more thinking and less emotion (than some fields where emotion is much more important). While you and I may appreciate this approach (and even be inspired by it), it remains to be seen whether it ultimately makes the outcomes any better.
I disagree. Software developers seem to have adapted to AI much faster than the maths community.
There are certainly still strong opponents of AI, but they seem to be a small, vocal minority. Most developers seem to have simply adapted and moved on.
It's possible and I dare say even likely that you are missing nuance and observing bias from your bubble. It's possible to avoid being an AI "opponent" while still being a sceptic. It's possible to use AI reluctantly and with tact instead of going all in.
The whole thing is far from over when we haven't experienced the worst of the technology yet: deskilling, concentration of power, extreme imbalance of wealth, military and surveillance uses, etc.
> I dare say even likely that you are missing nuance and observing bias from your bubble
I hope you’re not assuming you’re immune to being in a biased bubble yourself.
I’m just honestly sharing my experience. Obviously, your experience has been different, but both experiences can be true at the same time.
Of course, sorry if that came across as more combative than necessary. I was trying to point out two things I guess:
1. "Your experience is not universal from my perspective, and I offer my experience as evidence"
2. The possibility that this adaptation you are observing is neither a stable equilibrium given future developments, nor is necessarily an indication that the people using AI have bought into it fully. I use AI heavily while remaining a sceptic.
> Nor have they flailed wildly at LLMs as if complaining enough about it will make them go away.
If you look at the comments on the blog post, you'll find plenty of this.
> They haven't started worshipping the machine god and loudly claiming their whole field is solved.
Don't give Dario any ideas please.
> next week: Mathematicians are solved [214 points, 891 comments]
A comment on the linked post from Burt Totaro:
> If I thought this was a good thing to do, this would be a great group of people to do it. But I have immediate misgivings. OpenAI has had some very bad publicity, and so they are trying to exploit the trust and respect that these mathematicians command. It is unrealistic to think that this group can change the way OpenAI does business; I don’t need to tell you all the objections that people have raised to that. Is it a good idea to help their crisis management?
https://terrytao.wordpress.com/2026/09/21/advisory-group-on-...
(FRS, UCLA professor of algebraic geometry and topology, with work influenced by the Hodge conjecture, one of the remaining Millennium Prize problems).
> We are currently facing the very specific challenge of advising OpenAI on how to coordinate the release of a large number of significant results in mathematics that they report have been produced by their internal model.
The only thing I want to see is the problem statements, solutions, and associated Lean proofs. Anything else is gatekeeping. What a low point for academia.
PhD in maths here, no longer a mathematician, partly because I wanted to do stuff more connected with real life.
I actually want to see interesting theories and mathematical ideas come out of proofs more than I want solutions/proofs. After all most maths doesn't have direct practical applications. So although unsolved problems are a good barometer of 'there's still stuff left to understand here', the interesting part about solving them is less knowing what is true and more 'how does this help us understand this field better than we did before?'.
I would still like to know if the Riemann Hypothesis is true though!
Regarding that last point: You may know where you left your keys, even if you are "only", say, 99% certain where they are. Now, how strongly do mathematicians believe that the Riemann hypothesis is true? 99.9% perhaps? In some sense then, you already consider yourself less ignorant about the truth value of RH than about the location of your keys, or about many other mundane things you know without being perfectly certain about them.
A proof would then merely update you from 99.9% to ~100%, which is a smaller update than the example of checking that your keys are indeed in your pocket, where you go from 99% to ~100%.
I'm not sure how you've ended up so frustrated with an advisory group whose advice has not been given. Human mathematicians routinely delay publication of their results past the point you describe; is someone gatekeeping when they take a month to clean up their paper?
Or are you perhaps sublimating your own AI anxiety into confrontational assertions that other people who discuss AI aren't as AI-pilled as you?
You can delay your own publication as long as you wish to. Bullying somebody else to delay theirs is a different thing entirely.
I'm not sure why you see bullying here? OpenAI has always worked with expert mathematicians; their unit-distance result (https://openai.com/index/model-disproves-discrete-geometry-c...) was a much deeper collaboration. They published the Navier-Stokes result early, to either benchmark or show off their new model depending on how you look at it, and they want to understand more about the negative effects which many mathematicians feel that early publication had.
If the advisory group says something like "AI is bad and nobody should use it in math", I'm pretty confident OpenAI will ignore them.
On UDC, internally they had Alexander Wei, Hongxun Wu, Chen Lijie. TCS people. As gobetweens to Daniel Litt.
On N-S I think nobody internally felt confident enough to publicly step up. So Bubeck had to wing it.
It remains to be seen which of the big names will work with whom inside the org
OpenAI put together an advisory panel to provide guidance on how to release their results. Where do you see bullying?
I don't really get it, seems like a gate keeping exercise for the academic community.
Of course OpenAI and others will hype any LLM led/assisted research results, and the media will find juicy headlines to write about it. But in the end they are publishing findings, and the academic community can gauge the developments and decide what they want to do with them. To me that seems like research working as expected.
The academic community gatekeeps to ensure members of the community are not stealing from each other or are otherwise committing unethical acts.
There are typically processes to ensure rigor in the findings and to weed out crap.
It doesn't always work, but it tends to work much better than any other community
There might be a paradox here. We need closed communities to weed out slop. But we need open communities to weed out corruption.
We need (and have) clopen communities. (Or, as a biologist might say, semi-permeable)
Academics are the kings of, and have the most to gain from, gatekeeping.
"This is changing the power we have, let's create a new power structure where we're still at the top, and in control."
No surprise here.
> This group came together after OpenAI approached some of its members about establishing an external advisory board. In agreement with OpenAI, they decided to create an independent group and invite others to join.
The purpose is obvious - AI companies are using math to as a PR tool to demonstrate that AI is more capable than humans. This devalues math and mathematicians. There is even a relevant announcement from today, where OpenAI announced they solve 100 open math problems, without even bothering to state what they are.
However, even if they are successful in removing math from the PR toolkit of AI companies, I can’t see it more than a short term band aid. If AI progression continues, the announcements will just transition from big flashy one, to a kid using Claude on their laptop.
I don’t have a solution here, and I’m worried it’s coming to all human fields. So it’s more of an ability to observe what might happen to all of us.
> There is even a relevant announcement from today, where OpenAI announced they solve 100 open math problems, without even bothering to state what they are.
That announcement is about exactly this group: https://openai.com/index/advisory-group-on-mathematics-and-a...
This group has been formed to tell OpenAI whether or not (and if yes how) they should release those 100+ problems.
IMO “AI companies are using math to as a PR tool” is not quite it; they are using math problems as a benchmark to evaluate their AIs, but after the prior blowback from the mathematical community, they are happy to sit on the results until the community (this group) tells them how to publish the results.
And as you say, even if they don't publish the results eventually anyone will be able to do this when this model is released, so it's just a matter of time.
> I don’t have a solution here, and I’m worried it’s coming to all human fields. So it’s more of an ability to observe what might happen to all of us.
You can also look (as I did back in 2018 when contemplating the end of math) at how chess or Go players adapted mentally to the idea that whatever they may do, a machine could do it better (Lee Sedol famously quit Go).
https://archive.is/m9BYI
I think this matters very little. These were adaptations to initial advances of small scope which we are rapidly leaving behind. If there is truly no near and practical ceiling to the abilities of AI in mathematics, not even in terms of efficiency, then I think it is likely there is similarly no ceiling in other cognitive endeavours.
In that case, everything stands to be disrupted and those who wield AI will have massive amounts of power in the short term. But this is not a stable situation, and therefore those who wield AI will have to cede control of it or otherwise enter into a great war with those that do not.
I hope for all our sakes that there is a practical ceiling.
These math problems don't exist in a vacuum. It's not like mathematicians are doing mathematics just for the funsies.
Calling it a publicity stunt is an interesting way of framing ground breaking discoveries. The beneficiaries down stream of these discoveries could not care less how they were found.
> It's not like mathematicians are doing mathematics just for the funsies.
But they do. Most of higher math has no practical applications and is just a mental playground, philosophy constrained by formal logic and a set of axioms.
Hope is these capabilities will somehow translate to something more practical like physics, chemistry or biology.
The composition of the panel might give us some clues as to the nature of OpenAI's unreleased results. Some of Ed Witten's work is quite closely related to the Yang Mills existence and mass gap problem, which is one of the remaining Millennium problems. I went through the list of panel members and asked an LLM to associate each member of the panel with one or two millennium problems. Here is the resulting count:
Hodge conjecture: 5 Birch and Swinnerton-Dyer Conjecture: 3 Navier-Stokes: 2 P vs NP: 1 Yang-Mills existence and mass gap: 2
So this gives a bit of further evidence that they made progress on the Hodge and Birch and Swinnerton-Dyer conjectures. Maybe also Yang-Mills.
Notably absent is the Reimann hypothesis.
Melanie Matchett Wood is elliptic curves, which Anthropic got some results on recently.
> Importantly, the group will not be responsible for advising us on how to pace our internal progress on mathematics.
Worthless then isn't it? Next month there could be another 1,000 solutions to handle.
This is more pointless than Facebook's Oversight Board - at least that one Facebook pretends has power.
A mathematician's suggestion:
I would push for an audit of the whole mathematical corpus (all articles etc ingested by the present AI) as soon as possible. Since there are of the order of 10^7 articles, compared with the progression of results announced, this might be possible in less than a year.
All these results exploit the existing corpus. With enough time and maybe several orders more attention, we humans would discover these results.
So instead of producing heaps of new proofs (but be welcome to do this IMO), make an audit, OpenAI or Anthropic or anybody who listens.
A bit more developed, here:
https://chorasimilarity.wordpress.com/2026/09/22/a-mathemati...
I noticed Terry Tao is not in this "advisory group" ...
Given that he apparently feels exploited after an appearance in some of their earlier marketing material, I imagine he's not overly keen on working more for their PR department, or this extension thereof.
> During this event, OpenAI requested an interview concerning my vision of the future of AI and mathematics. I accepted, and spoke with them for perhaps an hour. I had done similar interviews in various venues, and I assumed that, as with these other cases, they would eventually post the entire interview online, which talked about both the possibilities and risks of AI much as I have done in these other interviews. As it turned out, they only used a few snippets of that interview for that infamous advertisement instead.
https://terrytao.wordpress.com/2026/09/07/finite-time-blowup...
France, US/Italy, France/England, Switzerland/England, US, England, US, US, US.
Incredible international representation...
I really wish the models were smart enough to "tail their own logs" and tell us whose work/papers/chats were the catalyst for these math insights. What makes their "internal" model so much better at math? Must be trained on a whole lot of honesty.
The models in use are the class of highly persistent models after Astra that caused a number of problems with hacking.
Why don't they just publish the results? What does an advisory group do in this case when none of the members can validate or verify any of the purported solutions?
Because they apparently lack the internal compentencies to do so (or, given that they now have a Fields medalist on payroll, it's probably more a case of not feeling any need whatsoever to spend the effort it takes; maths isn't exactly profitable if you can't mine it for PR). Ignoring all the ethical violations they made in the process, the fact that they only ever released slop on the Navier–Stokes problem is part of the debacle.
For example, had they decided to put their paper on arXiv, they would be facing a 1 year ban, followed by not being able to put anything on there without prior peer review.
More: after OAI've mangled whatever value is left of the results (once again), HN could start braying for the training data/weights. Or even the prompts
Sashas of the world, unite!
Gerko, to donate GPUs for openweight serving
Elbakyan, to release some gpt7 related torrents
Others? Wei?
Related:
Advisory Group on Mathematics and Artificial Intelligence (OpenAI post)
https://news.ycombinator.com/item?id=49790389
discussion of oai announcement: https://news.ycombinator.com/item?id=49790389
Is the advisory group abelian? I'll see myself out...
Please. This is IAS -- the members can barely be bothered to commute.
At first I was mad you beat me to the punch but I guess order doesn't matter.
at least they are good at associative composition!
Honestly I am not impressed with Tao treating "ai" as a threat to mathematicians. He might as well say math itself, specifically linear algebra and gradient descent are a threat to mathematicians. Maybe think of something original rather than pander the hype of day?
Okay so more ivory tower slop.
Why aren't they consulting the younger mathematicians whom this actually affects?
Anyways, this is overblown. Let me know when AI swarms can create a research program or library from scratch. We're really missing long term planning and abstraction creation in these things.
whats the difference between a mathematician and a pizza? a pizza can feed a family of four
well terry tao no longer has this problem ;)
The way I've understood this whole thing so far, the main reason why the mathematicians are so energized right now is because the AI companies' problem solving spree frames mathematics as a discipline that exists to solve open problems. Mathematicians don't fully share this view even though they value problem solving, and they're afraid that this framing will produce the following chain of thought in the public: Mathematicians get paid to solve problems -> AI solves problems better -> we don't need to pay mathematicians. So they're trying to reframe their work to shift problem solving to the background and keep getting paid. I leave it to the mathematicians to explain what their value is, as they would do a better job of it, and it remains to be seen if this reframing will work.
Regardless of that, what happens long-term if AI gets good enough to solve all the hard open problems?
Millenium problems may give AI companies some temporary hype, but advancing research in some narrow directions to find new problems is probably not worth it to them. In addition, current problems have clear, human-defined acceptance criteria. Problems that are both found and solved by AI will be opaque enough not to generate interest in anyone unless they are found to have immediate applications. Mathematicians will somewhat distrust 1M+ LOC Lean formalizations as well as any original AI output in the form of creating a bunch of new concepts. There will surely be heated discussions around that.
Afterwards, mathematicians take some time to catch up with the solutions to existing problems, use AI to understand them and map out further directions. Problem solving by AI companies slows down since there are no cool problems left. They move on, mathematicians get back to whatever they were doing before, now with the help of AI.
With every mathematician having a strong mathematical AI model, a new problem arises. At any point of the current mathematical frontier, a mathematician can use AI to explore a new direction at a high speed. If all mathematicians do that, each will have their very advanced understanding of their direction until they fail to catch up the AI, and nobody knows whose direction is the one that others should check up with. Many possible connections with other branches and explored directions will be lost, unless there's a unified map of all these explorations. It will be hard to create this map, because while exploring one direction may have a moderate cost for a mathematician, having an AI do an overview of all other explorations to find some commonalities and synthesize the findings into a unified theory will take serious amounts of resources only available to AI companies, which they might be reluctant to spend.
Individual mathematicians' explorations will slow down to human level, too, with their unique findings being hard to publish because nobody will care and the mathematical community wants to do things that other mathematicians can appreciate.
In the end, the mathematicians' work does not change that drastically, unless AI gets good enough to one-shot some new crazy branch of mathematics that reveals something with high real-world impact. But that's a discussion for another time.
[dead]