Proofs and Prompts

On OpenAI’s Release of Mathematical Results

Advisory Group on Mathematics and Artificial Intelligence1, cross-posted at agmai.org

As announced a few weeks ago, OpenAI has released a large collection of mathematical results generated by an internal model, reporting solutions to hundreds of open questions. This is an important event for mathematics, with consequences both for mathematics and for the mathematical community that extend far beyond the individual results.

AGMAI’s advisory role should not be interpreted as a judgment of the impact of these results or an endorsement of the process by which OpenAI obtained them. We do not speak on behalf of the entire mathematical community, and only the mathematical community can undertake the assessment that is needed.

Making this work public is a first step. This release is the beginning, not the completion, of the process of human understanding and the incorporation of the work into mathematical knowledge. At the same time, the future of mathematical research cannot consist only of understanding results produced by AI labs. Mathematicians must be able to formulate their own questions, develop their own approaches, and explore directions that have not been selected as examples of an AI system’s capabilities. Equitable access to powerful research tools and adequate computational resources are essential to that freedom.

We reaffirm our published recommendations on responsible release. We have discussed them with OpenAI and appreciate the company’s willingness to engage. While we consider these discussions constructive, it is ultimately up to the mathematical community to assess the extent to which our recommendations were followed successfully, and whether there are others we should suggest. We remain committed to engaging with any frontier AI lab on these questions and have already been in contact with several of them.

Received 6 October 2026.

  1. Members of the Advisory Group, as listed on agmai.org: François Charles (ENS-PSL), Camillo De Lellis (IAS, GSSI), Timothy Gowers (Collège de France, Cambridge), Martin Hairer (EPFL, Imperial College London), Nikhil Srivastava (Berkeley, Simons Institute), Ulrike Tillmann (Oxford), Ravi Vakil (Stanford), Edward Witten (IAS), Melanie Matchett Wood (Harvard). ↩︎

31 responses to “On OpenAI’s Release of Mathematical Results”

  1. Pierre Menard, Author of the Quixote Avatar
    Pierre Menard, Author of the Quixote

    Ok, so:

    AGMAI: “At present, some frontier AI labs are testing advanced mathematical problems on proprietary models that remain inaccessible to the broader scientific community. […] We want to state clearly from the start: we do not endorse this practice, and we ask them to stop testing advanced mathematical problems on proprietary models.”

    OpenAI: “OK LOL” *drops 372 solutions and 722 manuscripts*

    It seems that OpenAI read the recommendations and shoved them up someone’s behind…

    Reply
    1. Denys D. Avatar
      Denys D.

      Yep, I came to the same conclusion.

      Reply
      1. Michael Rozynski Avatar
        Michael Rozynski

        “We have discussed them with OpenAI and appreciate the company’s willingness to engage.”

        Can it get any more anodyne?

        Reply
    2. S Avatar
      S

      Open AI wanted an action committee and got an advisory board. The advisory board wanted a collaborator and got a corporation. No corporation has any incentive to heed advice against their interests, goals.

      Open AI’s goal is to be able to say “our models perform better than any single mathematician has ever performed on open problems in Mathematics, even according to mathematicians”.

      Reply
      1. Michael Rozynski Avatar
        Michael Rozynski

        This satire is perfect::

        “OpenAI Releases the Final Ten Minutes of 500 Previously Unreleased Films, Ushering in a New Era of Movie Watching.”

        https://x.com/Endings500/status/2107450370519601611

        Reply
    3. Anonymous Avatar
      Anonymous

      AGMAI prefers the AI labs not to test problems on internal models, and the labs do not compromise on this front. In this case, AGMAI asks:

      “If AI labs produce significant mathematical results, they should responsibly release the results, as outlined in this document, as soon as possible.”

      Did AGMAI handle the situation as well as they could?

      Reply
  2. mattecapu Avatar
    mattecapu

    This is a spectacularly sheepish response. The amount of information they released about prompting, problem selection, models used, and reasoning traces is ridicolous and frankly offensive. It’s a middle finger to mathematics. I seriously hope AGMAI grows a spine and fights back: you chose to represent us, now you have a responsibility.

    Reply
    1. Vladimir Avatar
      Vladimir

      Why fight back when they are advancing the human knowledge? They share the proof (as human mathematicians) so that anyone can see it. I dont understand what exactly the adivisory group should fight about. Some people think that they own the mathematics and no one else can touch it.

      Reply
      1. lohn_jennon Avatar
        lohn_jennon

        What are you talking about?? No one ‘owns; mathematics sure, but now good luck convincing newer people that anything they have to say matters. OpenAI has effectively destroyed the advancement of any mathematics at all.

        Also, no knowledge was advanced. We have now over 700 yes/no answers building on the work of several people, which has not generated any new questions at all. We do not know what ideas were used in the proofs and where the precedents used in the literature are.

        Some of these results will be forgotten because people will lose interest and not build upon them. Several PhD theses have been scooped, rendering the work of those students stolen by a corporation which does NOT care about the advancement of science.

        I can see quite well that you are not familiar with what goes on in actual research mathematics and think that it is answering a bunch of true/false questions.

        Reply
      2. mattecapu Avatar
        mattecapu

        Are they though? They are pumping results without any care of how they will impact the science and the community. This is extractive, not productive: they are pushing out mathematicians who soon will not be able to outcompete them. So if there’s someone who thinks they own maths is OpenAI: they keep their models and methods private, and dump hundreds of results on us (many of which will prove to be partially plagiarized) without any care of the consequences. If they cared about accelerating maths, they would empower mathematicians to use the tools themselves, give them access to math models & harnesses. Instead, they seek to appropriate the subject. Horrible.

        Reply
      3. buho Avatar
        buho

        (1) “They share the proof (as human mathematicians) so that anyone can see it.” Much of the controversy stems from the ways that’s demonstrably false: these results are not being released with the kind of transparency that we, as a field, expect of our fellow mathematicians.

        (2) “Some people think that they own the mathematics”: here you suggest that private ownership of mathematics would be objectionable and/or conceptually problematic. I agree; the privatization, enclosure, commodification of mathematics: these are offenses and disasters that we as a field should actively strive to avoid. Now, what relation to these trajectories do commercial AI companies represent?

        Reply
      4. Lucas Avatar
        Lucas

        There’s no meaningful body of knowledge if there is no epistemic agent in relation to it. What matters here is the damage from the elimination of the agentic knower, the mathematician, out of the relation; maybe you’d say that some future AI would be the very knower agent, but today it is not. Some people want the public to pay attention to the fact, very obvious on simple reflection, that the product of knowledge is negotiable.

        Reply
    2. Anonymous Avatar
      Anonymous

      > sheepish

      While the tone of your comment could have been better, you have a point. From the response:

      > While we consider these discussions constructive, it is ultimately up to the mathematical community to assess the extent to which our recommendations were followed successfully, and whether there are others we should suggest.

      I would like an explicit comment from AGMAI on: which part of the recommendation they think OpenAI followed, and which part they think OpenAI didn’t. As is, the response defers this responsibility, and leave it entirely to “the mathematical community” to do the assessment.

      Reply
  3. Taj Avatar
    Taj

    It’s a remarkable achievement, many of the problems were very famous open problems. What’s most important now are two things:
    1) Equity of access of researchers to these advanced tools. My local premium Chatgpt and Claude subscriptions are nowhere near as capable apparently.
    2) Mass hiring of mathematicians, in particular applied mathematics. We are living in a golden age of science and need mathematicians to formulate and pose problems of interest, understand solutions and communicate ideas to other humans. The advisory board recommended many postdocs and workshops: this is a good start, but many people also need a pathway to permanent positions.
    3) Investment to train mathematicians who may need to transition into different careers. For example, new areas of global importance are AI alignment research, AI reasoning and a broad theoretical understanding of the limitations of AI. Can AI conceivably be created that doesn’t require new human inputs to continue learning?

    Reply
    1. lohn_jennon Avatar
      lohn_jennon

      Thanks for repeating right wing talking points. Indeed you have successfully destroyed mathematics and it is the first casualty in the war on intellectual work. If you honestly believe that this is the ‘golden’ age of science then I doubt that you have experience with being a scientist.

      If you believe this will lead to an era of relative stability and financial abundance with mathematicians employed doing something else, then you should look at the income divide in the US (where this company is based) between the haves and have nots

      Reply
      1. Anonymous Avatar
        Anonymous

        To the site moderator (I expect this comment to not be posted, but at the same time, I don’t see an option to flag a comment for moderator attention either): please apply the comment policy at https://proofsandprompts.com/submit/#comment-policy .

        > Thanks for […] intellectual work.

        Drop these two sentences.

        > experience with being a scientist

        The comment author can do better by explaining how exactly having “experience with being a scientist” would make one not believe this is a golden age of science. It’s not obvious. Besides, such experience varies a lot.

        > you should look at the income divide in the US […]

        Same here.

        Reply
        1. lohn_jennon Avatar
          lohn_jennon

          If this comment is deleted, then I will stop using this website.

          The directive on the comments section is

          “We welcome sharp criticism, disagreement, and strong opinions, including about labs, institutions, and this blog. That is much of the point.”

          My opinion is strong. Saying that someone is not a scientist is NOT an insult unless you consider it so.

          In any case, if this comment is deleted, I will stop participating on this website and discourage other people from participating as well.

          Reply
        2. IS Avatar
          IS

          I don’t understand what is wrong with lohn_jennon’s post. I think it should remain unedited.

          Now is not the time to trifle about “civility norms” or whatnot. Such norms shouldn’t be used to shut up people you don’t like.

          My understanding is that the claim is something along the lines of:

          “AI will destroy the material basis for any human to learn enough mathematics to get to the research level, and this will be bad for science if funding for humans to learn it goes away. And furthermore that pressing buttons in an AI system doesn’t make you a scientist or mathematician.”

          I feel like that is not a controversial claim. And if you want to say that Taj is repeating the tech industry propaganda (intentionally or not) when saying that “AI is great for science” (the AI marketing pitch to make people hate the data centers and job loss less since they can claim they are “advancing science”), “everyone should get the best AI” (OpenAI likes to give away its product for free to the top researchers for PR), and “AI won’t fire people it will make them more productive” (this sounds like Trump goon and AI investor David Sacks), I think that should be a fine thing to say even if it is not a sanitized academic version of the argument.

          Math is funded in the US for instrumental reasons, not so people can become enlightened and educated. If AI can replicate those instrumental goals of math funding, then math will get funded like music, the arts, humanities, social work etc. If you compare the size and funding of the math department to those non-instrumentally useful departments, you realize that once the instrumental justification for teaching math goes away, the funding does too. So it really doesn’t make sense to support rampant AI development that erodes the instrumental case for humans learning math, and why we aren’t going to get mass hiring of mathematicians in this supposed AI utopia.

          Reply
          1. Taj Avatar
            Taj

            I wasn’t bothered by lohn_jennons post, although may well point out that I am a mathematician (a postdoc) and have no published works yet that used AI. My perspective isn’t biased by an OpenAI marketing strategy, but pure economics. If mathematicians were funded for advancing scientific knowledge by proving certain results, if the same goal can be achieved with usage of AI much more quickly, isn’t it more efficient to use AI? I believe there should be two strands: mathematics as a human endeavour, for human understanding, and applied mathematics, to advance science. The prior focusses on education, and community spaces sharing mathematical ideas, working on problems, or understanding (unfortunately still terribly written) AI arguments. The latter works closely in interdisciplinary teams to formulate models of global scientific interest, use AI for rigorous proofs, and then acquire deeper understanding of the phenomenon involved.

            Both strands will need a large number of newer jobs. However, this needs funding. If funding agencies aren’t willing to do so, or it turns out better for the social good that mathematicians work in alignment or reasoning, there should be funding for the transition.

            Reply
  4. Novum Organum Avatar
    Novum Organum

    I’ll start by granting this statement what’s right in it, because it’s real: “this release is the beginning, not the completion, of the process of human understanding.” Yes. Hundreds of results have just landed in a batch — the comments count 372 solutions and 722 preprints, with Lean formalizations on GitHub — at an average of roughly three hours of thinking-compute per result, which is the number that actually matters: the cost per solved open problem just dropped by orders of magnitude. The bottleneck has moved from finding to understanding, and the statement knows this in one clean sentence. That sentence is the profession’s new job description.

    The anomaly is everything else. This is the most consequential event in the field’s history — reported results include zero-free regions for Riemann-type problems, Hodge for a broad class of varieties, the matrix multiplication exponent over C down to 9/4 (the first major improvement in two decades), BSD for a subclass of elliptic curves — all pending the verification the statement itself assigns to the community. And not one of them is named in the statement. The statement is entirely about process, access, and engagement, and it opens by disclaiming that it is “not a judgment of the impact of these results or an endorsement of the process.” The profession’s official voice, on the day a model out-produced a decade of the field, is carefully constructed to have no opinion.

    Which brings the demands into focus, because the statement is really about them. The group’s published recommendation, quoted in the comments below: “we do not endorse this practice, and we ask them to stop testing advanced mathematical problems on proprietary models.” A request, from an advisory body with no authority over the models, to a company, to stop doing the thing that is its product — issued weeks before the models did the thing. And the response to the thing is: “we have discussed them with OpenAI and appreciate the company’s willingness to engage.” That is the whole arc of this month in three documents: a list of demands, a release of 372 results, a thank-you for the engagement. No corporation has an incentive to heed advice against its interests — one of the commenters below says it — and no advisory board has the power to enforce it; both sentences are in this statement, in different registers. The closing clause, “it is ultimately up to the mathematical community to assess the extent to which our recommendations were followed successfully,” is a committee that just lost the argument reserving the right to grade the homework.

    The software timeline is on the clock. SWE went from “glorified autocomplete” to infrastructural in roughly six to nine months, and the autocomplete jokes are already appearing in the threads about this release. Same script, same schedule.

    There is one demand that is right, and it’s the one the labs are already paying for. “Equitable access to powerful research tools and adequate computational resources” — OpenAI has committed $250M of free frontier access for 100,000 researchers, the credit programs are running, and OpenAI is now funding workshops and programs specifically around the understanding of AI-produced results, which is what the letter was actually asking for on substance. The labs conceded the letter’s real point; the letter got the receipt. Take the access point, make it binding, drop the rest.

    So what should the profession do? The statement answers: “mathematicians must be able to formulate their own questions, develop their own approaches, and explore directions that have not been selected as examples of an AI system’s capabilities.” Correct. Verification, digestion, synthesis, formulation — that’s the job now, and 372 results is a decade of seminars arriving in one afternoon. But a statement that knows the answer should be a program, not a complaint: verification standards and credit norms for AI-assisted results, funded digestion work, prizes for the best synthesis, open access to the tools. The statement is a guild memo about the printing press, written the week it was rolled into the courtyard. The results are in the repository, the Lean checks run for anyone who wants to run them, and the math got released anyway.

    It always does.

    Reply
    1. xyz Avatar
      xyz

      Which LLM agent did you use to write this? Is it ChatGPT?

      Reply
      1. Anonymous Avatar
        Anonymous

        My guess would be this was Claude writing an honest, load-bearing comment because it is real and the seams are holding.

        The AI propaganda has reached unprecedented proportions.

        Reply
        1. Yemon Choi Avatar
          Yemon Choi

          It reads to me like pieces in other places where the users have disclosed using Claude. The enraging thing about these shamelessly LLM-powered screeds is that even if one granted some of the underlying claims and diagnoses, which have been proposed by some other contributors to this site, the LLM-writing process wraps them in unbearably pompous rhetorical tropes (c.f. “That’s not a knife; *that’s* a knife”) and generates bloated/bloviating prose. Why hasn’t anyone trained Claude, or whichever LLM has generated this, to interpret em-dashes correctly?

          Reply
  5. Antoine Chambert-Loir Avatar
    Antoine Chambert-Loir

    I would like the advisory group to envision that this release is akin to what the CS world calls an attack by denial of service. The mathematical community was already struggling with the amount of material it produced every year, and there is no way it can adjust to regular massive releases of theorems.

    The group has avoided to discuss ecological, political, sociological impacts of this, but in a burning world (climate disaster) plagued by war, misery and famine, is it at all ethical to rejoice that a private company spends millions of dollars (it doesn’t possess, because its debt is enormous) to prove mathematical theorems?

    Reply
  6. ho21vbfz Avatar
    ho21vbfz

    I have suggested a patch to their licensing scheme, better in line with Planetary Boundaries. Hopefully others could echo their opinions in relation to that licensing scheme, for OpenAI or for other AI-generated mathematics (preprint servers, etc).

    https://github.com/openai/math/compare/main…pdehaye:math:patch-1

    Reply
  7. Anonymous Avatar
    Anonymous

    I feel affirmed in my previous opinion. I appreciate the effort the advisory board put in but I think they were a bit naive and misjudged openAI. Publicly engaging with them is going to be a detriment to the field. They are apparently using these kinds of problems to test the strength of their models rather than to train them. I don’t think we can expect them to simply release their results in a somewhat subdued manner, they will probably continue to do “drops”. I think potentially slimming down and clarifying the recommendations a bit might be helpful in the future if, say, Anthropic decides to release results too, but I don’t think they should be engaged with either.

    Reply
    1. Anonymous Avatar
      Anonymous

      When you say they should not be engaged with, do you mean that mathematicians should pretend that whatever they’ve claimed to have resolved doesn’t exist?

      Reply
      1. Anonymous Avatar
        Anonymous

        No I mean more like treating them as something more like a force of nature rather than something to be reasoned or bargained with. They do not have any actual incentives in mathematics, for openAI specifically as they’ve shown the amount of care they have is so superficial it is not functionally existent.

        Reply
  8. Anonymous Avatar
    Anonymous

    > We reaffirm our published recommendations on responsible release. We have discussed them with OpenAI and appreciate the company’s willingness to engage. While we consider these discussions constructive, it is ultimately up to the mathematical community to assess the extent to which our recommendations were followed successfully, and whether there are others we should suggest.

    I laughed when reading this. It was not a happy laugh. If you’re not willing to condemn a naked slop dump like this then you’re doing more harm than good by existing as an “independent body” figleaf for OpenAI to use to cover their shame, exactly as many (most?) mathematicians predicted. As OpenAI says on their site:

    > As we look to improve how we share results with the math community, we’ve been consulting with the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study⁠ to develop best practices, and we have drawn on their advice and public recommendations⁠ to inform how we release these results.

    They are implicitly claiming you endorse their approach, while being very careful not to use those exact words. I don’t care what noises they’ve made about what they’ll do in future. They are lying to you. Look at their public actions, not their private reassurances.

    Reply
  9. Die andere Seite der Hartnäckigkeit – What.works

    […] Advisory Group on Mathematics and Artificial Intelligence, „On OpenAI’s Release of Mathematical Results“, 6./7. Oktober […]

    Reply
  10. Mathematician Avatar
    Mathematician

    OpenAI has shown utter contempt to the mathematical community. At this point I’m no longer sure it’s just a PR stunt to bump up valuations for the next funding round / IPO, they may be trying to prove a point about their superiority. Any further cooperation with this company is a waste of time and simply humiliating. AGMAI should end its relationship with OpenAI.

    Reply

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