Look at everything that OpenAI failed to prove!

Posted on August 2, 2026 by Persiflage

I was heartened to see a recent list of results proved by OpenAI here. Heartened because we are now clearly in an age in which AI can truly contribute to serious research mathematics. But also heartened because one can only imagine how many thousand of open problems OpenAI tried and failed to solve, assuming these are the ones they consider the most impressive. It would be vastly more informative to see the list of problems they tried to solve and didn’t, as well as possible partial progress that was made on other problems.

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7 Responses to Look at everything that OpenAI failed to prove!

  1. Thomas says:
    August 2, 2026 at 5:59 pm

    Check Henry Yuen’s reaction: https://xcancel.com/henryquantum

    I doubt mathematicians working at OpenAI tried your favorite problems yet.

    Reply
    • Persiflage says:
      August 2, 2026 at 6:40 pm

      >I doubt mathematicians working at OpenAI tried your favorite problems yet.

      If this is what you have to say, then you certainly missed the point of this post.

      Reply
      • Thomas says:
        August 2, 2026 at 6:45 pm

        Yes at first I thought you were being ironic, but the usage of two “heartened” sounded like you are being serious. If you meant to be ironic then good.

        Reply
  2. Curious says:
    August 2, 2026 at 7:10 pm

    To be fair us mathematicians (as a general type) have little to preach about this as it is often also in our culture not to spend time on “negative results” and “limitations”, as they are just as informative on the relative strength of a method (of course there are noticeable exceptions, but generically this seems to be the case).

    That said I fully agree that it is crucial (for whoever has phd students postdocs and an active research agenda) to get a better sense of what are the current limitations of “automated generation” of remarkable mathematics.

    I think it would be great if SB from OAI would be flagged of this post of yours. He is very reasonable and seems to care also about having a positive influence to the scientific community. Would be great if they would release a list as the one you envision.

    They could also use it later as public proof of qualitative improvement of their future models.

    Reply
    • Persiflage says:
      August 2, 2026 at 7:22 pm

      Excellent point. In fact, there is much about the mathematics profession which could be improved, and a monumental shift is often one of the few moments where one can enact that change.

      I’ll certainly be talking about it more on this blog, but at Chicago this quarter we will run a seminar with precisely this in mind: testing the limitations and strengths of these models “in the wild”, and then reporting back each week on the successes and failures.

      Reply
  3. Grigori Avramidi says:
    August 2, 2026 at 7:19 pm

    One way to get a range of conjectures that the math community considers `important’ would be to take the conjectures/questions in icm proceedings for the last few decades (and then filter out the obviously unsuitable or solved ones). I do wonder if the questions they solved fit that bill.

    Reply
  4. Luka says:
    August 2, 2026 at 7:44 pm

    Are you heartened or disheartened? I cannot tell. Moreover, I very skeptical that they did not attempt problems in algebraic number theory. LLMs are very good at finding a certain kind of solution. Whether they will do more seems to be a very much open question. The theory is very far behind. Trend lines indicate they can. While their capabilities in the humanities indicate they cannot.

    Reply

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