Those OpenAI Math Results

OpenAI released 722 mathematics manuscripts containing 337 results on open mathematics problems, generated by an advanced model not yet available to the public, with the average result taking about three hours of computing, according to the company. The release drew scrutiny from mathematicians, and OpenAI's mathematics advisory group — formed after earlier concerns over the firm's Navier-Stokes breakthrough — called the public release "the beginning, not the completion, of the process of human understanding" and urged publication of all prompts to the AI agents and the agents' chains of thought. Harvard mathematician and advisory board member Melanie Wood said, "We want to create standards and practices so that results released from A.I. labs can be understood by mathematicians and can advance the field.

In what is being called https://x.com/afinetheorem/status/2107658843996000292?s=43&t=2obdZ1NcbbjQq9brB3UgPg “the most important event in the history of mathematics” by an AI , OpenAI, using an advanced model not yet available to the public, yesterday released https://openai.com/index/sharing-ai-progress-in-mathematics/ 722 mathematics manuscripts containing 337 results it has generated on open mathematics problems. “OpenAI deluged mathematicians with hundreds of new findings that span a wide swath of topics including algebra, number theory, theoretical computer science, mathematical logic and topology,” the New York Times reports https://www.nytimes.com/2026/10/06/science/openai-math-problems.html . Adding insult to injury, “the average result took about three hours of computing, the company said.” One AI engineer on x.com put it this way https://x.com/daniel mac8/status/2107604648328569030 : “Reasoning models are two years-old. In that time they went from incapable of basic arithmetic to solving problems humans couldn’t solve for decades.” What were the results like? Computer scientist Scott Aaronson shares some of his thoughts and those of his wife, complexity theorist Dana Moshkovitz, here https://scottaaronson.blog/?p=10169 . Moshkovitz says: “It feels like something written by someone who’s on psychedelics…” and “so horribly written that it’s impossible to read it without AI help…”, but: “of course there’s a lot for us to learn from the aliens”. After mathematicians raised concerns about an earlier breakthrough https://openai.com/index/navier-stokes-solution/ on the Navier-Stokes problem by OpenAI, the firm formed an mathematics advisory group https://openai.com/index/advisory-group-on-mathematics-and-ai/ to advise it on the “review and communication of emerging results.” Their job is to help OpenAI assess their significance, advise on how to coordinate their dissemination, and advise on academic and professional standards of mathematical research… The group will operate independently from OpenAI. The group will have the freedom to offer advice we have not requested, comment on OpenAI’s impact on mathematics, and make its advice public. In the wake of the new results, the advisory board released a statement that called the public release “the beginning, not the completion, of the process of human understanding and the incorporation of the work into mathematical knowledge.” “We want to create standards and practices so that results released from A.I. labs can be understood by mathematicians and can advance the field,” Melanie Wood, a mathematician at Harvard who is a member of the advisory board, said in an email The advisory group also called for the release of “all of the prompts to the A.I. agents and the agents’ chains of thought.” Mathematicians were already wondering about the future of their field in light of AI’s capacities. It seems like the discipline of mathematics must “change or risk extinction,” as Jordana Cepelewicz puts it in a recent piece https://www.quantamagazine.org/is-ai-the-end-of-math-as-we-know-it-20261005/ at Quanta . Readers of Daily Nous might be wondering about whether philosophy will face a similar reckoning. And indeed much of what Cepelewicz says about mathematics—especially on what seems to be missed when machines provide us with the answers—could be said about philosophy. Here are some examples: Many people don’t know what mathematics really is, or why mathematicians do it… I always found that “pure math” — the study of mathematical concepts for their own sake, without a care for real-world applications — existed somewhere between the sciences and the arts. It prizes logic and certainty, but at its core lie fuzzier notions of beauty, intuition, and depth. “Math is either the most science-y humanities or the most humanities-type science, depending who you ask,” said Marcel Goh, a doctoral student at McGill University… In mathematics, it’s not a cliché that the journey matters more than the destination. Problems are posed not so much because their answers will be practical and important, but because they represent interesting journeys. The hope is that as mathematicians struggle to solve a problem, they’ll come up with intriguing tools and connections, stumble on novel ideas and directions, take fruitful detours, and answer new questions they never would have thought to ask…. Mathematicians have always known that understanding is more valuable than an answer… The whole piece, worth reading, also discusses some ways that academic mathematics will likely have to change. Still, it is not obvious that philosophy is susceptible to the same kind of threat that mathematics is currently dealing with. While there are no shortages of open problems in philosophy, one might nonetheless say: philosophy is not in danger of its problems being solved by AI because its problems cannot be solved . I think such a response is both too pessimistic and too optimistic. It’s too pessimistic because some of philosophy’s problems are at least in principle solvable. Examples: Is principle P compatible with judgment J? Is argument A valid? What are the implications of belief B? Which theory of X is most compatible with this particular theory of Y and current science? And so on. It’s too optimistic because it seems quite likely that some future form of AI will be able to answer these kinds of questions and similar ones with scopes too wide and variables too numerous for a human mind to keep track of . Generally, most of the philosophical “solutions” that humans offer are the consequents of explicit or tacit conditionals, and I would think that AIs will be quite good at conditional reasoning. See “ Hey Sophi https://dailynous.com/2021/03/24/hey-sophi-or-how-much-philosophy-will-computers-do/ “. Tomorrow there will be a guest post about how AI might change philosophy, but I wanted to give people a chance to discuss the mathematics results, and perhaps the relevant similarities and differences between mathematics and philosophy.