OpenAI releases 722 mathematical manuscripts it says were produced by an unreleased internal model

OpenAI said in a research post dated 6 October 2026 that it is “releasing a broad range of new mathematical results produced by an internal frontier model”, and published them in a public GitHub repository, openai/math.^[1][2] The repository says it holds 722 manuscripts organised into 372 “families” of related papers, each classified by mathematical discipline.^[2][6] Scientific American reported that OpenAI revealed the results at 6 P.M. EDT (22:00 UTC, or 03:30 IST on 7 October); GitHub shows the repository’s first commit at 21:58 UTC.^[2][5] Gizmodo’s headline and report give the figure as 377 results.^[7]

According to the repository, the model was posed about 4,000 problems during the evaluation, and the outputs were grouped into families and manuscripts after “requiring an appropriate level of significance”.^[2] OpenAI says the average result used the equivalent of roughly three hours of ChatGPT Pro thinking, and that it is publishing ten summaries of the model’s reasoning.^[1][2][6] The repository says the results are “at different stages of verification”, that not all have Lean formalisations — proofs that a computer can check — and that “Some of the unformalized results could have issues.”^[2] It names two exceptions to its fixed procedure: work on a zero-free region for the Riemann zeta function and a proof of the Hodge Conjecture for CM abelian varieties, and says one Riemann zeta write-up was “human edited for readability”.^[2] Scientific American reported that many of the results have already been verified in Lean and are therefore “all but certain to be correct”.^[5]

The repository’s catalogue describes, among other results, a proof that the Riemann zeta function and every Dirichlet L-function have no zeros where the real part exceeds 7/8, which it calls the quasi-Riemann hypothesis.^[2] It also describes a proof of the full Birch–Swinnerton-Dyer leading-term formula for elliptic curves over the rationals that meet a condition on their Selmer groups, a result Gizmodo also cited.^[2][7] Scientific American reported that the claimed results also include a solution to the four-dimensional Kakeya conjecture and improvements to important computer algorithms.^[5] A spokesperson for OpenAI told Scientific American that the model, which OpenAI has not released, produced almost every result in response to a single prompt given to a single AI agent, and also said some results might have taken multiple attempts.^[5] The spokesperson also told the magazine that many of the newly released results are not yet understood by OpenAI’s own mathematicians.^[5] OpenAI says it is “working to responsibly release the model that produced these results” and will fund workshops, conferences and special programmes on major results produced by AI.^[1]

OpenAI says it consulted the Advisory Group on Mathematics and Artificial Intelligence (AGMAI), based at the Institute for Advanced Study, on how to release the results.^[1][3] The group’s nine members include Timothy Gowers, Martin Hairer and Edward Witten, and it says it operates independently of any AI company.^[3] AGMAI says the group “came together after OpenAI approached some of its members about establishing an external advisory board”, and that, in agreement with OpenAI, they created an independent group instead.^[3] In a statement dated 6 October, AGMAI called the release “an important event for mathematics” and said its 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”.^[3] It added that “only the mathematical community can undertake the assessment that is needed”.^[3]

AGMAI’s recommendations of 29 September 2026 say a lab should publish, for each result, “the name of the model, the prompts used, a (summarized) chain of thought, the time taken, and the estimated cost of computation”.^[4][6] They also say: “we do not endorse this practice, and we ask them to stop testing advanced mathematical problems on proprietary models.”^[4][7] OpenAI spokesperson Lindsay McCallum Rémy told Gizmodo: “AGMAI’s advice and public recommendations have informed how we’re sharing the results.”^[7] Scientific American reported that OpenAI is revealing only the average compute time for a problem, with some additional statistics and no prompts, and that an OpenAI spokesperson said the company is taking the group’s guidelines seriously and doing its best to comply but is not bound by its recommendations.^[5] Gizmodo and Scientific American reported that the results came from the same unreleased model as OpenAI’s earlier Navier–Stokes result.^[5][7]

Andrew Sutherland, a mathematician at the Massachusetts Institute of Technology, told Scientific American: “Until and unless they release the model and people can replicate their results, I think you should treat any claims about one-shotting problems with a single agent as unverified.”^[5] Daniel Litt, a mathematician at the University of Toronto, told the magazine: “To me, it’s going to be a good thing for mathematics.”^[5] Scientific American also reported that the mathematician Terence Tao has criticised OpenAI and other frontier AI labs for the “insane” pace of their AI-generated results.^[5] Scientific American said the results will take mathematicians months to work through, and The Verge said their full impact will likely take time to be felt.^[5][6]