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OpenAI Releases 722 Math Manuscripts From Internal Model

OpenAI published 722 mathematical manuscripts from an unreleased internal model on 6 October 2026, with Lean proofs for many results but no prompts or model name.

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OpenAI Releases 722 Math Manuscripts From Internal Model

OpenAI on Tuesday, 6 October 2026, published 722 mathematical manuscripts produced by an unreleased internal model, grouped into 372 result families in a public GitHub repository. The company says the model was posed about 4,000 problems and that the average result used compute equivalent to roughly three hours of ChatGPT Pro thinking. Many of the proofs come with Lean formalizations, but OpenAI's own README says not all of them do and that some unformalized results "could have issues."

What OpenAI put in the openai/math repository

The blog post, titled Sharing AI progress in mathematics, describes the release as a broad range of new results from an internal frontier model. The files sit in the openai/math repository, which OpenAI chose as the venue for this release while it looks at community-hosted alternatives.

According to the README, a family groups related papers: a principal result plus companion arguments, consequences or alternative proofs. Each family is classified by mathematical discipline. The repository includes an overview document, a manuscript map, a preprints directory with PDFs and source files, and a Lean library with a formalization catalogue that links formal proofs to the papers they support.

OpenAI is also publishing ten abridged summaries of the model's reasoning. The README lists their subjects, which include the irrationality exponent of pi, the symmetric and general Mahler conjectures, Kaplansky's direct-finiteness conjecture in characteristic two, the isomorphism of free group factors and the three-dimensional relativistic Vlasov–Maxwell system.

The README says the vast majority of results came from one fixed procedure using the unreleased model. It names two exceptions: work on a zero-free region for the Riemann zeta function and a proof of the Hodge Conjecture for CM abelian varieties. It adds that the write-up for the Re(s) > 11/12 zero-free region was edited by humans for readability. In a post on the OpenAI Developer Community forum, OpenAI said revisions will be tracked with earlier versions kept accessible.

How the release compares with IAS advisory guidance

OpenAI says it consulted the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study and drew on the group's public recommendations. Those recommendations, dated 29 September 2026, set out what labs should disclose when they release AI-generated mathematics that nobody yet understands.

The group asks labs to 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. It also asks that results go into scholarly repositories not controlled by any AI lab, that proofs be formalized where possible, and that a bulk release come with a document explaining how many comparable problems the models tried and failed to solve and how the problems were chosen.

OpenAI's release covers parts of that list. It provides Lean artifacts for many manuscripts, the roughly 4,000-problem figure, an average compute estimate and the ten reasoning summaries. It does not name the model. Scientific American reported that OpenAI is revealing only the average compute time per problem, with some additional statistics, and no prompts. The magazine said an OpenAI spokesperson described the company as taking the guidelines seriously while adding that it is not bound by them.

The advisory group also says it does not endorse testing advanced mathematical problems on proprietary models and asks labs to stop. OpenAI's blog says the company is working to responsibly release the model that produced the results, but it gives no date.

What mathematicians told Scientific American

Scientific American, which said the repository went live at 6 p.m. EDT, reported that the claimed results include a solution to the four-dimensional Kakeya conjecture and progress toward the Riemann hypothesis. It quoted an OpenAI spokesperson as saying the model produced almost every result in response to a single prompt given to a single AI agent, while also noting that some results might have taken multiple attempts.

Andrew Sutherland, a mathematician at the Massachusetts Institute of Technology, told the magazine that claims about one-shotting problems with a single agent should be treated as unverified until the model is released and others can replicate the results. "We should ask for receipts," he said. Daniel Litt of the University of Toronto took a different view, saying he saw no reason the community should ask the company to keep the answers secret.

The magazine also reported that the spokesperson said many of the newly released results are not yet understood by OpenAI's own mathematicians. That detail matters under the advisory group's framework, which treats papers nobody understands as a separate category with extra disclosure and support duties for the lab.

Scientific American wrote that the release will take mathematicians months to work through, including judging whether the proofs contain new ideas or mainly recombine existing techniques. It added that results already checked in Lean are all but certain to be correct.

Verification, citations and funding commitments

The README says OpenAI will add Lean formalizations as it obtains them, will try to fix any issues in unformalized results quickly, and will record corrections as new versions. Each manuscript directory carries a BibTeX block so researchers can cite individual papers. In the blog, OpenAI says it will fund a series of workshops, conferences and special programs aimed at understanding major results produced by AI, with details to come.

That funding pledge lines up with the advisory group's second principle, which says labs releasing output without accompanying human understanding should pay to help that understanding develop. The group adds that the direction of that work should stay community-led and that existing nonprofit institutions, not AI labs, should decide which efforts get support.

The release adds to a run of Lean-centred AI mathematics announcements. PromptCrates has covered Anthropic's account of Claude agents formalizing Fermat's Last Theorem in Lean and Google's claim that Antigravity Teamwork solved seven open problems. It also reported on an open letter from Fields Medal winners arguing that the race to claim breakthroughs threatens mathematical culture.

researchOpenAImathematicsLeanAI research disclosure

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