OpenAI on October 6, 2026 published a large batch of new mathematical results produced by an internal model that hasn’t been released to the public. According to OpenAI, the collection contains 722 math manuscripts grouped into 372 “families” of results, and many of the proofs also come in Lean, a formal language that lets a computer check every step of a proof. Everything is in a public GitHub repository, along with details on how the results were obtained.
What’s in the 722 math manuscripts from OpenAI
Each family bundles related papers: a principal result plus companion arguments, consequences or alternative proofs, classified by mathematical discipline. Alongside the manuscripts, OpenAI is sharing source files and citation instructions for each paper, a Lean library with a catalog of the proofs formalized so far, and ten abridged summaries of the model’s reasoning. Those summaries cover subjects including the irrationality exponent of pi, the Mahler conjectures, Kaplansky’s direct-finiteness conjecture in characteristic two, the isomorphism of free group factors, the Mezard-Parisi formula for diluted spin glasses, and the three-dimensional relativistic Vlasov-Maxwell system.
OpenAI is upfront that the collection sits at different stages of verification. Not every result has a Lean formalization, and the company itself warns that some of the unformalized results could have issues, which it says it will fix quickly. Corrections will be published as new versions, and earlier versions will stay accessible.
How the model got there
OpenAI says it started testing its models on open research problems after they saturated its existing math benchmarks. Over the evaluation, the model was given roughly 4,000 problems, and only results that cleared a significance bar made it into the catalog. Most results came from the same fixed procedure, using on average the equivalent of about three hours of ChatGPT Pro thinking compute per result. The company flags two exceptions to that procedure: work on a zero-free region for the Riemann zeta function, and a proof of the Hodge Conjecture for CM abelian varieties. The zeta function writeup was also edited by humans for readability.
Keep in mind that these are OpenAI’s claims. Mathematicians haven’t yet reviewed most of the results, and checking hundreds of manuscripts will take time. The Lean proofs make verification easier, but only part of the collection is formalized.
Transparency and the math community
OpenAI says it consulted the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study in Princeton on best practices for releasing results like these, and that it’s looking at community-hosted alternatives to GitHub. The company also plans to fund workshops, conferences and special programs focused on understanding major results produced by AI, and says it’s working to release the model behind them responsibly. It hasn’t given a release date.
Why it matters
This isn’t the first time a major AI lab has tried to show its models can contribute to real math research. Just days ago we covered how mathematicians used Meta’s Muse Spark to tackle open research questions. What stands out here is the scale: hundreds of manuscripts, disclosed compute and attempt counts, and machine-checkable proofs. For researchers and students, it’s open material to scrutinize. For everyone else, it’s a hint of what the next generation of models after GPT-6.1 Sol might bring. More updates in our AI News section.
Sources
- OpenAI, official blog: Sharing AI progress in mathematics, October 6, 2026, openai.com
- OpenAI, openai/math repository on GitHub, README, October 6, 2026
