Blog
OpenAI publishes hundreds of AI-generated math papers, then withdraws three
On 6 October 2026 OpenAI posted about 720 math manuscripts from an unreleased internal model to GitHub. About 42% of top-line results are Lean-formalized, and three papers were withdrawn a day later after a sign error.
Hundreds of papers, one unreleased model
On 6 October 2026, OpenAI published a large set of mathematical results produced by an internal frontier model that the public cannot use. The manuscripts sit in a public GitHub repository, openai/math, with Lean formalizations for some of the proofs.
The release was reported as 722 manuscripts. After a first round of corrections, the repository now lists 719 manuscripts in 372 families. A family groups a main result with companion papers, consequences or alternative proofs, so 719 manuscripts does not mean 719 solved problems.
How the results were produced
According to the repository's README:
- The model was posed about 4,000 problems during evaluation.
- On average, each result used compute equal to about three hours of ChatGPT Pro thinking.
- OpenAI expanded these open-problem tests after its existing math evaluations "saturated."
- Two results did not follow the standard procedure: work on a zero-free region for the Riemann zeta function, and a proof of the Hodge Conjecture for CM abelian varieties, a special case rather than the full conjecture.
OpenAI also released 10 abridged summaries of the model's reasoning. Topics include the irrationality exponent of pi and the Mahler conjectures in geometry.
OpenAI does not name the model or give a release date. It says it is "working to responsibly release" it.
Verification is uneven
The README is direct: "Some of the unformalized results could have issues."
Lean is a programming language that lets a computer check a proof. As of the latest update, OpenAI says 300 of 719 top-line results (about 42%) are formalized. The rest rely on human readers to check the written argument.
Corrections started within a day. The repository's history log, dated 7 October, records:
- 3 withdrawals. A sign error in "Algebraicity of Weil classes on split abelian eightfolds" broke its argument and two papers that depended on it, including one on the rational Hodge conjecture for products of K3 surfaces.
- 14 manuscripts revised with proof repairs, corrected statements and clearer hypotheses.
- 6 new formalizations added.
OpenAI researcher Dan Roberts announced the update on X and said more formalizations and errata would follow. OpenAI says earlier versions stay accessible, so changes can be traced.
The advisory group and the open question
OpenAI says it consulted the Advisory Group on Mathematics and Artificial Intelligence, hosted at the Institute for Advanced Study, on how to release the results. Coverage, including The Daily Inference, notes that the group's 29 September recommendations asked labs to stop testing advanced problems on proprietary models. OpenAI has published the papers but kept the model closed.
That leaves a gap. Mathematicians can check individual proofs. They cannot test the model on new problems, or see how many of the roughly 4,000 attempts failed. Those details would show how reliable the system actually is.
OpenAI says it will fund workshops, conferences and special programmes to help people understand AI-produced results. It has not given amounts or dates.
Why it matters
Machine-generated research is moving from single headline results to bulk releases. The lesson from week one is that volume needs checking: three papers have already been withdrawn and most results are not yet computer-verified. Treat any one result as a claim to check, not a settled fact, until it is formalized or reviewed by specialists.