OpenAI Releases 722 Math Manuscripts From Unreleased AI Model

OpenAI has released 722 mathematical manuscripts produced by an unreleased internal frontier model, covering 372 groups of results across mathematics and theoretical computer science.

The release, announced on October 6, includes results from an evaluation involving approximately 4,000 mathematical problems. OpenAI said the manuscripts are organised into 372 related result families, with each family potentially containing a principal result, companion arguments, consequences or alternative proofs.

The OpenAI math manuscripts have been published through a public GitHub repository that also includes supporting proof materials, Lean formalisations for many results and 10 abridged summaries of the model’s reasoning.

The company said the collection includes results at different stages of verification. Not every manuscript has a Lean formalisation, and OpenAI acknowledged that some unformalised results could contain issues.

The OpenAI math manuscripts cover a wide range of subjects, including number theory, geometry, algebra, combinatorics, mathematical physics and theoretical computer science.

OpenAI said the vast majority of the results were produced using the same unreleased internal model. On average, each result used computing equivalent to about three hours of ChatGPT Pro thinking.

The company has also provided protocols for revisions and citations, allowing the published papers to be updated as mathematical scrutiny continues. OpenAI said it consulted an independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study while developing its approach to releasing the work.

The scale of the release is notable, but the manuscripts should not automatically be treated as independently established mathematical breakthroughs.

Lean formalisation can provide computer-checkable verification for a formal statement, but OpenAI’s repository makes clear that such formalisation is not available for every result. The company expects the collection to be updated as additional formalisation and corrections are made.

The OpenAI unreleased frontier model has previously been linked by the company to major mathematical research claims. In September, OpenAI published what it described as a solution to the Navier Stokes existence and smoothness problem, including a Lean formalisation.

The immediate focus will be on independent examination of the manuscripts and their underlying proofs. OpenAI’s latest release gives researchers access to a much larger body of AI-generated mathematical work, while leaving the broader mathematical community to assess individual claims.

For OpenAI, the release also provides a public record of how an unreleased frontier AI model performs on open research problems and how those results can be documented, revised, and checked over time.