OpenAI publishes 722 math papers produced by AI

What happened?

OpenAI has shared 722 mathematics papers produced by an unreleased internal frontier model in a public GitHub repository. The work was filtered by significance and organized into 372 result families.

The model worked on roughly 4,000 problems

According to OpenAI, the model was confronted with about 4,000 math problems during evaluation. The company says producing an average result took compute roughly equivalent to three hours of ChatGPT Pro thinking capacity.

Verification is still ongoing

The independent Advisory Group on Mathematics and Artificial Intelligence (AGMAI) says the collection contains results on hundreds of open problems that had long resisted solution. However, OpenAI itself notes the results are at different verification stages and that some not yet formalized papers may contain errors. A significant portion of the proofs was checked with Lean, a system that uses computers to verify the logical validity of mathematical proofs; not all papers have Lean verification yet.

Transparency and academic publishing debate

OpenAI also shared condensed reasoning summaries, compute estimates and the number of problems attempted for 10 selected problems. Examples include the irrationality measure of π, Mahler's conjectures, Kaplansky's direct finiteness conjecture and the three-dimensional relativistic Vlasov-Maxwell system. AGMAI, meanwhile, wants AI companies to publish mathematical results through academic channels where possible, be more transparent about the model, cost and methods used, and avoid turning mathematical discoveries into marketing tools.

What's next?

OpenAI says it will keep updating the GitHub repository as new formal verifications are completed, and that it will fund workshops, conferences and special programs to help people understand significant AI-derived mathematical results. The company adds that it is working to release the internal model behind the work responsibly.