OpenAI publishes 722 math manuscripts from an unreleased internal model, and says it is working to release the model

OpenAI has published 722 mathematical manuscripts written by an unreleased internal frontier model, grouped into 372 families of related results. They are in a public GitHub repository, openai/math, under the Apache 2.0 license. OpenAI says it is "working to responsibly release the model that produced these results" but has not named it or given a date.

HOW THE RESULTS WERE PRODUCED

Per OpenAI's repository, the model was posed about 4,000 open research problems after OpenAI's existing math evaluations saturated. Most results came from one fixed procedure, averaging about three hours of ChatGPT Pro thinking compute per result. Grouping the output into families and keeping only results judged significant enough produced the catalogue. OpenAI says two items were done outside that procedure, a zero-free region for the Riemann zeta function and a proof of the Hodge Conjecture for CM abelian varieties, and that the zeta write-up was edited by humans for readability.

WHAT IS IN THE RELEASE

- The manuscripts as PDFs and source files, with citation instructions for each - Lean formalizations for many, but not all, of the proofs, with more promised as OpenAI gets them - Abridged reasoning summaries for ten families, including the irrationality exponent of pi, the Mahler conjectures and the isomorphism of free group factors

OpenAI says it consulted the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study on how to release the work, and that it will fund workshops and conferences on understanding AI-produced results.

WHAT WE DO NOT KNOW

Whether the results hold up. OpenAI's own repository says the collection includes results "at different stages of verification" and that "some of the unformalized results could have issues". Several of the listed subjects are long-standing open problems, so every claim here is OpenAI's until mathematicians check it or a Lean proof covers it. The model's name, size and release date are unknown.