OpenAI said it is releasing a large collection of mathematical research produced by an unreleased internal model as the company seeks to "improve" how it shares results with the broader math community.
In a GitHub repository published on Tuesday, the company said the collection includes 722 manuscripts grouped into 372 families of related results covering fields ranging from ordinary two-point correlations of multiplicative functions to the Vlasov-Maxwell system. OpenAI cautioned that the results are at different stages of verification and that some of the work without formal proofs could contain errors.
The model worked through roughly 4,000 problems, with each result using the equivalent of about three hours of ChatGPT Pro thinking time on average, the company added. Most of the work followed the same procedure, although some results were handled separately, including a zero-free region for the Riemann zeta function and a proof of the Hodge Conjecture for CM abelian varieties.
"We want to directly empower scientists with state-of-the-art capabilities and are working to responsibly release the model that produced these results," the company said in a statement. "This is why it is important to continue to evaluate our internal frontier models on mathematics and other sciences, so we can accelerate developing the tools to advance those fields."
OpenAI said it developed the release with input from the Institute for Advanced Study’s independent Advisory Group on Mathematics and Artificial Intelligence. The repository also includes Lean formalizations of many of the proofs, along with 10 abridged summaries of the model’s reasoning.
The release follows the company's announcement last month that about 10,000 AI agents had worked on the Navier-Stokes existence and smoothness problem.
That announcement sparked a dispute with NYU professor Tristan Buckmaster, who said OpenAI moved too quickly after he and Anthropic mathematician Levent Alpöge used Codex while working on the problem. OpenAI said it could not rule out de-identified data from their use of its products having contributed to model improvements. The company also said it would not seek the $1 million Clay Millennium Prize.