OpenAI has published 722 mathematical manuscripts on GitHub, all generated by an undisclosed internal AI model. The company stated that the majority of these results were produced from a single prompt provided to one AI agent. The collection is organized into 372 families of related results, derived from approximately 4,000 problems posed to the system.
According to OpenAI, the average result required compute resources equivalent to roughly three hours of ChatGPT Pro usage. Currently, only 162 of the 722 manuscripts, or about 22%, have been verified using Lean, a software tool for mechanical logical checking. The company acknowledged that some unformalized results may contain errors and plans to add further Lean formalizations over time.
The release has drawn scrutiny from the mathematical community, including researchers from MIT and the Institute for Advanced Study. Critics point out that the model itself remains private, and the repository does not accept external contributions or pull requests. OpenAI has not yet disclosed the specific prompts, full chains of thought, or detailed compute costs for individual results.
While some experts describe the output as significant progress within existing mathematical programs, others emphasize the need for transparency. The collection includes one result related to the Quasi-Riemann Hypothesis. In contrast to this release, Anthropic recently published a 13-million-line Lean-checked proof of Fermat's Last Theorem in its entirety.
