OpenAI publishes AI math results on GitHub

On October 6, OpenAI announced the release of a large number of mathematical results generated by one of its internal frontier models. This followed the company's previous claim that the model had resolved the Navier–Stokes existence and smoothness problem, among other Millennium Prize Problems. The company disclosed 722 manuscripts encompassing 372 groups of results, which involve solutions to or significant progress on numerous unsolved problems in mathematics and theoretical computer science.

These findings are available in a GitHub repository, equipped with protocols for paper revisions and citations.

OpenAI collaborated with an independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study to refine the sharing of these results with the broader mathematical community. This advisory group helps the company establish best practices for releasing AI-generated mathematical research. The earlier Navier–Stokes claim by OpenAI has been met with both enthusiasm and skepticism from the mathematical community, particularly regarding the verification and crediting of AI-generated mathematical results.

The internal frontier model was fed approximately 4,000 mathematical problems, with the average result needing about three hours of computing time comparable to ChatGPT Pro. The company has also published 10 summaries outlining how the model approached specific problems. Many of these proofs have been formalized using Lean, a programming language that enables mathematical proofs to be verified by computers. OpenAI plans to add more formalized proofs to the repository in the future.

Moreover, the scale of this release has raised questions about the verification and crediting of AI-generated mathematics. Researchers have advocated for more transparency, independent verification, and proper acknowledgment of human work. OpenAI incorporated the advisory group's recommendations into the latest release, which includes protocols for revising and citing the papers.

The company also stated its intention to continue testing its most advanced models on mathematics and other scientific problems, believing that AI could eventually provide researchers with new tools for making discoveries.