OpenAI Releases New Mathematical Results from Internal Frontier Model with Lean Formalizations

OpenAI has released a broad range of new mathematical results produced by an internal frontier model, aiming to share progress with the math community. The release follows best practices developed in consultation with the independent Advisory Group on Mathematics and Artificial Intelligence at the Institute for Advanced Study.

Results are published in a GitHub repository that includes protocols for paper revisions and citations. To enhance transparency and verifiability, OpenAI is sharing formalizations of many proofs in Lean, a programming language that allows mathematical proofs to be checked by a computer. The repository will be updated with additional formalizations as they become available.

The release also details the methodology behind the results, including 10 summaries of the model’s reasoning and statistics on attempted problems. Compute usage was estimated in terms of ChatGPT Pro usage, with the average result requiring the equivalent of roughly three hours of ChatGPT Pro thinking.

OpenAI plans to fund workshops, conferences, and special programs focused on understanding these major AI-produced results. The company states it is working to responsibly release the model that generated these findings to empower scientists with state-of-the-art capabilities.