OpenAI shares summaries of math problems solved by its unreleased model

OpenAI has released 722 manuscripts covering 372 families of mathematical results, including solutions to hundreds of open questions.

In September, OpenAI said an unreleased frontier model had solved the nearly 90-year-old “Navier-Stokes” problem, one of mathematics’ most famous open questions, in a breakthrough that stunned the mathematics community. Now, the company has released 722 manuscripts covering 372 families of mathematical results, including solutions to hundreds of open questions.

 

OpenAI has published the papers on GitHub alongside summaries of the reasoning produced by its internal frontier model, estimates of the compute used and statistics on the number of problems it attempted.

 

OpenAI said the average result required compute equivalent to roughly three hours of ChatGPT Pro thinking. It has also released formalised versions of many of the proofs in Lean, “a programming language that allows mathematical proofs to be checked by a computer". OpenAI said it will update the repository with more formalisations as they become available.

 

The company said it consulted the independent Advisory Group on Mathematics and Artificial Intelligence (AGMAI) at the Institute for Advanced Study to develop best practices for releasing the results, and drew on the group’s advice and public recommendations. 

 

OpenAI formed AGMAI, an independent panel, to advise it and other AI companies on their interactions with mathematical research and the wider mathematics community, including how new results are presented and released.

 

The panel was formed after OpenAI said later in September that an internal AI model had resolved more than 100 long-standing open problems in mathematics in less than a month of training.

 

The advisory panel had urged AI companies to publish mathematical results promptly, disclose details including the model, prompts and compute used, and avoid turning such breakthroughs into marketing exercises.

 

OpenAI said it is publishing the results in a GitHub repository with protocols for revisions and citations, while continuing to explore community-hosted alternatives. The company also said it plans to improve the quality of future releases through better citations, mathematical exposition, and presentation of the results.