OpenAI publishes 722 math manuscripts generated by unreleased AI model

Repository of math proofs

OpenAI published 722 manuscripts grouped into 372 result families on GitHub on Tuesday, October 6, 2026. Other sources catalogued the release as 377 distinct mathematical results. The repository covers fields such as algebra, number theory, theoretical computer science, mathematical logic, and topology. One paper in the release claims a proof of the Birch-Swinnerton-Dyer leading term formula for elliptic curves over rational numbers where the q-power Selmer group has a corank of zero or one at a prime q. OpenAI accompanied the papers with estimates of compute usage and summaries of the model reasoning process for 10 of the solutions. According to OpenAI, each result required compute equivalent to roughly three hours of thinking time on ChatGPT Pro.

The proofs were generated by an unreleased internal AI model that OpenAI began training on August 28, 2026. A portion of the proofs was formalized using Lean, an interactive theorem prover and programming language that enables automated verification of mathematical arguments. OpenAI stated in repository documentation that not all manuscripts have been formalized, acknowledging that some unformalized results might contain errors while adding that it will continue publishing formalizations and revisions.

Advisory group recommendations

The release follows consultations with the Advisory Group on Mathematics and Artificial Intelligence (AGMAI), an independent committee hosted at the Institute for Advanced Study in Princeton, New Jersey. The advisory group was formed to develop standards for communicating AI-generated mathematical findings. Melanie Wood, a mathematician at Harvard University serving on the advisory board, described the committee's objective in an email.

We want to create standards and practices so that results released from A.I. labs can be understood by mathematicians and can advance the field.

In late September, AGMAI published recommendations urging artificial intelligence laboratories to publish results through established academic channels, disclose compute resources and prompt records, and avoid using mathematical findings as promotional marketing vehicles. In a blog post published on September 29, the committee discouraged closed-door model evaluations.

At present, some frontier AI labs are testing advanced mathematical problems on proprietary models that remain inaccessible to the broader scientific community.

Academic concerns and past releases

Tensions between AI developers and the academic mathematics community had surfaced in preceding months. In August 2026, OpenAI convened approximately 40 mathematicians to discuss the consequences of AI systems solving open problems. Attendees, including Northwestern University mathematician Bryna Kra, asked OpenAI not to release hundreds of solutions simultaneously and requested explanatory papers that researchers could absorb and verify.

Apparently, that input was ignored.

In September 2026, OpenAI reported that the same internal model produced an exception disproving the Navier-Stokes equations, one of the Millennium Prize problems established by the Clay Mathematics Institute with a $1 million reward. That release generated debate over attribution when it emerged that the system finished work initiated by another team of mathematicians. OpenAI spokesperson Lindsay McCallum said the company is drawing on AGMAI recommendations to guide how it shares findings, while OpenAI committed to funding workshops, conferences, and research programs to assist mathematicians in evaluating the generated papers.