OpenAI Publishes 372 AI-Generated Math Solutions, Sparking Verification Debate

OpenAI released 722 mathematical manuscripts grouped into 372 result families on GitHub on Tuesday, all generated by an unreleased internal model. The collection spans algebra, number theory, theoretical computer science, mathematical logic, and topology, and includes progress on three Millennium Prize problems such as the Riemann and Hodge conjectures.

The company stated the model required an average of three hours of computing time per solution and that nearly all outputs came from a single prompt to a single agent. Only 162 of the 722 papers, roughly 22 percent, include Lean-formalized main results that mechanically verify every logical step.

“Until and unless they release the model and people can replicate their results, I think you should treat any claims about one-shotting problems with a single agent as unverified.”

MIT mathematician Andrew Sutherland said the single-prompt claim remains unverified until the model is released and the prompts are disclosed. He and other researchers have demanded independent replication before accepting the results.

The publication follows OpenAI's September claim of solving the Navier-Stokes equations, another Millennium Prize problem. That announcement triggered allegations from NYU professor Tristan Buckmaster that the AI solution closely mirrored his unpublished work, which he had checked using OpenAI's Codex tool.

OpenAI said it followed guidelines from its Independent Advisory Group on Mathematics and AI, hosted at the Institute for Advanced Study in Princeton. The company pledged to release the model responsibly after further evaluation and community feedback.