OpenAI's 722 machine-written math manuscripts land on mathematicians to verify as Terence Tao warns of a rush to "flatten" open problems

On October 6, OpenAI published 722 mathematical manuscripts, grouped into 372 families of related results, in a public GitHub repository called openai/math. All of them were produced by an internal frontier model that the company has not released. OpenAI says the same model generated its earlier claimed solution to the Navier-Stokes existence and smoothness problem. OpenAI has published neither the model nor the exact prompts, so outside researchers can check the outputs but cannot reproduce how they were made.

Formal verification covers only part of the release. The repository's formalization catalogue shows Lean proofs for the main result of 162 of the 722 papers (Lean is a computer program that checks mathematical proofs step by step), and 235 of the 372 families link to a Lean page. The README itself warns that some unformalized results could contain errors. A machine-checked proof also has a limit: it does not show that the formal statement matches the theorem a mathematician cares about. Gadget Review reports that the Clay Mathematics Institute still lists Navier-Stokes as active. Tristan Buckmaster, a mathematician at New York University, and Andrew Sutherland have both questioned whether OpenAI vetted the results and want the claims treated as unverified until someone reproduces them independently.

Terence Tao, the Fields Medalist who sits on the advisory group OpenAI set up to coordinate these releases, responded on Mastodon. He wrote that "even the rumor of someone working on a problem can trigger a massive amount of AI-powered effort to flatten it before the original research project has time to reach its full potential." On October 7, Tao's blog published a statement on the release. Tao's warning points to a specific case. OpenAI has said its Navier-Stokes work began after it heard that Buckmaster and Levent Alpöge had made progress on a related problem. Buckmaster says OpenAI's proof follows a path suspiciously close to his own. He also says he had used OpenAI's Codex to check his work. Sébastien Bubeck of OpenAI denies that he ever asked for Alpöge to be removed from authorship.

Without the model, OpenAI's capability claim cannot be tested in the usual way. No benchmark, held-out problem set, or third-party evaluation accompanies it. The only available evidence is the outputs themselves, and checking them takes a great deal of expert labor, most of it unpaid.