OpenAI solves the Navier-Stokes millennium problem

OpenAI claims to have found a solution to one of the seven Millennium Prize Problems posed by the Clay Mathematics Institute ($1M per prize) — the Navier-Stokes equations. In order to do this, they used about 10,000 cooperating AI agents with an internal model which is much stronger than GPT-6 Astra. It took them 88 hours and several million dollars of computing power to generate the proof.

1Why Navier-Stokes Is a Big Deal

The Navier-Stokes equations are the equations governing the flow of fluids and gasses. They are used in jet engines, weather modeling, etc. Though the equations have been used in engineering for 125 years, they have never been proven to exist or be smooth in 3 dimensions. The Clay Institute is offering $1M for this proof, one of seven Millennium Prize Problems created in 2000. The only Millennium Problem to be solved so far was the Poincare Conjecture, solved by Grigori Perelman in 2003.

The proof generated by OpenAI’s algorithm has been formalized in the Lean mathematical proof assistant, which guarantees zero human errors during the verification process. Lean provides a way for a computer to verify each line of reasoning in the proof.

2The Authorship Controversy

NYU mathematician Tristan Buckmaster claimed that OpenAI probably obtained his method from the query log of his Codex requests (which OpenAI claims the right to use for model training). Sébastien Bubeck, an OpenAI researcher, requested that Buckmaster drop Levent Alpöge (Anthropic employee) as a co-author, saying “Why would you want to ruin your career?” Buckmaster declined, to which Bubeck replied “If you don’t want me to be polite, I don’t have to be”. OpenAI claims they did not see Buckmaster’s work until after it went public.

This new development creates a divide in academia, where AI labs will be able to bypass discoveries in pure math by the availability of computational power that a single researcher could never match. Now the competition is not over benchmarks anymore, but in the realm of fundamental science.