OpenAI's internal model solves one of the seven problems of the Millennium Prize

Ten thousand agents mobilized for 88 hours produced proof showing that the Navier-Stokes equations can, under certain conditions, cease to have a regular solution.

On September 8, OpenAI published proof, produced by an internal model not yet publicly released and more advanced than GPT-6 Astra, providing an answer to the Navier-Stokes existence and regularity problem — one of the seven Millennium Prize problems posed by the Clay Mathematics Institute, each with a $1 million award. The model mobilized about 10,000 agents working in parallel, to arrive at a solution in about 88 hours.

The proof describes a configuration in which a vortex tightens and accelerates indefinitely in finite time — what mathematicians call a finite-time explosion — while keeping total energy bound, demonstrating that regular three-dimensional fluid motion can break. OpenAI made available both the full writing of the proof and its formalization in the Lean language, allowing for independent verification by the mathematical community.