On the Navier–Stokes Millennium Prize Problem

OpenAI has produced a proof resolving the Navier-Stokes existence and smoothness problem, one of mathematics' seven Millennium Prize Problems, using an internal AI system described as significantly more capable than GPT-6 Astra. The proof establishes that a smooth, initially resting fluid with finite energy can develop a velocity singularity in finite time, answering a question open for roughly 90 years. The solution was generated by approximately 10,000 concurrent AI agents over 88 hours, consuming 2.7 million messages and 130 billion output tokens, with Lean formalization completed in an additional 17 hours. The agents also independently resolved the related Euler equations regularity problem. OpenAI reached out to concurrent researchers at Anthropic and NYU after completing verification to coordinate announcement of the results.