OpenAI AI System Claims to Solve Navier-Stokes Millennium Prize Problem

OpenAI announced on September 8, 2026, that an internal AI system had solved the Navier-Stokes existence and smoothness problem, one of seven Millennium Prize Problems set by the Clay Mathematics Institute in 2000, each carrying a $1 million reward. The AI determined that mathematical singularities — points where fluid velocity becomes infinite in finite time — can genuinely occur within the equations, meaning the equations themselves break down under certain conditions. The proof was produced by a multi-agent system of roughly 10,000 simultaneous agents working for 88 hours, exchanging 2.7 million messages and consuming approximately 130 billion output tokens, at a cost estimated by OpenAI executives at several million dollars. GPT-6 Astra subsequently formalized the proof in the Lean verification language within 17 hours, and both the analytical proof and its formal verification have been made publicly available. The result still awaits broader peer review by the mathematical community before it can be considered definitively verified.