OpenAI Claims Solution to Navier–Stokes Millennium Problem Amid Priority Dispute

OpenAI announced that an unreleased internal AI model produced a mathematical proof and Lean formalization resolving the Navier–Stokes existence and smoothness problem. However, the achievement has sparked controversy after NYU professor Tristan Buckmaster and Anthropic researcher Levent Alpöge raised concerns over research priority and user data access. If verified by the mathematical community, this would mark the first Millennium Prize Problem solved primarily by artificial intelligence, representing a major milestone for automated mathematical reasoning. It also intensifies discussions around AI research ethics, IP leakage from cloud coding tools, and competitive dynamics between major AI firms. OpenAI's process involved autonomous agents sending 2.7 million messages and consuming roughly 130 billion output tokens over 88 hours, followed by 17 hours of automated verification using GPT-6 Astra in Lean. Buckmaster questioned whether OpenAI had trained its internal model on their confidential Codex project sessions, though OpenAI denied looking up user data during the run.