OpenAI Announces AI‑Generated Solution to Navier‑Stokes Millennium Problem

OpenAI announced that one of its AI systems has produced a proof that the Navier‑Stokes equations can develop blow‑ups, a result that satisfies the Clay Mathematics Institute’s Millennium Prize Problem. The company deployed 1,000 agents to find blow‑ups in the related Euler equations, completing the task in 50 hours, before scaling to 10,000 agents that extended the finding to the full Navier‑Stokes system in just 11 hours. OpenAI said the effort would cost about $15 million for a customer to replicate. The claim follows earlier AI breakthroughs on long‑standing conjectures, but it has sparked controversy after mathematicians Tristan Buckmaster and Levent Alpöge raised concerns about the transparency of the method and the use of their prior work. OpenAI denied using their proofs or data and said its agents operated independently. The Clay Mathematics Institute will now review the proof before deciding on the $1 million prize.