OpenAI says its AI solved the Navier-Stokes Millennium Prize problem — mathematicians want independent proof

#What happened

OpenAI announced on Tuesday that an internal AI system has solved the Navier-Stokes problem, one of the Clay Mathematics Institute's famous Millennium Prize questions. The equations describe how liquids and gases move, and ask whether the mathematics can suddenly break down under certain conditions; a correct solution carries a $1 million prize. OpenAI said around 10,000 AI agents worked on the problem for roughly 88 hours, exchanging millions of messages and generating around 130 billion output tokens before producing a computer-verified proof. The company says the result satisfies the official wording of the prize problem but does not intend to claim the money, and presented the feat as evidence of how rapidly its internal AI systems are advancing. Verified Oct 18, 2026.

#Why it matters

The announcement drew mixed reactions. Some researchers called it an exciting day for mathematics; others accused OpenAI of exaggerating the achievement to boost excitement and valuation ahead of a potential IPO. NYU mathematician Tristan Buckmaster accused OpenAI of throwing massive resources at the problem only after learning that he and Anthropic researcher Levent Alpöge were making progress on a related approach. Diego Cordoba, whose work helped pioneer the approach used by the AI, said a valid solution would be a "big surprise." Mathematicians cautioned against declaring the problem solved before the proof is independently examined. OpenAI acknowledged the project began after hearing rumors that outside mathematicians had made progress on related problems, but denied accessing their unpublished work; it said it could not rule out that anonymized data from their use of OpenAI products had helped improve its models.