OpenAI says AI model solved one of mathematics' Millennium Prize Problems

Unreleased AI model takes 88 hours, uses up to 10,000 AI agents working in parallel to solve the Navier-Stokes problem

OpenAI said on Tuesday that an unreleased artificial intelligence (AI) model had solved the Navier-Stokes existence and smoothness problem, one of mathematics' seven famed Millennium Prize Problems.

The company said the model took 88 hours to produce the solution, deploying as many as 10,000 AI agents working in parallel, in what could mark one of the most significant demonstrations yet of AI's growing ability to tackle advanced mathematical research.

The Navier-Stokes problem concerns equations used to describe the motion of fluids such as water and air, and asks, broadly, whether their solutions always remain well-behaved or could develop singularities under certain conditions.

OpenAI's proof claimed to show such a breakdown, or "blowup," answering a problem that had remained unresolved for decades.

We’re sharing a solution to the Navier-Stokes Millennium Prize Problem, one of the deepest problems at the frontier of mathematics.

The proof was produced by a group of agents, using an OpenAI next-generation model significantly more capable than GPT-6 Astra.

The problem… pic.twitter.com/8zol3BPTL4

— OpenAI (@OpenAI) September 8, 2026

The problem was one of seven Millennium Prize Problems designated by the Clay Mathematics Institute in 2000, with a $1 million prize offered for a correct solution to each. Only one of the seven had previously been solved.

OpenAI also released a paper detailing its proposed solution, including a proof written in Lean, a programming language and theorem-proving system used to verify mathematical arguments formally.

Read: OpenAI unveils new ChatGPT with enhanced reasoning capabilities for Math and Science problems

The claim, however, would require scrutiny by the wider mathematical community before the problem could be considered definitively settled.

The announcement came amid a dispute about parallel research by New York University mathematician Tristan Buckmaster and Levent Alpoge, a mathematician working at rival AI company Anthropic. OpenAI acknowledged that it intensified its work on the problem after learning that other mathematicians were pursuing a similar direction, but said it had not seen their work.

We congratulate Levent Alpöge and Tristan Buckmaster on their remarkable mathematical work.

We (the researchers and the agents) did not see any of their work through any means until they released it publicly — in particular, no specific user data was accessed in order to solve… https://t.co/otJKRHnQgb

— OpenAI (@OpenAI) September 8, 2026

The development highlights the rapidly expanding role of AI in higher mathematics, after AI systems in the last year solved several longstanding problems that had resisted mathematicians for years or decades.