A next-generation internal OpenAI model working through about 10,000 concurrent agents produced a proof that smooth three-dimensional fluid motion can develop a finite-time singularity under a smooth external force, the company said. OpenAI said the effort reached a result in about 88 hours, GPT-6 Astra then spent another 17 hours formalizing and verifying the proof in Lean, and the work used millions of dollars of computing power. The Navier-Stokes Millennium Prize Problem has remained unresolved for roughly 90 years.

OpenAI said the construction uses smooth external forcing and that outside mathematicians still need to inspect the proof. The company also said its researchers and agents did not see Tristan Buckmaster and Levent Alpöge's work before it was released publicly, though it could not rule out that de-identified data from use of its products helped improve its models. Buckmaster said that amounted to using customer data to try to scoop a customer.