OpenAI Says AI Proved 90-Year Navier-Stokes Blowup, Formalizing Result in Lean
Updated
Updated · OpenAI · Sep 8
OpenAI Says AI Proved 90-Year Navier-Stokes Blowup, Formalizing Result in Lean
3 articles · Updated · OpenAI · Sep 8
Summary
An internal OpenAI system produced a proof that smooth 3D incompressible Navier-Stokes flow can develop a finite-time singularity, resolving one of the seven Millennium Prize Problems, the company said.
The result shows an initially smooth fluid at rest, driven by a smooth external force, can form a vortex whose speed blows up while total energy stays finite; OpenAI released both a writeup and a Lean formalization.
OpenAI said the effort used a model more capable than GPT-6 Astra and a multiagent setup of about 10,000 concurrent agents; the Navier-Stokes proof emerged roughly 88 hours after launch, with verification taking another 17 hours.
Across the project, agents sent 4.9 million messages and used about 300 billion output tokens, including 2.7 million messages and 130 billion tokens on Navier-Stokes alone.
The announcement lands amid a credit dispute: OpenAI says it contacted Tristan Buckmaster and Levent Alpöge after finishing its proof, recognized their priority on forced Euler work, and denied accessing their unpublished results.