Finite Time Blowup for Navier–Stokes and Euler

OpenAI's claim on a Millennium Prize problem. The 166-page paper, authored simply "OpenAI," states as Theorem 1.1 that for every viscosity there exist a smooth, compactly supported force and a solution of the 3D incompressible Navier–Stokes equations starting from rest whose velocity becomes unbounded in finite time while its kinetic energy stays uniformly bounded, on R³ and on the torus, which are breakdown alternatives (C) and (D) in the Clay Institute's problem statement (the forced versions, not the unforced Cauchy problem). A companion paper constructs smooth, compactly supported, divergence-free initial data whose unforced Euler solution blows up. Both results are formalized in Lean 4 (4.34.0-rc2 with Mathlib) in a repository that reached 1,750 stars on its first day.

OpenAI's blog is blocked to crawlers, so the run details rest on press coverage: roughly 10,000 concurrent agents on an unreleased model it describes as more capable than GPT-6 Astra, with the Navier–Stokes result reached on September 5 after about 88 hours and Astra handling the Lean formalization. The result awaits independent mathematical review, and the announcement drew a priority dispute. Two smaller Lean repositories on prime gaps preceded it on September 2.