OpenAI Claims Navier–Stokes Singularity Proof
OpenAI says an internal model more capable than GPT‑6 Astra, run as roughly 10,000 coordinating agents, produced a proof and Lean formalization that Navier–Stokes solutions can blow up in finite time.
OpenAI said an unreleased internal model, run as a large multi-agent system, produced both a written proof and a Lean formalization showing that a three-dimensional incompressible Navier–Stokes flow starting smoothly from rest, under a smooth external force and with finite energy throughout, can blow up in finite time. The company says this settles statements "C" and "D" of the Clay Mathematics Institute's official formulation of the problem, one of the seven Millennium Prize Problems named in 2000 and open in some form for roughly 90 years. The claimed solution is described as an inward-spiraling vortex that elongates and shrinks while speeding up, with the equations' terms cancelling precisely enough to keep the applied force smooth as fluid velocity grows without bound.
The operational details are the other half of the disclosure. OpenAI says it began training the model on August 28, that training is ongoing, and that it is "significantly more capable than GPT‑6 Astra." After hearing rumors on September 1 that two Millennium problems had fallen, it pointed coordinating agent groups — with cached web access and code execution — at all of them, prompting separate groups with proof and disproof variants. Roughly 100 agents working about 50 hours first disproved regularity for the unforced Euler equations; the group that produced the Navier–Stokes result ran on the order of 10,000 concurrent agents.
The claim is first-party. Independent verification, Clay's assessment, and the model itself remain outstanding.