OpenAI says it solved Navier-Stokes. Nobody has seen the proof.

OpenAI says an internal model proved that 3D Navier-Stokes can develop a singularity in finite time, using about 10,000 agents over 88 hours. It described the result on a press call and had not published the proof. Tristan Buckmaster and Levent Alpoge, working on related problems, published preprints with Lean formalisations that anyone can machine-check.

OpenAI says an internal model more capable than GPT-6 Astra produced a proof that the three-dimensional Navier-Stokes equations can develop a singularity in finite time. Madison Mills reported the claim and the dispute around it for Axios.

The company says the effort started on 1 September. Roughly 10,000 concurrent agents reached the result in about 88 hours, at a cost it puts in the millions of dollars.

What has actually been published

Tristan Buckmaster of NYU and Levent Alpöge of Anthropic posted preprints on closely related problems. They cover finite-time blowup for the incompressible porous medium equation, the 2D Boussinesq system and the 3D incompressible Euler equations.