
openai.com
September 8, 2026
7 min read
62/100
Summary
On the Navier–Stokes Millennium Prize Problem We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. This proof, produced by an internal OpenAI system, shows that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. We’re sharing both a writeup of the proof and a formalization in Lean. ...