On the Navier–Stokes Millennium Prize Problem

OpenAI announced a solution to the Navier–Stokes existence and smoothness problem, a Millennium Prize Problem, demonstrating that the equations for fluid motion can develop a singularity in finite time. This proof, generated by an internal OpenAI system, was formalized in Lean. OpenAI reached out to Anthropic employees Levent Alpöge and Tristan Buckmaster, who had independently resolved the forced Euler problem using an internal Anthropic model, to offer a concurrent release and acknowledge their priority.

This report uniquely details how OpenAI's internal AI system solved the Navier–Stokes problem, unlike other accounts focusing on the Anthropic team's parallel efforts.