On the Navier–Stokes Millennium Prize Problem
OpenAI claims to have solved the Navier–Stokes existence and smoothness problem, a major Millennium Prize challenge in mathematics. The proof, generated by an internal AI model, suggests that fluid motion dynamics can develop a singularity in finite time.
Why it matters
Solving this problem would be a monumental breakthrough in fluid dynamics, impacting fields from aerospace engineering to weather forecasting.
Loading… Share The problem The problem The result How we found the proof Concurrent work Progress and responsibility The problem The result How we found the proof Concurrent work Progress and responsibility 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.
The Millennium Prize Problems (opens in a new window) represent some of the deepest questions at the frontier of mathematics. The question of whether smooth three-dimensional fluid motion can break down has remained unresolved for roughly 90 years.
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