OpenAI Claims Proof of Singularity in Navier-Stokes Equations

We’re sharing a solution to the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems.

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 ti…

Our system produced an analytical proof and a Lean formalization that an initially smooth fluid at rest can develop a singularity in a finite time. The fluid has a smooth force applied to it, and its energy remains finite through the entire dynamics, from rest to the formation o…