OpenAI reports that an internal AI system has produced a proof showing that the dynamics of the Navier-Stokes equations for fluid motion can develop a singularity in finite time. The solution, derived by a multi-agent system powered by a model significantly more capable than GPT-6 Astra, establishes statement "C" of the Millennium Prize formulation.
The system utilized approximately 10,000 concurrent agents that sent 2.7 million messages and used about 130 billion output tokens to resolve the problem in roughly 88 hours. The proof identifies a vortex structure where fluid speeds grow without bound while energy remains finite, marking a breakdown in the continuum approximation despite viscosity.
OpenAI released both a writeup of the analytical proof and a Lean formalization to inform the world about the pace of AI progress and the capabilities of upcoming frontier models.