OpenAI Claims AI Has Solved 90-Year-Old Navier–Stokes Problem

OpenAI has announced that an internal artificial intelligence system has produced a proof that, according to the company, resolves the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems identified by the Clay Mathematics Institute. The problem, which has remained unresolved for roughly 90 years, asks whether smooth three-dimensional fluid motion governed by the Navier–Stokes equations can develop a singularity in finite time. These equations are fundamental to fluid dynamics and are used in areas including weather forecasting, aircraft design and the study of blood flow. OpenAI says its system demonstrated that a smooth fluid can develop a finite-time singularity through the dynamics of a tightening and stretching vortex while the fluid’s energy remains finite.

The claimed breakthrough was achieved using a large multi-agent AI system. OpenAI says around 10,000 agents worked concurrently on the Navier–Stokes problem, exchanging about 2.7 million messages and generating roughly 130 billion output tokens. The agents reached their result in about 88 hours, while formalisation and verification using Lean took another 17 hours. However, the announcement does not mean the problem has already been officially accepted as solved. The proof must undergo detailed scrutiny by independent mathematicians. The development has also triggered debate over related research by mathematicians Tristan Buckmaster and Levent Alpöge, although OpenAI has denied accessing their unpublished work and said its proof is substantially different.