OpenAI reports a proof for a Millennium Prize problem
OpenAI says an experimental AI system has produced a proposed solution to the Navier-Stokes existence and smoothness problem. The problem is one of the seven Millennium Prize Problems, and it carries a $1 million prize. The equations describe how fluids like water and air move. The unsolved question asks whether a smooth flow can eventually break down and create speeds that grow without limit.
The company says its system found that it can. The proof describes a fluid vortex that stretches and concentrates until its speed blows up in finite time, while total energy stays finite. That result would conflict with the usual understanding of real fluids. At extreme scales, the assumption that a fluid is one continuous substance would stop matching physical reality.
How the system worked
OpenAI says the result came from an internal model that is much more capable than GPT-6 Astra, its most advanced public model. Around 10,000 agents exchanged 2.7 million messages and generated roughly 130 billion tokens while working on Navier-Stokes. Astra then spent another 17 hours formalizing and checking the proof. The company published the proposed solution, but outside verification will take time.
The practical impact is not immediate. Navier-Stokes equations are used in aircraft design, weather forecasting and blood-flow research. A better understanding of where the equations break down could help scientists model extreme and turbulent flows later. That is the cautious hope, at least. I think the more interesting part is the method. If thousands of AI agents can attack a 90-year-old math problem in days, the same approach might be tried on hard problems in materials science, energy, aerospace and medicine.
Mathematicians push back
Not everyone is convinced. NYU mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge were separately working on a related fluid-dynamics problem. They had used AI tools during their research. Buckmaster has questioned whether unpublished work entered into OpenAI products could have influenced the company’s model. He made the argument in a series of posts on Mastodon. OpenAI has not settled that concern publicly.
The dispute matters because math relies on independent checking. A proof posted by a company is not the same as a proof accepted by the field. The Navier-Stokes claim may be correct, or it may have gaps. Mathematicians will now fight over the details. That fight is normal. It is also how hard problems get resolved.
