OpenAI says an unreleased AI model has solved the Navier-Stokes existence and smoothness problem, one of seven Millennium Problems selected by the Clay Mathematics Institute in 2000. The result marks a significant step in AI’s growing ability to tackle mathematical questions that have challenged researchers for decades, tells The New York Times (full article available to subscribers).
The Navier-Stokes equations describe the movement of water and other fluids and are widely used in applications such as weather prediction. The Millennium Problem asks whether these equations can mathematically break down under certain conditions. OpenAI says its proof identifies such a situation. Although this could theoretically suggest unusual physical behavior, mathematicians and physicists do not expect the mathematical breakdown to occur in the real world.
OpenAI reports that its model reached the solution in 88 hours using as many as 10,000 AI agents working together. Researchers helped by transferring promising ideas among different groups of agents. The process was computationally expensive and likely cost millions of dollars.
The achievement reflects rapid improvements in AI-based mathematics. Neural networks can be refined through reinforcement learning, allowing models to test different approaches and learn which methods produce correct results. Mathematics is particularly suited to this technique because solutions can often be objectively evaluated. AI systems can also use Lean, a programming language for formally verifying mathematical proofs.
OpenAI released a paper describing its solution along with a Lean proof so outside mathematicians can evaluate the claim.
The development has also intensified debate about AI’s impact on mathematics. UCLA mathematician Terence Tao warns that solving difficult problems is valuable partly because the effort itself generates knowledge and develops human understanding. If AI quickly produces solutions, researchers may spend less time exploring alternative approaches.
OpenAI’s result therefore represents more than progress on a famous problem. It highlights a broader shift in mathematical research, where AI may increasingly participate directly in discovering and proving new mathematics.
