OpenAI says it has achieved a breakthrough on one of mathematics’ most difficult problems, claiming that its artificial intelligence systems have produced an answer to the Navier-Stokes existence and smoothness problem, a challenge that has remained unresolved for nearly 90 years.
The reported achievement came after OpenAI deployed around 10,000 AI agents powered by a new internal model. According to the company, the systems worked for roughly 88 hours, exchanging nearly three million messages and generating about 130 billion output tokens. OpenAI estimates that reproducing the computational effort using its current pricing could cost around $10 million.
The significance goes beyond the speed of the calculation. Navier-Stokes equations are fundamental to understanding how liquids and gases move and are closely connected to the scientific challenge of explaining turbulence. The problem is one of the seven Millennium Prize Problems, each carrying a $1 million reward for a verified solution.
But this is not yet a formally accepted mathematical solution. OpenAI says its work addresses two of the four statements required under the Millennium Prize formulation and that it does not intend to claim the prize. Independent mathematicians must still examine the proof before the broader mathematical community can determine whether the claim stands.
The announcement has also triggered questions over how the result was reached. NYU mathematician Tristan Buckmaster has raised concerns about the timing because he and Anthropic-linked mathematician Levent Alpöge were independently working on the problem using OpenAI’s Codex. OpenAI denies accessing their work and says its proof differs significantly.
For AI, the bigger story may therefore be the method rather than the prize. If independently validated, the experiment would suggest that coordinated AI agents can attack mathematical problems previously considered beyond practical machine reasoning—potentially changing how difficult scientific research is approached.
