by Ali Azhar | September 15, 2026

OpenAI says one of its AI systems has solved a math problem that has stumped mathematicians for nearly a century. The Navier–Stokes problem is one of seven Millennium Prize Problems, some of the toughest problems in mathematics, with a $1 million prize attached to each one. If OpenAI’s proof holds up, it would be a major achievement for maths and another sign of how quickly AI is moving into scientific discovery.

But there’s already a dispute over how OpenAI got there. Two mathematicians had been working on a related solution using OpenAI’s own Codex, and they now have questions about whether their work could have influenced OpenAI’s AI and who should get credit.

The reason this is such a big deal goes back to a question mathematicians have been unable to answer for such a long time.

The Navier–Stokes equations are used to describe the movement of fluids. They can model everything from water flowing through pipes to air moving around an aircraft. We know the equations work and they are widely used, but mathematicians still don’t know whether their solutions will always behave smoothly in three dimensions.

The question is whether a fluid that starts in a smooth state can eventually reach a point where the math essentially breaks down. This is known as a singularity, and proving whether one can occur is at the heart of the Navier–Stokes problem.

(A snapshot of local incompressible motion. Orange marks faster angular rotation; teal marks slower rotation. Circulating speed also depends on radius. The trajectories show inward spiraling and axial stretching. Source:OpenAI)

OpenAI says its AI has shown that this kind of breakdown is possible. In the solution, the fluid forms a vortex, or a spinning swirl, that gets tighter and faster. As the vortex gets smaller, the speed keeps rising until it becomes infinite, while the total amount of energy remains finite.

Does this finally settle the Navier-Stokes problem? Well, that’s what OpenAI claims. It says that its system produced the mathematical proof needed to solve the problem. OpenAI also released a version in Lean, a tool used to formally check mathematical proofs.

How OpenAI got there is almost as interesting as the result itself.

On September 1, after hearing rumors of major progress on the Millennium Prize problems, the company decided to put its new internal AI model to work on them. OpenAI claims the model is significantly more capable than GPT-6 Astra.

The big break came when the AI solved a related problem involving the Euler equations, which are similar to Navier-Stokes but without viscosity. That convinced OpenAI to focus its resources on Navier-Stokes.

And it threw a lot of resources at it. Around 10,000 AI agents worked on the problem, trying different approaches and sharing useful findings. It took them about 88 hours to reach the result, generating 2.7 million messages and roughly 130 billion output tokens along the way. Formalizing and verifying the proof in Lean took another 17 hours.

But the timing of all this has become part of the controversy.

NYU mathematician Tristan Buckmaster and Anthropic mathematician Levent Alpöge had already been working on related research using several AI tools, including OpenAI’s Codex. Their work had produced a result on the Euler equations, which they had verified in Lean and were preparing for publication.

Buckmaster contacted OpenAI on September 3 to say the pair were close to releasing a paper and formal proof, although he did not tell the company which problem they were working on. According to Buckmaster, discussions later became contentious, including a proposal that would have given him authorship but left Alpöge off the work.

OpenAI tells the story differently. The company says it reached out after completing its proof and offered to announce the results together while recognizing Buckmaster and Alpöge’s earlier work. OpenAI also says the two teams ultimately solved different problems: Buckmaster and Alpöge worked on a version of the Euler problem with an external force, while OpenAI’s AI solved a version without one.

(Performance of GPT-6 Astra and our Internal Model on a curated set of open math problems. Source:OpenAI)

There was also another uncomfortable question: Could OpenAI’s AI have learned anything from the pair’s use of Codex?

OpenAI says neither its researchers nor its AI agents saw their work before it became public, and that no specific user data was accessed to solve Navier-Stokes. But the company does leave one possibility open. It says it “cannot rule out” that de-identified data from the researchers’ use of its products helped improve its models.

As HPCwire reported in May, Google is also making a major push into AI for science. OpenAI’s Navier-Stokes result shows how quickly the field is advancing.

If the proof holds up, AI will have helped solve a problem that generations of mathematicians could not. That would be a big step beyond using AI to summarize research, write code or help scientists analyze their work. It would show that these systems can start taking on some of the unanswered questions themselves.

It points toward a future where AI doesn’t just help scientists work faster, but takes on problems they have been unable to solve themselves. Mathematics may be an early proving ground, but the same approach could eventually be used to search for breakthroughs in physics, biology, materials science and other fields. For OpenAI, Navier-Stokes could be an early glimpse of that shift.