OpenAI’s Navier-Stokes solution looks like a win for mathematics. But some mathematicians aren’t so sure.

OpenAI has announced one of its unreleased artificial intelligence models has found an answer to one of the biggest open questions in mathematics, the Navier-Stokes Millennium Prize problem. The Millennium Prizes offer million-dollar rewards for solutions to seven notoriously difficult mathematical puzzles, and until now only one had been solved.

Mathematical problems at this level are extremely complex. A solution to the similarly difficult ABC conjecture ran to more than 500 pages, and it took mathematicians six years to understand it enough to spot potential flaws. Researchers can devote entire careers to these problems, in the hopes of getting close to a solution.

And this is what seems to have happened here. Building on the work of several human mathematicians, OpenAI unleashed a swarm of 10,000 AI agents running a new experimental model, which churned through millions of dollars’ worth of computing power in the space of a few days to complete what the American Mathematical Society called “the final steps” of the solution process.

So what is the Navier-Stokes problem, and what did OpenAI do? And why are a lot of mathematicians impressed with the result but unimpressed with the AI company’s behavior?

OpenAI’s announcement concerns the Navier-Stokes equations, which model the behavior of fluids such as water and air. These equations underpin modern science and engineering, but our mathematical understanding of them is incomplete.

To explain the problem, imagine looking at the flow of water, before zooming in with a camera .

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