A.I. May Have Solved a Longstanding Math Problem With a Million-Dollar Prize. It Ignited a Controversy Over Who Gets Credit

The Navier-Stokes problem, a famous theoretical math problem regarding the movement of fluids, has stumped mathematicians for almost 200 years. At the turn of the 21st century, the Clay Mathematics Institute decided that it would award $1 million to whoever solved it. Twenty-six years later, a solution may have finally come to light—but it wasn’t a mathematician who came up with it.

On Tuesday, OpenAI, the developer of ChatGPT, announced in a blog post that an “internal OpenAI system” had just found a solution to the longstanding puzzle. The company used around 10,000 artificial intelligence “agents,” or bots, that worked largely autonomously on the Navier-Stokes equations for 88 hours, using computational power that likely cost millions of dollars. OpenAI’s breakthrough is the latest indication that A.I. models can crack mathematical conundrums that have long eluded humans.

But the feat has also sparked a controversy: While the Navier-Stokes problem may have been solved by A.I., the achievement has become contentious because of a possible association with the work of two human researchers—one of whom is employed by OpenAI’s rival company Anthropic. This story starts some 200 years ago, when Claude-Louis Navier and George Gabriel Stokes wrote equations to describe how fluids move. Since then, mathematicians have been investigating whether these equations work in all situations or whether they allow for a theoretical case in which a small part of the fluid moves infinitely quickly and the solution breaks down—or “blows up.” So, in its simplest terms, the problem is a yes or no question—to solve it, one must either prove that the equations always result in smooth solutions or find one specific situation where they don’t.

OpenAI claims to have found one such “blowup” scenario, involving a vortex of fluid that spirals inward and becomes stretched out, like spaghetti. The company says it verified its A.I. agents’ work with a programming language called Lean. We’re sharing a solution to the Navier-Stokes Millennium Prize Problem, one of the deepest problems at the frontier of mathematics.The proof was produced by a group of agents, using an OpenAI next-generation model significantly more capable than GPT-6 Astra.The problem… pic.twitter.com/8zol3BPTL4 Navier-Stokes might seem like a wildly theoretical consideration, far removed from the daily life of the average person.

Its equations assume that fluids are smooth and continuous, while in the real world, of course, they are made of atoms and molecules. (This means that no “blowup” scenario could happen in real life.) Still, the equations involved with the problem are used in the field of fluid dynamics for applications such as designing aircraft and creating climate models. Because of the longstanding interest in these equations, Navier-Stokes, officially called the Navier-Stokes existence and smoothness problem, is one of seven mathematical problems with a $1 million award offered for each solution—they’re known collectively as the Millennium Prize Problems. Now, the question of who should get credit in the face of OpenAI’s announcement is attracting attention.

Key context: A.I. solves famous math problems Artificial intelligence has already been used to solve multiple decades-old math problems this year. An OpenAI internal model found a clever solution to an “Erdős problem” posed in 1946. The mathematician Levent Alpöge also used one of Anthropic’s A.I. models to disprove the Jacobian conjecture.