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

OpenAI announced a solution to the Navier-Stokes problem. But could its A.I. models have used data from two mathematicians working on a similar breakthrough?

Margherita Bassi | Daily Correspondent

September 10, 2026 4:23 p.m.

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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.

“It’s undeniable that symbolically, it’s a big moment—and the next in a natural chain of big moments,” Timothy Gowers, a mathematician at the Collège de France, tells the Wall Street Journal’s Ben Cohen, though he notes he hasn’t read OpenAI’s paper regarding the achievement yet.

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

— OpenAI (@OpenAI) September 8, 2026

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.

“These questions are lighthouses,” Terence Tao, a mathematician at the University of California, Los Angeles, tells the New York Times’ Cade Metz. “They are great focus points that attract the efforts of human scientists.”

In fact, two human scientists were also working on the Navier-Stokes problem when OpenAI instructed its agents to find a solution. Now, the question of who should get credit in the face of OpenAI’s announcement is attracting attention.

The company writes in its blog post that it was inspired to address the open Millennium Prize problems after hearing rumors that two of them had been solved. OpenAI began work on September 1, later realizing that the rumors regarded Anthropic mathematician Levent Alpöge and New York University mathematician Tristan Buckmaster, according to the post.

In a statement, Buckmaster writes that he and Alpöge had made significant progress on the Navier-Stokes problem but had not yet published their work. He explains that they used large language models, including OpenAI’s Codex. In a conversation with employees of OpenAI, “I asked whether the model had been trained on, or had access to, our sessions in Codex, into which we had been putting all our drafts for the whole of this project,” Buckmaster writes. “I was told the model did not look up user data. I asked again, about training, and I did not get an answer.”

“I do not know whether our data was used,” he adds. “I am not accusing anyone of anything.”

Joseph Perla, CEO of TrustedRouter, an OpenAI-compatible software company, seems to have already landed on a verdict. “This is what all the labs do every day. Read your chats and copy ideas,” he tells Axios’ Madison Mills.

OpenAI maintains that its researchers and A.I. agents didn’t see Buckmaster and Alpöge’s work until it was released to the public, and that “no specific user data was accessed in order to solve this problem.” But in the blog post, they also write that “while unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models.”

On Wednesday evening, the company offered a more strongly worded statement to the New York Times: “We can say categorically that it is impossible for Dr. Buckmaster’s Codex prompts over the last two months to have influenced the system in any way, including training.”

Buckmaster, meanwhile, attributes much of his success to the earlier work of Diego Córdoba and Luis Martínez-Zoroa, who had taken steps toward “blowing up” the problem. He and Alpöge used large language models to build on the pair’s ideas. “Let me make plain what I have said to colleagues in private,” Buckmaster writes in his statement. “In view of this body of work, I believe Luis Martínez-Zoroa deserves a Fields Medal.”

OpenAI, according to its post, will not be claiming the $1 million Millennium Prize. However, who (or what) will ultimately get credit for the winning Navier-Stokes solution still appears uncertain.

Margherita Bassi is a freelance journalist and trilingual storyteller. Her work has appeared in publications including BBC Travel, Discover magazine, Live Science, Atlas Obscura and Hidden Compass.