OpenAI Uses 10,000 AI Agents to Solve Navier-Stokes Millennium Prize Math Problem
OpenAI claims its AI model, backed by 10,000 agents, solved the Navier-Stokes Millennium Prize problem in 88 hours. The breakthrough sparked a fierce academic dispute over independent research timing.
If the proof published by OpenAI holds up under peer review by mathematicians, it may well be remembered as a watershed moment when artificial intelligence leveled up. According to the company, a new internal model significantly more capable than GPT-6 Astra succeeded, with the help of roughly 10,000 AI agents working simultaneously, in solving within 88 hours a mathematical question that specialists have wrestled with for nearly 90 years.
The problem in question is the existence and smoothness of the Navier-Stokes equations, which describe the motion of fluids and gases. They are utilized in aircraft design, weather forecasting, and blood flow research, among other fields. The catch is that while the equations work remarkably well for countless practical applications, no one has been able to prove mathematically that in three dimensions they always continue to behave smoothly, or whether under certain conditions a singularity might develop—a point where the mathematical velocity of the flow grows infinitely large in finite time.
In the year 2000, the Clay Mathematics Institute placed the question on its list of seven Millennium Prize Problems, offering a $1 million reward for its solution. To date, only one of the seven has been officially solved: the Poincaré conjecture, which was resolved by Grigori Perelman, who famously declined the prize. As of this morning, the Clay Institute website still lists the Navier-Stokes problem as unsolved.
The Vortex That Turns to Spaghetti and Accelerates Without Bound
OpenAI claims its system has successfully demonstrated that this mathematical breakdown can indeed occur.
The proof describes a fluid starting from rest and acted upon by a smooth external force. Within the flow, a vortex forms, spiraling inward, contracting in width while simultaneously growing longer and thinner. The company compares it to a strand of spaghetti being stretched further and further.
As the region where the motion takes place shrinks, the flow velocity inside it increases relentlessly—until it becomes unbounded in finite time, even though the total energy remains finite.
This does not mean one can create a vortex in a kitchen that reaches infinite speed; a real fluid cannot do that. If the proof is correct, it means that under certain conditions the equations themselves reach a point where their continuous model can no longer describe physical reality.
There is also an important mathematical caveat. The way OpenAI reached this singularity relies on a smooth external force applied to the fluid. This possibility is explicitly mentioned in the official formulation of the Clay Institute Millennium problem, and OpenAI's paper states that the proof satisfies two of the alternatives sufficient to settle the question.
However, the version without an external force is the one many mathematicians have considered for years to be the intuitive core of the problem—and it is not what OpenAI claims to have solved here. Therefore, even if the proof is validated, a debate is expected over its broader mathematical significance.
10,000 Researchers Who Never Need to Sleep
No less extraordinary than the result itself is the method OpenAI employed to achieve it.
On August 28, the company began training a new internal model, which it stated showed a particularly dramatic leap in mathematical performance. The model is not yet publicly available, and its training is ongoing.
Four days later, on September 1, the company heard rumors that a breakthrough had been achieved on two Millennium Prize problems. OpenAI decided to redirect its new system toward all remaining unresolved problems to test its limits.
Instead of a single AI agent working on the proof, numerous groups of agents were deployed to tackle different directions, run code, and exchange ideas. Initially, about 100 agents spent roughly 50 hours on a closely related problem concerning the Euler equations. Once a promising result was achieved there, the company allocated additional resources to Navier-Stokes.
Ultimately, around 10,000 agents participated simultaneously in the relevant group. They exchanged approximately 2.7 million messages and generated about 130 billion output tokens. After 88 hours, the proof was obtained, and according to OpenAI, another 17 hours were required to formalize it and verify it using Lean and GPT-6 Astra.
OpenAI Head of Research Mark Chen stated that the compute cost reached "millions of dollars."
And Then It Turned Out Two Humans Were Already Close
This is where the drama begins.
For months, Prof. Tristan Buckmaster of New York University and mathematician Levent Alpoge, who works at Anthropic, had been working on a research line very close to the one that ultimately led OpenAI to its solution.
Buckmaster emphasizes that this was a private collaboration between the two rather than an official Anthropic project. Throughout their work, they utilized both Anthropic's Claude and OpenAI's Codex tools, including models from the GPT family.
The basic idea did not originate with them either. They built upon the work of mathematicians Diego Córdoba and Luis Martínez-Zoroza, who spent years developing a method to create singularities using an external force. Buckmaster and Alpoge attempted to overcome one of the remaining hurdles: making that force mathematically smooth enough.
On August 15, according to Buckmaster, the two achieved a significant breakthrough on the Euler equations and other closely related systems. By August 22, their proof had already been verified in Lean, and they began the painstaking work of turning the AI-generated output into a human-readable paper.
Buckmaster even described one of the early versions received from the model as "the most horrifying LLM proof I've ever read in my life."
«When I heard that word, a red light went off in my head.»
OpenAI Denies Misuse but Leaves a Crack Open
On September 3, after hearing rumors that information regarding his and Alpoge's progress had reached OpenAI, Buckmaster contacted a senior mathematician at the company.
Three days later, he spoke with Sebastian Bubeck, who leads mathematical research at OpenAI. According to Buckmaster, during the conversation he was told that an internal company model had already succeeded in proving singularity formation in the Navier-Stokes equations using a smooth external force.
That was the moment he began to suspect foul play.
"The path to the Clay problem via a smooth force is the path Luis and Diego opened, and that is the path Levent and I quietly chose to attack," he wrote, noting that almost no one else he knew was working in that direction. "When I heard 'with an external force', that was a blazing red light."
OpenAI itself does not dispute a key timeline detail: the company acknowledges that its effort began on September 1 following rumors of a breakthrough, which it later realized were connected to Alpoge and Buckmaster.
From this point, the two narratives diverge sharply.
Buckmaster claims that during the talks, he was offered two options. In one, he and Alpoge would publish their result regarding Euler first, with OpenAI publishing Navier-Stokes the following day.
In the second option, he claims he was asked to write a paper presenting OpenAI's Navier-Stokes solution while crediting the company's internal model—but omitting Alpoge as an author.
According to Buckmaster, Bubeck stated twice that he did not want Alpoge among the authors and expressed frustration that he worked at Anthropic, one of OpenAI's chief competitors.
Buckmaster refused the proposals, stating that if OpenAI published the result in that manner, he would publicly disclose what had transpired. According to Buckmaster, the response he received was: "Why would you want to ruin your career?".
When he resisted, he claims he was told: "If you don't want me to be nice, I don't have to be nice."
Buckmaster is careful to clarify that he does not accuse OpenAI of stealing the proof. He states that he has not seen the company's proof, does not know how the model arrived at it, and does not know whether his data was used.
OpenAI rejects the suspicion that its researchers or agents gained access to the unpublished work of Buckmaster and Alpoge. The company states that neither the researchers nor the agents saw their work prior to publication, and no specific user data was accessed to solve the problem.
However, a concluding statement underscores why this story is far from over.
OpenAI conceded that it cannot entirely rule out the possibility that de-identified data derived from the pair's use of its products may have previously helped improve its models. The company emphasizes that it views this possibility as highly unlikely, and that the proofs and achievements of both sides differ significantly.
Bubeck himself called the accusations against him "false and inflammatory," maintaining that he acted in accordance with academic norms. OpenAI CEO Sam Altman also stood by him, stating that Bubeck and the rest of the team acted "with integrity and generosity," and that the company initially attempted to coordinate a joint publication because it believed the other group had also solved Navier-Stokes.
Thus, two conflicting versions of these conversations currently exist—with no public evidence available to adjudicate between them.
Has the Problem Really Been Solved?
It is still too early to state this without a question mark.
OpenAI published a full analytical proof alongside formalization in Lean, which goes far beyond a PR statement about a "breakthrough." On the other hand, the proof must still undergo independent review by the mathematical community, and the Clay Institute has not yet recognized the solution.
OpenAI also announced it does not intend to claim the $1 million prize.
If the proof passes verification, the dispute over who knew what and when may temporarily overshadow the larger story: an AI system succeeded in concentrating within days a workforce equivalent to thousands of researchers operating simultaneously on a single problem, generating results at a level that previously required years of human labor at the absolute cutting edge of mathematics.
Buckmaster himself, despite the bitter dispute, called it mathematics' "Deep Blue-Kasparov moment." He was referring to the moment in 1997 when a computer defeated world chess champion Garry Kasparov, changing overnight how people viewed the limits of machine capabilities. If what OpenAI published this week proves correct, this time it may not be a game a computer learned to play better than us—but a problem we did not even know how to solve.
