OpenAI Says AI Agents Solved 90-Year-Old Navier–Stokes Problem in 88 Hours

OpenAI says a new artificial intelligence system has produced a proposed solution to the 90-year-old Navier-Stokes problem, one of the seven Millennium Prize Problems in mathematics, after deploying about 10,000 AI agents over 88 hours.

The company said in a release published Tuesday that its researchers used a system of coordinating AI agents powered by an internal model to work on the problem, which concerns the mathematical equations used to describe the motion of fluids such as water and air.

OpenAI said the agents began working on the problem on September 1 and arrived at what the company described as a resolution on Saturday, September 5, roughly 88 hours after the first agents were launched.

The claim has not yet been independently validated by the mathematical community. The Clay Mathematics Institute, which established the Millennium Prize Problems and offers a $1 million prize for a correct solution to each, had not commented on OpenAI's proposed solution at the time of the announcement.

OpenAI's announcement therefore marks a significant AI research claim rather than a formally recognized solution. For the problem to be considered solved, mathematicians would need to scrutinize the proposed proof and establish that it satisfies the requirements of the problem.

10,000 AI Agents Worked In Parallel

OpenAI said the system differed from a conventional chatbot interaction because it deployed large numbers of agents that could work on different aspects of the problem and communicate within groups.

"The agents had access to tools such as the ability to read from a cached version of the internet and the ability to run code," OpenAI said.

The company said the agents were divided into groups of different sizes, with individual groups able to communicate internally. The group responsible for the Navier-Stokes work involved "on the order of 10,000 concurrent agents," according to OpenAI.

The approach points to a broader shift in AI research from models that generate individual answers toward systems capable of coordinating large numbers of specialized computational tasks. Rather than asking one model to produce a mathematical proof from beginning to end, the architecture allows agents to explore possible approaches, test calculations, run code, and exchange information.

In principle, that can give an AI system substantially more opportunities to identify and correct errors in a difficult proof.

The speed claimed by OpenAI is notable because Navier-Stokes has resisted attempts by mathematicians for decades.

Why Navier-Stokes Matters

The Navier-Stokes equations are fundamental to fluid dynamics. They are used to describe how fluids move and have applications across physics and engineering, including the study of airflow, water, weather, and other fluid systems.

The Millennium Prize version of the problem asks mathematicians to establish whether sufficiently smooth solutions to the three-dimensional Navier-Stokes equations always exist and remain smooth, or whether solutions can develop singularities in finite time.

The difficulty is not simply solving the equations for a particular physical system. The challenge is proving a general mathematical result about the behavior of three-dimensional fluid flows.

That distinction is important when assessing OpenAI's claim. Producing numerical evidence or solving particular cases would not be enough. A valid solution must provide a rigorous mathematical proof that addresses the full problem.

Mathematician Raises Questions About OpenAI's Route

OpenAI's announcement quickly attracted scrutiny from Tristan Buckmaster, a mathematics professor at New York University who has been working on Navier-Stokes with Levent Alpöge, a mathematician who works at OpenAI rival Anthropic.

Buckmaster said in a statement on his website that he and Alpöge had been collaborating personally on mathematical problems, including Navier-Stokes, and that Alpöge received information suggesting that details of their progress had reached OpenAI.

According to Buckmaster, the approach described by OpenAI appeared similar to work the two mathematicians had been pursuing. He questioned whether information from their work could have been accessible to OpenAI's models, including through sessions conducted using the company's Codex products.

Buckmaster was careful to distinguish those questions from an allegation that OpenAI had improperly accessed the mathematicians' work.

"I would like to be clear about what I am not claiming. I have not seen OpenAI's proof. I do not know what their model did, or how. I do not know whether our data was used," he said.

His comments introduce a separate issue from whether the mathematics itself is correct: the provenance of the information used by an AI system in reaching a claimed breakthrough.

OpenAI said its work on Navier-Stokes began on September 1 after the company heard a rumor about progress on the problem. It later determined that the rumor concerned the work by Buckmaster and Alpöge.

The company said its researchers and AI agents did not see the mathematicians' work before it was publicly released.

"We (the researchers and the agents) did not see any of their work through any means until they released it publicly - in particular, no specific user data was accessed in order to solve this problem," OpenAI said.

The company added that, while it considered it unlikely, it could not rule out the possibility that de-identified data derived from users' interactions with its products had contributed to improving its models.

That could become important as AI companies increasingly position their models as tools for scientific and mathematical research. Questions over training data, model access, confidentiality, and the boundaries between publicly available knowledge and private user work are becoming more consequential as AI systems are used to generate original research.

A Test for AI's Role in Advanced Mathematics

If OpenAI's proof survives independent mathematical scrutiny, the significance would extend beyond Navier-Stokes.

AI systems have already demonstrated an ability to assist with theorem proving, mathematical discovery, coding, and scientific research. A rigorously verified solution to a Millennium Prize Problem would represent a much more consequential milestone because it would demonstrate that AI can contribute to solving a problem that has resisted generations of human mathematicians.

It would also strengthen the case for multi-agent AI systems, in which large numbers of models cooperate rather than relying on a single model to reason through a problem.

But the most important test remains mathematical verification.

A computer-generated argument, no matter how sophisticated the underlying AI system or how many agents participated, does not become a proof simply because an AI company describes it as a solution. Independent mathematicians will need to examine the argument line by line, identify any hidden assumptions or logical gaps, and determine whether it actually resolves the question posed by the Clay Institute.

Seven Problems, Seven $1 Million Prizes

The Clay Mathematics Institute established the Millennium Prize Problems in 2000, selecting seven of the most important unresolved problems in mathematics and offering $1 million for a correct solution to each.

The institute said the prizes were intended to draw public attention to the fact that fundamental mathematical questions remain unresolved and to recognize achievements of "historical magnitude."

Navier-Stokes is one of the seven problems. The others include the Riemann Hypothesis, which concerns the distribution of prime numbers, and the Birch and Swinnerton-Dyer Conjecture, which concerns elliptic curves.

Only one of the seven, the Poincaré Conjecture, has been officially solved.

OpenAI's Navier-Stokes claim now enters that same long-running mathematical test: whether an AI-generated result can withstand the standards of proof that have governed mathematics for centuries.

Until independent experts validate the proposed solution, the most precise description of OpenAI's achievement is that its AI system has produced a proposed resolution to one of mathematics' most difficult open problems.