OpenAI claims that an experimental AI system has made a potential breakthrough on the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize Problems that have challenged mathematicians for decades.

The company says the system deployed approximately 10,000 AI agents to investigate the problem over an 88-hour period. Together, the agents reportedly exchanged 2.7 million messages and generated around 130 billion tokens before producing a proposed solution.

The Navier-Stokes problem concerns a set of equations used to model the movement of fluids such as air and water. The central mathematical question is whether a fluid that begins with a smooth flow can develop a singularity in finite time, causing its velocity to become unbounded.

OpenAI’s proposed argument suggests that such a scenario can occur. The proof describes a vortex that becomes increasingly compressed and stretched until its velocity grows without bound within a finite period, while the total energy of the system remains finite.

That mathematical result should not be confused with a claim that physical fluids can actually reach infinite velocity. According to current physics, real-world limitations would become important at extreme scales, where the assumption of a fluid behaving as a continuous material would no longer accurately apply.

OpenAI’s Multi-Agent Approach

The company said the research was conducted using an unreleased internal model that it considers significantly more capable than GPT-6 Astra, its most advanced publicly available model.

After the thousands of agents explored the problem and generated their proposed reasoning, Astra reportedly spent another 17 hours formalizing and verifying the proof.

A successful solution could have consequences beyond abstract mathematics. Navier-Stokes equations are used in areas ranging from aircraft development and weather forecasting to studies of blood circulation.

Understanding the conditions under which the equations may fail could eventually help researchers develop better models for turbulent and extreme fluid behavior.

The broader significance could come from the method used to reach the result. Deploying thousands of AI agents simultaneously could offer a new way to tackle complex scientific problems, potentially extending into fields such as medicine, aerospace, energy and materials research.

Questions Surround the Research Process

However, OpenAI’s announcement has raised questions about how independently the AI system developed its approach.

NYU mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge had been investigating a closely related fluid-dynamics problem and had used AI tools during their work.

Buckmaster said the pair had spent approximately a year exploring an unconventional strategy involving a smooth external force. Codex was among the AI systems they used extensively.

He questioned how OpenAI’s researchers could have arrived at a similar approach so quickly after learning about the pair’s progress, particularly because he said relatively few researchers were pursuing the same direction.

Buckmaster also described discussions with OpenAI in which he was initially told that the company’s internal research began without human guidance beyond the original problem statement.

He later said OpenAI acknowledged that the first prompt had been submitted only days earlier, after information about Buckmaster and Alpöge’s research had reached the company.

OpenAI rejected the claim that its researchers or AI agents had viewed the pair’s unpublished research before it was released publicly. The company also said that no specific user information had been accessed.

At the same time, OpenAI acknowledged that it could not completely rule out the possibility that de-identified information originating from interactions with its products had contributed to model improvements. The company maintains that the resulting proofs are substantially different.

No Official Millennium Prize Yet

Despite OpenAI’s claim, the Navier-Stokes problem has not officially been declared solved.

The Clay Mathematics Institute requires proposed solutions to undergo extensive examination and receive broad acceptance from mathematicians before recognizing a solution and awarding its $1 million prize.

The proof will therefore need to survive independent mathematical scrutiny before its significance can be established.

OpenAI has also said it does not intend to pursue the prize. Instead, the company is framing the result as a demonstration of how rapidly its AI research systems are advancing and how large-scale agent collaboration could potentially help address longstanding problems in mathematics and science.