OpenAI says an experimental AI system has generated a possible solution to the Navier-Stokes existence and smoothness problem, one of seven mathematical challenges known as the Millennium Prize Problems. The company says the effort involved roughly 10,000 AI agents working together for about 88 hours.
The Navier-Stokes problem comes with a $1 million prize and focuses on equations that describe the behavior of fluids, including water and air. Researchers have long sought to determine whether a fluid that starts with a smooth flow can develop a singularity in which its velocity becomes infinitely large.
OpenAI’s proposed proof argues that such a breakdown is mathematically possible. The system describes a vortex that becomes progressively more concentrated and stretched until its velocity becomes unbounded within a finite period, while the system’s total energy remains finite.
That conclusion does not mean real-world fluids can actually reach infinite speeds. Under current physics, physical limitations would intervene at extreme scales, where treating a fluid as a continuous substance would no longer provide an accurate description.
A 10,000-Agent AI Research Effort
OpenAI said the discovery came from an unreleased internal model that is substantially more capable than GPT-6 Astra, which the company describes as its most advanced publicly available model.
During the research process, approximately 10,000 AI agents exchanged 2.7 million messages and produced about 130 billion tokens. Astra then spent an additional 17 hours turning the proposed reasoning into a formal proof and checking it.
If the proof eventually survives independent review, the implications could extend beyond theoretical mathematics. Navier-Stokes equations are important in areas such as aircraft engineering, weather forecasting and research into blood circulation.
A clearer understanding of where these equations can break down could help scientists better model extreme and turbulent fluid behavior.
The bigger development, however, may be the scale of AI collaboration. The ability to deploy thousands of agents against a longstanding mathematical problem could provide a blueprint for using similar systems to investigate difficult questions in medicine, energy, aerospace and materials science.
Concerns Over the Source of the Approach
The announcement has also created controversy over whether OpenAI’s system arrived at the result independently.
NYU mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge were already studying a related fluid-dynamics problem and had incorporated AI into their research. Buckmaster later questioned whether information from their unpublished work could have influenced OpenAI’s efforts.
Buckmaster said he and Alpöge had spent roughly a year developing an unusual approach involving a smooth external force. He said Codex had played a significant role in their research and noted that very few researchers were pursuing the same strategy.
That led Buckmaster to question how OpenAI’s system could have developed a similar approach within days of the company learning about their progress.
In a series of posts on Mastodon, Buckmaster described his conversations with OpenAI. He said he was initially told that the company’s internal research began without human involvement beyond providing the mathematical problem.
According to Buckmaster, that explanation later changed. He said OpenAI eventually acknowledged that the initial prompt had been submitted only days earlier, after information about his and Alpöge’s work had reached the company.
OpenAI has denied that its researchers or agents saw the researchers’ unpublished work before publication. The company also said that no specific user data had been accessed.
However, OpenAI acknowledged that it could not entirely exclude the possibility that de-identified information from users’ interactions with its products had contributed to model improvements. The company maintains that its proposed proof differs substantially from the researchers’ work.
Mathematicians Still Need to Verify the Proof
For now, the claim does not amount to an officially recognized solution.
The Clay Mathematics Institute, which administers the Millennium Prize Problems, requires proposed solutions to undergo extensive examination and receive broad acceptance within the mathematical community before the $1 million prize can be awarded.
That means independent mathematicians will have to scrutinize OpenAI’s proof and determine whether every part of the argument holds up.
OpenAI has said it does not plan to seek the prize itself. Instead, the company is presenting the work as evidence that increasingly capable AI systems may be able to make rapid progress on mathematical questions that have resisted conventional approaches for decades.
