OpenAI says an experimental internal AI system has produced a potential answer to the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize Problems. The claimed breakthrough was reportedly achieved by coordinating about 10,000 AI agents over roughly 88 hours.
The problem carries a $1 million prize and has remained unresolved for decades. It concerns the Navier-Stokes equations, which are used to describe the movement of fluids such as air and water. At the heart of the challenge is whether a fluid that begins with smooth behavior can eventually develop a singularity where its velocity becomes unbounded.
OpenAI’s proposed solution argues that this type of breakdown can happen. Its proof describes a vortex becoming increasingly concentrated and stretched until its velocity reaches an infinite value in finite time, even though the total energy remains finite.
In the physical world, however, fluids cannot accelerate to infinite speeds under current scientific understanding. At extreme scales, the continuous-fluid assumption behind the Navier-Stokes equations would eventually stop accurately describing reality.
OpenAI Uses Thousands of AI Agents
The company said the work was carried out by an internal model that is considerably more powerful than GPT-6 Astra, which OpenAI identifies as its most capable publicly available system.
The roughly 10,000 agents exchanged about 2.7 million messages and generated close to 130 billion tokens while exploring the problem. Astra then spent another 17 hours formalizing the proposed argument and checking the resulting proof.
The potential importance extends beyond mathematics. Navier-Stokes equations play a role in aircraft design, weather modeling and studies of blood flow. Understanding precisely when their mathematical assumptions can fail could eventually help researchers deal with extreme and turbulent fluid systems.
The multi-agent method could also have much broader applications. If large groups of AI systems can collaborate on problems that have challenged mathematicians for generations, similar techniques could eventually be applied to difficult questions in medicine, energy, aerospace and materials science.
Mathematicians Question How Independent the Result Was
The announcement has nevertheless triggered controversy over the origins of OpenAI’s approach.
NYU mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge had been working on a closely related fluid-dynamics problem and had used AI tools as part of their research.
Buckmaster said he and Alpöge had spent approximately a year pursuing an unusual strategy involving a smooth external force. He said Codex was used extensively during their work and questioned how OpenAI could have reached a similar direction so soon after becoming aware of their progress.
In posts on Mastodon, Buckmaster described conversations with OpenAI in which he was initially told that the company’s internal effort had begun without human input other than supplying the problem itself.
According to Buckmaster, OpenAI later acknowledged that the first prompt for the project had been submitted only days earlier, after information concerning his and Alpöge’s research had reached the company.
OpenAI rejected the suggestion that its researchers or AI agents had accessed the pair’s unpublished work before it became public. The company also said no specific user data had been accessed.
At the same time, OpenAI acknowledged that it could not completely rule out the possibility that de-identified information generated through users’ interactions with its products had contributed to model improvements. The company said its proposed proof is substantially different from the researchers’ work.
The $1 Million Prize Is Still Out of Reach
Despite OpenAI’s claim, the Navier-Stokes problem has not officially been solved.
The Clay Mathematics Institute requires proposed solutions to undergo extensive mathematical review and gain broad acceptance before recognizing a solution and awarding its $1 million prize.
The proof will therefore need to withstand scrutiny from independent mathematicians before its status becomes clear.
OpenAI has also indicated that it does not plan to pursue the prize. Instead, the company is presenting the result as evidence of progress in AI-assisted mathematical research and the potential of large-scale, multi-agent systems to tackle longstanding scientific problems.
