OpenAI said that an experimental artificial intelligence system that has not yet been made public recently achieved major progress: after about 10,000 AI agents worked together for 88 hours, they completed a proposed solution to the Navier—Stokes existence and smoothness problem. This problem is one of the best-known unsolved problems in mathematics, is one of the seven Millennium Prize Problems, and carries a $1 million prize.
The Navier—Stokes equations are mainly used to describe the movement of fluids such as water and air. The core of the problem is whether originally completely smooth fluid motion can break down at some point, causing the velocity to increase without bound.
The results produced by OpenAI's experimental system suggest that this can happen. Its proof constructs a type of fluid vortex that is continuously stretched and gradually concentrated during its evolution, ultimately causing the fluid velocity to increase explosively within a finite period of time, while the overall energy of the system remains finite.
However, according to current physical understanding, fluids in the real world cannot actually reach infinite velocity. When the scale enters a sufficiently extreme range, the continuum assumption adopted by the Navier—Stokes equations will no longer accurately describe the real physical world.
This result came from an internal model developed by OpenAI. OpenAI said that the model's capabilities significantly exceed those of GPT-6 Astra, which is currently the company's most advanced publicly available model. While processing the Navier—Stokes problem, about 10,000 AI agents exchanged 2.7 million messages with one another and generated about 130 billion tokens. Astra then spent another 17 hours formalizing and verifying the relevant proof.
The extent of the practical impact this mathematical proof can have in the future remains to be seen. The Navier—Stokes equations are already widely used in aircraft design, weather forecasting, and blood-flow research. If the conditions under which the equations may fail can be further clarified, it could help scientists gain a deeper understanding of modeling problems involving extreme fluids and turbulent motion.
But compared with the proof itself, the AI system behind this result may have broader significance. If thousands of AI agents can jointly work on a mathematical problem that has existed for about 90 years within a matter of days, similar collaboration methods could in the future also be used to solve complex problems in fields such as materials science, energy, aerospace, and medicine.
However, controversy has already emerged over whether this research result can be regarded as a completely independent discovery.
Tristan Buckmaster, a mathematician at New York University, and Levent Alpöge, a researcher at Anthropic, had previously also been studying a fluid dynamics topic closely related to this problem and used artificial intelligence tools during their research. Buckmaster subsequently raised questions about whether the previously unpublished research results could have entered OpenAI products and further influenced the company's models. He expressed this concern in a series of posts on the social network Mastodon.
Buckmaster said that he and Alpöge spent about a year pursuing a relatively unusual research path, using smooth external forces to solve the related problem. Codex was one of the artificial intelligence tools they widely used during their research.
According to Buckmaster, almost no other researchers he knew had adopted the same approach, so he also questioned how OpenAI was able to develop this research path within days after learning that the two had made relevant progress.
Buckmaster revealed that during communication with OpenAI, he initially saw a prompt and was told that OpenAI's internal research had been initiated without human input and based only on the problem statement.
But according to Buckmaster, this statement subsequently changed during the conversation. OpenAI eventually acknowledged that the first prompt had only been sent a few days earlier, while before that, information related to Buckmaster and Alpöge's research work had already been passed to the company.
In response, OpenAI said that before the relevant results were published, neither its researchers nor AI agents had seen the two researchers' work, and they had not accessed any specific user's data. OpenAI also said that although it could not rule out the possibility that de-identified data generated during the use of its products may have contributed to model improvements, there were significant differences between the company's proof and the research conducted by the two researchers.
Because the above controversy still exists, the proof has not yet been formally recognized by the mathematical community as a solution to the Navier—Stokes problem. The Clay Mathematics Institute stipulates that a proposed solution must undergo long-term review and receive broad recognition from the mathematical community before it will consider whether to award the $1 million prize.
OpenAI said that the company does not plan to claim the prize, but instead regards the result as evidence of the rapid improvement in the capabilities of its research systems.