On September 8, 2026, OpenAI announced it had solved one of the hardest mathematical problems in the world: the existence and smoothness problem for the Navier-Stokes equations, one of the seven "Millennium Prize Problems" identified by the Clay Mathematics Institute. A result that, if confirmed, would change forever the way we think about the relationship between artificial intelligence and pure mathematical research.
What is the Navier-Stokes problem, and why does it matter so much
The Navier-Stokes equations describe the motion of fluids: water, air, the steam rising from a moka pot, ocean currents, atmospheric winds. They underpin much of modern engineering, from aerodynamics to meteorology.
The problem, unsolved for roughly 90 years (since Jean Leray's foundational 1934 work), asks a deceptively simple question: can the description of smooth three-dimensional fluid motion modeled by these equations "break down"? In other words, are there perfectly ordinary initial conditions that, following the equations, cause a fluid to reach infinite velocity in finite time?
It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute in the early 2000s, each carrying a one-million-dollar prize for a rigorous solution.
OpenAI's announcement
According to OpenAI, a group of agents built on a new-generation internal model, more capable than GPT-6 Astra, produced a proof answering exactly this question: the existence of fluids that, starting from entirely ordinary conditions, reach infinite velocity in finite time under the Navier-Stokes equations. A behavior that is physically impossible for a real fluid, which would suggest that, under certain circumstances, the equations do not faithfully mirror physical reality.
Mathematician Sébastien Bubeck, who now leads OpenAI's math team (previously a VP of AI at Microsoft), said he took up the problem after hearing rumors about the work of two other researchers, and estimated the computational cost of reaching the result at several million dollars. Martin Bridson, president of the Clay Mathematics Institute, described the day as an important one for humanity's understanding of mathematics, while making clear that the institute's official evaluation will be "deliberately unhurried" and rigorous: for now, the institute has not accepted the result and still lists Navier-Stokes among its unsolved Millennium Problems.
To reach this result, OpenAI reportedly deployed an unprecedented amount of computing power: first, around a hundred AI agents working for roughly 50 hours on a simplified version of the problem (the Euler equations, without viscosity), then up to 10,000 concurrent agents, working for 88 hours plus another 17 hours of formalization and verification in Lean, to tackle the full Navier-Stokes problem.
A race against time: the role of Anthropic and other researchers
Behind the announcement lies a genuine scientific race. According to reports, OpenAI decided to focus its resources on the problem after learning that two mathematicians, Levent Alpöge (now a researcher at Anthropic) and Tristan Buckmaster (New York University), were working on a version of the fluid-motion problem. On September 7, just one day before OpenAI's announcement, Alpöge and Buckmaster published their own work claiming to have found a solution for the fluid equations that also reaches infinite velocity, but for the simplified case of a fluid without viscosity (the Euler equations). On the same day, researcher Anima Anandkumar of Caltech, together with her collaborators, published an independent solution to the same simplified problem, obtained through a different approach: a "physics-informed" neural network, not a general-purpose language model.
This overlap in timing sparked controversy that went well beyond a simple academic back-and-forth. Buckmaster accused OpenAI of a lack of transparency, asking whether the company's model had had access to their working sessions (OpenAI denied this). Buckmaster also said that, during a call, he was reportedly presented with a choice: publish jointly with OpenAI, crediting the company with the full solution, or publish alone and claim the Millennium Prize, but only on condition of removing the name of Alpöge, his co-author at Anthropic, from the paper. OpenAI has disputed this account of events.
What the experts say
Not every observer responded with pure enthusiasm. Several mathematicians, including Luis Martínez Zoroa of CUNEF Universidad in Madrid (who, together with Diego Córdoba, conducted foundational research on precisely this problem), called the result "genuinely remarkable," while stressing the need for thorough verification by the mathematical community before it can be called a definitive proof formally recognized by the Clay Mathematics Institute. It's worth remembering that, throughout the history of mathematics, announcing a proof is only the first step: formal validation can take months or years of peer review, especially for a problem of this complexity and significance.
Why this result matters for the future of AI
Beyond its purely mathematical significance, the episode marks a turning point in the debate over what artificial intelligence is truly capable of in advanced scientific research. If confirmed, OpenAI's result would join a string of recent AI milestones in mathematics, including other cases where large language models have helped formalize historic proofs. A crucial question remains open, though: how much of these results comes from genuine, original "reasoning" by the model, and how much comes from the ability to rapidly explore, with enormous amounts of compute, a solution space already partly mapped out by the scientific community's prior work.
Regardless of the outcome of the official verification, OpenAI's announcement about solving the Navier-Stokes equations marks an important symbolic moment: for the first time, an artificial intelligence company claims to have independently tackled one of the most celebrated open problems in modern mathematics, in a context of fierce competition with other research labs, Anthropic included. In the coming months, the international mathematical community will need to examine the proposed proof in detail: only then will it be possible to say with certainty whether the Navier-Stokes problem, after 90 years, has truly been solved.
What stands out in this story isn't really the result itself, but everything surrounding it: thousands of AI agents working in parallel, companies fighting over credit for a proof, a scientific community that will take months to say whether the work actually holds up. At M's Works we start from the same premise every time we write code for a client: AI makes things faster, it doesn't replace verification. A website or web app that's "AI-generated" with no human review isn't a shortcut, it's a risk.