For decades, one of the most consequential unsolved questions in mathematics sat at the intersection of physics and pure abstraction: do the equations that describe how fluids move always produce sensible answers, or can they break down? On September 8, OpenAI announced it had generated a proof showing they can, in fact, break down. This makes it the first truly major open problem in mathematics to be solved by a computer, according to the company.
The Problem That Stumped Mathematicians for Generations
The Navier-Stokes equations are the standard mathematical model for fluid motion. They describe how liquids and gases behave, from blood flowing through arteries to air moving around an aircraft wing. The question at the heart of one of the seven “Millennium Problems” posed by the Clay Mathematics Institute was deceptively simple: do these equations always produce smooth, well-behaved solutions, or can they generate something physically impossible?
OpenAI’s answer is the latter. According to computer scientist Ven Chandrasekaran, who spoke at a press briefing, the proof demonstrates that there exist fluids which, when governed by the Navier-Stokes equations, can theoretically reach infinite speed in a finite amount of time. That outcome is physically impossible for any real fluid. No liquid or gas actually behaves this way. What the result reveals is that under certain conditions, the equations may not reliably mirror physical reality. The math, in other words, can produce nonsense, and now there is a formal proof of it.
Each of the seven Millennium Problems carries a prize of US$1 million from the Clay Mathematics Institute. Martin Bridson, the institute’s president, described the announcement as “an exciting day” as the world contemplates “major advances in the human understanding of mathematics.”
A Race With Multiple Fronts
What makes this moment particularly striking is that OpenAI was not alone in pursuing the problem. The announcement came amid a cluster of parallel efforts that unfolded within days of each other.
On September 7, mathematicians Levent Alpöge of Harvard University and Tristan Buckmaster of New York University released a paper presenting a solution for a simplified version of the fluid-motion puzzle: the case in which the fluid has no viscosity. Their work also demonstrated that infinite speed could be achieved under those conditions. To reach that result, they used a combination of tools: Anthropic AI’s Claude model, and OpenAI’s Codex and Astra models. They also stated that a solution to the more general problem was forthcoming.
On the same day, Anima Anandkumar, a computer scientist at the California Institute of Technology, and her collaborators released their own solution to the zero-viscosity version, using a different technical approach: a physics-informed neural network rather than a general-purpose large language model.
OpenAI, meanwhile, had been testing its latest AI prototype across all six currently unsolved Millennium Problems. On September 1, after hearing reports that Alpöge and Buckmaster were close to a result, the company redirected its resources toward the Navier-Stokes problem specifically. The scale of computation involved was substantial. OpenAI mathematician Sebastian Bubeck told reporters that the model first solved a simplified version of the question in 50 hours using 1,000 AI agents. The team then escalated, deploying 10,000 agents to tackle the full Navier-Stokes problem. Bubeck described the moment as “the spectacular culmination of the arc we have seen over the last 12 months,” as AI systems tackled problems of increasing complexity and significance.
Terence Tao, a mathematician at the University of California in Los Angeles, described the work by Alpöge and Buckmaster as a “remarkable achievement.”
Why This Matters Beyond the Equations
Here is what most coverage of this story risks missing: the significance is not just that a famous problem got solved. It is what the process reveals about the changing relationship between human expertise and computational power in scientific discovery.
The Navier-Stokes result did not emerge from a single AI system working in isolation. It emerged from a dense collaboration: human mathematicians directing the effort, AI models handling the computational load at a scale no human team could sustain, and multiple research groups working in parallel, each using different tools and approaches. The 10,000 agents OpenAI deployed represent a form of intellectual labor that augments what human researchers can pursue, not a replacement for the mathematical intuition that framed the question in the first place.
The fact that three separate groups converged on related results within days of each other also signals something about the current moment in AI-assisted science. The tools have reached a threshold where genuinely hard problems, problems that resisted human effort for generations, are now within reach. That changes what research teams can attempt, and it changes the pace at which mathematics and physics can advance.
In Short
OpenAI announced on September 8 that it had proved the Navier-Stokes equations can break down, solving one of the seven Millennium Problems posed by the Clay Mathematics Institute. The proof shows that theoretical fluids governed by these equations can reach infinite speed, a physically impossible outcome that reveals limits in the model itself. Two other research groups, one led by mathematicians Alpöge and Buckmaster using multiple AI tools, and one led by Anandkumar using a physics-informed neural network, released related results on the same day. OpenAI used 10,000 AI agents to tackle the full problem. The result is a landmark not just for mathematics, but for what AI-augmented scientific research can now accomplish.
Based on reporting from Nature: Machine Learning.