OpenAI Solves Navier-Stokes Millennium Problem Using Autonomous AI Agents

Cracking a Famed Millennium Problem with Autonomous AI Agents

For the first time, a truly major open problem in mathematics has been solved by computer, according to OpenAI. The artificial-intelligence company based in San Francisco announced on September 8, 2026, that it has generated a solution to the Navier-Stokes equations, one of the thorniest problems in mathematics. The physical model describes the motion of fluids like liquids and gases. Whether these equations can break down under certain conditions was designated as one of the seven Millennium Problems by the Clay Mathematics Institute at the turn of the twenty-first century, with a prize of US$1 million attached to a verified solution.

The breakthrough originated from an internal model significantly more capable than GPT-6 Astra. Following rumors on Tuesday, September 1, that two Millennium Prize problems had been resolved, OpenAI launched an effort to evaluate its technology on all open Millennium Prize problems. The company deployed a system of coordinating agents powered by the internal model, giving them access to tools such as code execution and a cached version of the internet.

The scale of the computational effort was unprecedented. OpenAI mathematician Sebastian Bubeck told reporters that the model initially answered a simplified version of the question in 50 hours using 1,000 AI agents. Then we decided to go for the full Navier-Stokes, and we increased the amount of compute, Bubeck said. The group that ultimately produced the Navier-Stokes resolution involved on the order of 10,000 concurrent agents.

Proving Infinite Speed and Fluid Breakdown

The Navier-Stokes equations use Newton’s second law of motion to describe fluid movement as a continuous medium rather than tracking individual molecules. Dating back to the nineteenth-century work of Claude-Louis Navier and George Gabriel Stokes, the equations are widely used for aircraft design, weather forecasting, and blood flow study. In 1934, Jean Leray proved that solutions exist in a generalized sense, but whether they always remain smooth became a central unanswered question.

OpenAI’s system produced both an analytical proof and a formalization in Lean showing that an initially smooth fluid at rest can develop a singularity in a finite time. The fluid maintains finite energy from rest through the formation of the singularity. Our proof does show that there exist fluids which start out perfectly normal, and under the Navier-Stokes equations, actually achieve infinite speed in a finite amount of time, OpenAI computer scientist Ven Chandrasekaran said in a press briefing.

Because physical fluids cannot move infinitely fast, Chandrasekaran noted that this behavior suggests the equations may fail to mirror physical reality under specific circumstances. The solution describes a vortex—a spinning swirl of fluid—spiraling inward and elongating like spaghetti. While the central region shrinks and accelerates, its energy remains finite, satisfying the laws of physics. Mathematically, terms describing acceleration, pressure gradients, momentum transfer, and viscosity grow large yet cancel in a precise balance.

Parallel Discoveries and Community Reaction

OpenAI’s announcement coincides with independent work from other researchers exploring fluid dynamics and artificial intelligence. On September 7, mathematicians Levent Alpöge of Harvard University and Tristan Buckmaster of New York University released a paper detailing a solution for the fluid equations achieving infinite speed in the simplified case of zero viscosity. Their work utilized Anthropic AI’s Claude as well as OpenAI’s Codex and Astra models. Simultaneously, Anima Anandkumar of the California Institute of Technology and her collaborators released a zero-viscosity solution using a physics-informed neural network rather than a general-purpose large language model.

Reacting to the rapid pace of developments, mathematician Martin Bridson, president of the Clay Mathematics Institute, called it an exciting day for human understanding of mathematics. Meanwhile, UCLA mathematician Terence Tao described the work by Alpöge and Buckmaster as a remarkable achievement on Mastodon.