OpenAI claims AI solved Navier-Stokes Millennium Problem

September 9, 2026 at 12:46 AM2 min

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OpenAI announced on 8 September that its AI prototype generated a solution to the Navier-Stokes equations, showing they can break down and produce infinite speed in finite time. The claim addresses one of the seven Clay Mathematics Institute Millennium Problems, which carries a $1 million prize. The announcement came one day after two mathematicians released a paper solving a simplified zero-viscosity version using Anthropic AI's Claude and OpenAI's Codex and Astra models.

Key Facts

OpenAI announced on 8 September that its AI prototype solved the Navier-Stokes equations, showing they can break down and achieve infinite speed in finite time.
The Navier-Stokes existence and smoothness problem is one of seven Millennium Problems posed by the Clay Mathematics Institute, each with a $1 million prize.
On 7 September, mathematicians Levent Alpöge of Harvard University and Tristan Buckmaster of New York University released a paper solving the zero-viscosity version using Anthropic AI's Claude and OpenAI's Codex and Astra models.
On the same day, Anima Anandkumar of Caltech and collaborators released a solution for the zero-viscosity problem using a physics-informed neural network.
OpenAI researchers began focusing on the Navier-Stokes problem on 1 September after hearing rumours of the mathematicians' work.

The Claimed Solution

OpenAI computer scientist Ven Chandrasekaran said the proof shows fluids that start out perfectly normal can achieve infinite speed in finite time under the Navier-Stokes equations. Because this behaviour is physically impossible for a real fluid, Chandrasekaran said the equations may not be a reliable mirror of physical reality under certain circumstances. OpenAI mathematician Sebastian Bubeck called the result the spectacular culmination of AI solving problems of increasing complexity over the last 12 months. The Clay Mathematics Institute president Martin Bridson said it is an exciting day as the announcement contemplates major advances in human understanding of mathematics.

Competing Solutions

Levent Alpöge of Harvard University and Tristan Buckmaster of New York University released a paper on 7 September solving the zero-viscosity case of the fluid equations. They used Anthropic AI's Claude and OpenAI's Codex and Astra models to obtain the solution. They also said they had obtained a solution to the more general problem, to be released soon. Anima Anandkumar of the California Institute of Technology and collaborators released a solution for the zero-viscosity problem on the same day using a physics-informed neural network.