Visualizing the OpenAI solution to the Navier-Stokes problem
Did an AI just solve a $1,000,000 math problem?
On September 8, 2026, OpenAI announced that one of its internal AI systems — roughly 10,000 agents working together — produced a proof that the Navier-Stokes equations, which describe the flow of every fluid from water in a pipe to air over a wing, can "blow up": reach infinite speed in finite time from smooth, reasonable starting conditions. The full argument was formalized and checked line-by-line in the Lean proof assistant.
This video builds the flow the proof is about from scratch: a spinning column of fluid that gets stretched thinner and thinner, spinning faster and faster — like a skater pulling in their arms — until (in the mathematical limit) its speed becomes infinite while its energy stays finite.
Why it matters: the 3D Navier-Stokes existence-and-smoothness problem is one of the seven Clay Mathematics Institute Millennium Prize Problems, open since 1934.
The visualization in the video is based on the original repo where OpenAI published their solution: https://github.com/openai/NavierStokesAndEuler. Based on a custom Three.js/WebGL renderer, with streamlines computed in Python from the exact flow solutions.
Video Summary
AI GeneratedThe video discusses the Navier-Stokes equations, which describe fluid dynamics. While used widely in engineering, it remained unproven whether they always provide sensible answers in 3D. A recent claim suggests a proof that fluid speed can become infinite in finite time, potentially solving a Millennium Prize problem and revealing a fundamental breakdown in these equations.