In 1822, Claude-Louis Navier took Euler’s inviscid equations and added what real fluids actually do: they resist.
Working from Laplace’s picture of molecules tugging on one another, he wrote the first viscous-flow law. His memoirs of 1821–1823 (read 18 March 1822, printed 1822 and 1827) gave the world the Navier–Stokes equations.
George Gabriel Stokes found them again in 1845, recast them in the continuum form we still use, and argued that fluid at a wall should not slip. That no-slip condition, once debated, became the everyday boundary of pipes, wings, and arteries.
Engineers compute them every day. Mathematicians still cannot close the book. In three dimensions nobody knows whether a smooth flow stays smooth forever or can blow up.
The Clay Millennium Prize for that question remains unclaimed in 2026. The equations work. Their deepest proof does not.
We’re sharing a solution to the Navier-Stokes Millennium Prize Problem, one of the deepest problems at the frontier of mathematics.
The proof was produced by a group of agents, using an OpenAI next-generation model significantly more capable than GPT-6 Astra.
The problem concerns whether the description of smooth three-dimensional fluid motion modeled by the Navier-Stokes equations can break down. It has remained unresolved for roughly 90 years.
Just the example itself is so fun to play with! 🔆
I can't wait to pull the code and swap the rendering pipeline to achieve even more cool effects.
This is the dream of TypeGPU, AI inference, complex compositing, all on the GPU in a seamless, type-safe pipeline.