OpenAI claims Navier-Stokes proof as rival teams post their own

OpenAI says it has a proof that the Navier-Stokes equations, one of the Clay Mathematics Institute's Millennium Problems, can break down. The company told Nature that an internal system ran 1,000 agents for 50 hours on a simplified version, then 10,000 agents on the full problem.

"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. Because that behaviour is physically impossible for a real liquid or gas, it implies the equations are not always a faithful description of physical fluids.

The announcement did not arrive in isolation. A day earlier, Harvard's Levent Alpöge and NYU's Tristan Buckmaster released a solution for the zero-viscosity case using Anthropic's Claude and OpenAI's Codex and Astra models. Caltech's Anima Anandkumar posted a separate zero-viscosity result built on physics-informed neural networks. Terence Tao of UCLA called the Alpöge-Buckmaster work a "remarkable achievement."

Clay Mathematics Institute president Martin Bridson told Nature, "It is certainly an exciting day." OpenAI's Sebastian Bubeck described the company's result as "the spectacular culmination of the arc."

None of the three claims have been through peer review.