OpenAI Claims AI Model Solved Century-Old Navier-Stokes Mathematics Problem

The Navier-Stokes equations describe how fluids move and are used in aircraft design, ocean modelling and meteorology. A key unresolved question for nearly a century: can a smooth flow spontaneously develop an infinite spike in finite time? The Clay Mathematics Institute formalised this as one of seven Millennium Prize Problems in the early 2000s, each offering a $1 million reward.

OpenAI claimed this week that an unreleased internal AI model produced a proof that a version of the Navier-Stokes equations can indeed blow up in finite time. The company said roughly 10,000 AI agents worked in parallel on the problem, with costs running into millions of dollars, and the proof was formally verified using the language Lean.

However, mathematicians have raised concerns. OpenAI's proof applies to the 'forced' version of the equations with an external forcing term, not the exact 'unforced' version specified by the Clay Institute's prize condition.