OpenAI claims solution to Navier–Stokes Millennium Prize Problem

OpenAI has announced a solution to the Navier–Stokes equations, one of the seven Millennium Prize Problems in mathematics. Using approximately 10,000 simultaneous AI agents over an 88-hour period, the company developed an analytical proof and a formalization in the Lean proof-checking language.

The result demonstrates that solutions to the equations can break down in finite time, addressing the Clay Mathematics Institute’s formulation by establishing alternatives C and D. The Navier–Stokes equations, which describe the motion of fluids like liquids and gases, have remained an open question for 90 years regarding whether velocities can grow without bound despite viscosity.

OpenAI’s proof utilizes a construction of a vortex that spirals inward and stretches, where acceleration, pressure gradient, momentum, and viscosity become extremely large yet cancel each other out with high precision. The company noted that the work was powered by an internal model described as significantly more capable than GPT-6 Astra.