Quanta Magazine · Science

AI Solves $1 Million Navier-Stokes Problem

OpenAI's AI agents have reportedly solved a Millennium Prize Problem by finding a singularity in the Navier-Stokes equations. The result, verified in Lean, addresses a long-standing question in fluid dynamics.

The breakthrough, achieved by 10,000 AI agents, is a significant AI contribution to mathematics. The Navier-Stokes equations describe fluid behavior but have puzzled mathematicians for decades regarding solution behavior.

This problem, one of seven Millennium Prize Problems, offers $1 million for its solution. It concerns whether fluid solutions can develop infinite speeds over time, creating a singularity.

Two teams, OpenAI and a collaboration including Tristan Buckmaster, announced solutions. Both leveraged a novel strategy from mathematicians Diego Córdoba and Luis Martínez-Zoroa.

While the mathematical findings on idealized fluids have limitations due to molecular reality, they reveal counterintuitive aspects of turbulence.

Previous work had shown singularities in related equations. The challenge was proving it for Navier-Stokes without boundaries and with smooth forcing functions.

The AI teams appear to have overcome this final hurdle, building on Córdoba and Martínez-Zoroa's analytic techniques. The exact timeline and collaboration details are still being clarified.

The AI-generated proofs were formally verified, marking a new era in AI-assisted mathematical discovery.

AI-samenvatting op basis van de bron.