OpenAI claims 10,000 of its AI agents solved one of mathematics' hardest problems in 88 hours

OpenAI has published a paper asserting that its AI model solved the Navier-Stokes existence and smoothness problem, classified as one of the Clay Mathematics Institute's Millennium Prize Problems. The system achieved this in 88 hours by utilizing up to 10,000 AI agents, which collaborated to generate a formal proof in Lean, a formal proof language.

The Navier-Stokes equations, which describe fluid motion, are crucial in fields such as weather forecasting and aerodynamics. The Millennium problem inquires whether the equations consistently yield smooth solutions in three dimensions or if they can develop singularities under certain conditions. OpenAI's proof indicates such a breakdown, yet it does not imply that fluids will behave in a physically impossible manner; rather, it concerns the mathematical system's limitations.

The Clay Mathematics Institute first selected the Navier-Stokes question as a Millennium Prize Problem in 2000, with a $1 million prize, and only one other problem has been solved since—Poincaré's conjecture. OpenAI's work hinged on a multi-agent approach, where different groups of AI agents pursued distinct reasoning paths, with researchers exchanging useful insights between them.

Mathematicians will review the paper to validate the proof. If successful, this breakthrough could demonstrate that AI systems can tackle some of mathematics' most challenging open problems. The Navier-Stokes problem pertains to the mathematical behavior of fluids, not a prediction of physical impossibilities. The company acknowledges that the effort was costly, requiring significant computational resources, but asserts that costs should decrease as they enhance their systems and infrastructure.

Some mathematicians, like Terence Tao, warn that AI might undermine the discipline if major problems are solved with minimal human intervention.