Did AI Just Solve One of Mathematics’ Biggest Problems?

OpenAI recently announced something extraordinary: an internal AI system had produced a proposed solution to the Navier-Stokes existence and smoothness problem, one of mathematics' legendary Millennium Prize Problems.

More precisely, the system constructed a finite-time singularity for the three-dimensional Navier-Stokes equations with a smooth external force, one of the routes permitted by the official Clay Mathematics Institute formulation of the problem. It does not settle the better-known question of whether the unforced equations always remain smooth.

According to OpenAI's official report, the Navier-Stokes effort involved on the order of 10,000 concurrent AI agents, 2.7 million messages and roughly 130 billion output tokens. The agents reached their proposed solution about 88 hours after the experiment began, followed by another 17 hours of Lean formalization and verification.

At first glance, it sounds like the kind of result people have long imagined from highly autonomous AI: give a system a problem mathematicians have struggled with for decades, let it work for a few days, and get a proof back.

But the story of how OpenAI got there is considerably more interesting.

The Story Started With Two Human Mathematicians

Before OpenAI launched those 10,000 agents, mathematicians Tristan Buckmaster of NYU and Levent Alpöge, who works at Anthropic, had already been making major progress on closely related fluid dynamics problems.

They weren't working without AI either.

Their research used tools including Claude and OpenAI Codex, and their results were formally verified using Lean. Their work included constructing finite-time blowup for the three-dimensional incompressible Euler equations with smooth forcing.

Their result did not solve Navier-Stokes, but it pushed further into a closely related area.

Then something interesting happened.

OpenAI later realized the rumors were connected to Buckmaster and Alpöge.