OpenAI solves longstanding math problem with 10,000-agent swarm — but can't rule out benefitting from a researcher's private Codex data

OpenAI today announced an internal AI system solved the Navier–Stokes existence and smoothness problem, one of the seven notoriously challenging Millennium Prize Problems in mathematics that has remained unsolved since its introduction 26 years ago, using a coordinated system that involved roughly 10,000 concurrent AI agents.

The problem, named for 19th-century mathematicians Claude-Louis Navier and George Gabriel Stokes, asks a basic but extremely difficult question about equations used to describe how fluids such as air and water move: can a fluid that starts out behaving smoothly eventually develop a mathematical breakdown?

OpenAI says its system produced a new proof showing that, under certain conditions, a smoothly moving three-dimensional fluid can reach a point where its calculated speed grows without limit in a finite amount of time. In practical terms, that would mean the equations themselves eventually stop providing a physically meaningful description of the fluid.

But OpenAI's announcement also comes with a dispute over how the work was produced and who should receive credit.

An NYU mathematician involved in closely related AI-assisted research released a statement on Mastodon last night, prior to OpenAI's announcement, questioning whether the company's model could have been trained on or otherwise benefited from research he and a collaborator from Anthropic had conducted in part using Codex, OpenAI's coding and work-focused AI harness and application.