OpenAI’s unreleased experimental artificial intelligence model found an answer to the Navier-Stokes Millennium Prize problem in 88 hours after deploying a swarm of 10,000 agents. The computational feat cost millions of dollars in compute power, drawing intense reactions from the mathematical community over speed, competitive pressure, and credit attribution.
OpenAI announced that an unreleased artificial intelligence model has resolved the Navier-Stokes equations challenge. The breakthrough targeted one of seven Millennium Prize problems carrying million-dollar rewards. Only one of these puzzles had ever been solved.
OpenAI Deploys 10,000 Agents
OpenAI deployed a swarm of 10,000 AI agents running on a new experimental model, churning through millions of dollars’ worth of computing power over a few days. The system completed what the American Mathematical Society called the final steps
of the solution process in just 88 hours, with verification requiring another 17 hours.
OpenAI researchers heard rumors that mathematicians at rival company Anthropic were close to solving two Millennium problems on September 1, prompting OpenAI to deploy its in-development model to beat them to it. Both companies are heading toward planned share market listings.
Solving Fluid Dynamics Equations
The Navier-Stokes equations model the behavior of fluids like water and air. While zooming into water flow should theoretically look identical except for speed, real-world molecules eventually appear, meaning the equations must break down at microscopic scales.
The Millennium Prize problem involved determining whether fluid swirls could shift their energy into smaller, faster swirls—accelerating infinitely to create a blow-up
in speed, also known as a singularity. OpenAI’s model found that the Navier-Stokes equations do indeed allow a blow-up under specific conditions.
The problem remains officially unsolved for now. The Millennium Prize conditions mandate that prizes cannot be awarded until at least two years after the publication of a potential solution.
Buckmaster Questions OpenAI over Data Use and Collaboration
One rival team closing in on a Navier-Stokes solution featured Anthropic staffer Levent Alpöge, who collaborated in a private capacity with New York University mathematician Tristan Buckmaster.
Buckmaster stated that he and Alpöge had used OpenAI’s publicly available models in their work and pursued a similar line of thinking. When Buckmaster asked whether OpenAI’s model had used their data to produce its results, he received no answer. He reported that OpenAI offered a collaboration on the condition that he remove Alpöge’s name from the work because of Alpöge’s Anthropic affiliation—an allegation OpenAI denies.
German mathematician Andreas Thom raised concerns that OpenAI’s models may have hoovering up unpublished human work and presented it as AI-generated. US-Australian mathematician Terence Tao expressed reservations regarding the indiscriminate use of powerful solution-extraction tools
to solve problems at the expense of broader understanding, warning that such practices could discourage researchers from sharing promising work with the wider community.
