AI agent swarm may have cracked million-dollar math problem open since 1934 in 88 hours
OpenAI said on Sept. 8 that autonomous AI agents had produced a proof resolving the Navier-Stokes problem, one of the seven Millennium Prize Problems in mathematics.
An AI-powered swarm of agents may have solved a math problem that has perplexed experts since 1934, according to a report by Nature. The equations in question, the Navier-Stokes equations, are a fundamental model for describing fluid dynamics and have significant applications in predicting weather patterns, designing aircraft, and understanding blood flow in the human body.
The problem, one of the seven Millennium Prize Problems, was officially posed by the Clay Mathematics Institute in 2000, with a $1 million prize for a solution.
In a groundbreaking effort that began on September 1, a group of roughly 100 AI agents worked for about 50 hours to disprove regularity for a simpler version of the Euler equations. Building on this work, a subsequent team of around 10,000 agents spent 88 hours tackling the full Navier-Stokes system. The final verification phase, which lasted 17 hours, involved an additional model to ensure the results were accurate in the Lean formalization system.
The collaborative process involved the exchange of nearly five million messages among the AI agents, and the entire project reportedly cost millions of dollars in computing resources. While OpenAI claims it did not use any data from the pair's unpublished work, Tristan Buckmaster of New York University and Levent Alpöge from Anthropic published their related results just 12 hours before OpenAI began its own project.
The pair's claims have sparked controversy, with allegations of OpenAI researcher Sébastien Bubeck attempting to exclude Alpöge from authorship and questioning the role of private Codex material from OpenAI.
Regardless of the controversy, the AI-assisted proof, if verified, would represent a significant milestone in the history of mathematics. It could potentially mark a turning point in how mathematicians approach difficult problems, as the result would be considered one of the most important mathematical proofs ever produced by an AI model.
The Clay Mathematics Institute, which has yet to award the $1 million prize, has stated that a proposed solution must be published in a qualifying outlet, remain in print for at least two years, and win the acceptance of the mathematical community before an award is considered.
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