OpenAI's 10,000 AI agents solve 90-year-old maths problem; NYU prof says it cheated

OpenAI claims an unreleased AI model has resolved the Navier-Stokes existence and smoothness problem, a fluid dynamics conundrum that has puzzled mathematicians for around 90 years and comes with a $1 million prize from the Clay Mathematics Institute. To tackle the issue, the company deployed approximately 10,000 AI agents who managed to produce a proof within 88 hours.

The announcement, however, took a surprising turn when NYU mathematics professor Tristan Buckmaster, in a joint effort with Levent Alpöge, published his own findings on a closely related problem and accused OpenAI of using his unpublished work to zero in on a potentially advantageous research direction. Buckmaster and Alpöge had spent months incorporating their drafts into Codex, OpenAI's own coding tool.

The Navier-Stokes equations, which describe the behavior of liquids and gases, are crucial for aircraft design, weather forecasting, and simulating blood flow. Mathematicians have been striving to determine whether these equations can break down—whether a fluid that starts off smooth can suddenly reach infinite speed within a finite timeframe, a phenomenon known as a singularity.

OpenAI's proof argues that it can. This solution describes a vortex that spirals inward, stretches out, and maintains finite energy throughout. The 10,000 agents and 130 billion tokens employed by OpenAI managed to turn a 90-year-old question into a four-day endeavor. OpenAI initiated training on the internal model on August 28, naming it significantly more powerful than GPT-6 Astra.

On September 1, the company learned of rumors that two Millennium Prize problems had been resolved. It then shifted its focus to the remaining problems, with the team working on Navier-Stokes exchanging around 2.7 million messages and utilizing roughly 130 billion output tokens before arriving at the proof on September 5. Verification of the proof in the Lean proof language took an additional 17 hours.

The estimated compute bill for the broader effort ranged between $10 million and $22.5 million. OpenAI states it will not claim the prize money. Buckmaster's contention is that no model can achieve this specific route within four days. He had been collaborating with Levent Alpöge, a mathematician employed by Anthropic on a personal basis, using both Codex and Claude.

On August 15, the duo proved that the Euler equations, the frictionless counterpart of Navier-Stokes, can indeed blow up. This approach was based on a technique called forcing, which had only recently been explored by Diego Córdoba and Luis Martínez-Zoroa, a fact that Buckmaster emphasized was not widely pursued. He posted his results at 11:58 PM on Monday, along with a statement addressing his inquiries about the Codex sessions.

He reported not receiving any answers regarding the training sessions. Buckmaster alleges that he was offered sole authorship in a paper that omitted Alpöge's name, and when he threatened to go public, the response was: "Why would you ruin your career?" OpenAI denies having seen the work but acknowledges that they cannot rule out the possibility that de-identified data from their users' use of their products may have improved their models.

The company's post states that "no specific user data was accessed in order to solve this problem" and that neither its researchers nor its agents saw the pair's work before its publication. Both OpenAI researcher Sébastien Bubeck and OpenAI CEO Sam Altman have denied asking for Alpöge's name to be removed from the paper, with Altman stating that the two approaches now appear distinct as both are now public.

The Clay Mathematics Institute has not yet verified anything, and some mathematicians point out that OpenAI's cracked version relies on a term that many mathematicians generally exclude from the problem. This cleanup, therefore, remains unclaimed twice over. What has been established, however, is the warning accompanying the announcement, directed at every researcher currently engaged in unpublished work with a frontier lab's tools.

Terence Tao, who has previously cautioned about the implications of this development for the field, succinctly expressed the broader cost: "It's like having machines that can lift weights for you at the gym."