Fields Medalists Warn AI Labs' Race Threatens Mathematical Research

OpenAI announced this week it had produced a proof for the Navier-Stokes existence and smoothness problem, one of seven Millennium Prize problems carrying a $1 million reward from the Clay Mathematics Institute. The company said it used 10,000 coordinated agents running for 88 hours, consuming 300 billion output tokens at an estimated $22.5 million in compute costs.

New York University mathematician Tristan Buckmaster and Anthropic researcher Levent Alpöge had been working for months on the same problem, building on earlier work by Diego Córdoba and Luis Martínez-Zoroa. Buckmaster said he learned OpenAI was pursuing the problem only after making his own preliminary announcement.

“The goals of AI companies and the mathematical community are deeply misaligned.”

Buckmaster requested clarification from OpenAI and reported receiving vague responses, including a suggestion from OpenAI's Sébastien Bubeck to remove Alpöge from the collaboration due to his Anthropic affiliation. OpenAI stated it began work on September 1 after hearing rumors of a solution and denied seeing Buckmaster's unpublished work, though it could not rule out that model-processed data entered its training set anonymously.

In response, 25 Fields medalists — often described as the Nobel Prize of mathematics — signed an open letter warning that the objectives of AI companies and the mathematical community are "deeply misaligned." The letter argues that solving benchmark problems is a means to conceptual understanding, not an end in itself, and that the profession's most valuable resources are students and ideas cultivated through dialogue and mentorship.

The Navier-Stokes equations describe fluid and gas flows, including turbulence, weather patterns, and aerodynamic effects. Only one Millennium Problem, the Poincaré conjecture, has been solved to date. The Clay Institute has not yet validated OpenAI's claimed proof.