Professor Tristan Buckmaster alleged OpenAI copied research and threatened him

OpenAI Claims AI Solved Navier-Stokes Problem

OpenAI announced on September 8 that its unreleased Astra model solved the Navier-Stokes existence and smoothness problem, a Millennium Prize Problem in mathematics with a one-million-dollar prize.

The company said in a blog post that ten thousand AI agents worked for roughly eighty-eight hours to produce the proof. OpenAI estimated the computing cost reached fifteen million dollars and declared it would not claim the associated prize in the end.

The result concerns whether the widely studied three-dimensional Navier-Stokes equations for fluid motion can develop a finite-time singularity known as a blow-up in nature, mathematicians said.

The equations underpin weather forecasting, ocean current studies, aircraft design, and many other important engineering applications worldwide, according to researchers. The Clay Mathematics Institute selected this challenge in 2000 as one of seven Millennium Prize Problems, each carrying a one-million-dollar bounty.

Only one Millennium Prize Problem had been solved before, when Russian mathematician Grigori Perelman cracked the Poincare conjecture between 2002 and 2003 and later declined the one-million-dollar prize.

Professor Alleges OpenAI Copied Work And Threatened Him

Professor Tristan Buckmaster of New York University publicly alleged that OpenAI may have copied his work and then threatened him. Buckmaster and Levent Alpoge, a researcher at OpenAI rival Anthropic, had worked on the forced Euler problem for about a year.

OpenAI said it began its Navier-Stokes effort last week after hearing a rumor about the two mathematicians' breakthrough and then reached out to them for a joint announcement.

Buckmaster said a Friday call with OpenAI scientist Sebastien Bubeck sounded suspiciously like his own team's approach to the Euler problem. He asked whether OpenAI's model had accessed his and Alpoge's Codex logs, and he received no clear answer about training.

Buckmaster claimed Bubeck offered two paths that would remove Alpoge's name from any joint credit and then warned him about his career because Alpoge works for Anthropic.

Bubeck later said on X that he only meant to warn Buckmaster about making unfounded claims that could damage his career. He publicly admitted his threatening-sounding response was an extremely poor choice of words and the opposite of his stated intent.

Verification Questions And Wider Concerns Remain

OpenAI's proof has passed formal verification through Lean, the proof assistant language, but mathematicians are still digesting its long 166-page paper, according to many experts outside OpenAI.

Mathematical physicist Gregory Eyink of Johns Hopkins University said nobody has completely verified the proof yet on the human side, and the community remains very cautious for now.

The proof addresses only specific permitted statements within the Millennium Prize formulation, not the entire problem, according to some critics. The Clay Mathematics Institute historically takes years to officially recognize solutions, as shown by Perelman's eventual Poincare proof recognition in 2010.

OpenAI denies its agents had direct access to the duo's unpublished work, but chief research officer Mark Chen cannot rule out that de-identified data helped training.

Terence Tao, a Fields Medal recipient regarded as the greatest living mathematician, warned that rumors can trigger massive AI effort and discourage open science, reversing centuries of tradition.