OpenAI has published a claimed solution to the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize Problems — each carrying a $1 million bounty from the Clay Mathematics Institute. According to the company, an internal, unreleased model orchestrated roughly 10,000 coordinating AI agents that arrived at the result in 88 hours, at a cost of millions of dollars in compute. OpenAI posted a writeup and a formal proof in the Lean proof assistant, called the outcome a milestone, and said it does not intend to claim the prize.

The timing is what turned a triumph into a controversy. One day earlier, New York University mathematician Tristan Buckmaster published related findings with Levent Alpöge, a researcher at OpenAI rival Anthropic (who, the company has stressed, was not acting for his employer). Buckmaster says he contacted OpenAI after learning it knew of their progress, to ask when its effort began and what data its model had been trained on. He describes the exchange as souring fast: an OpenAI researcher asked him “Why would you ruin your career?” when he said he would go public, and, when challenged, replied, “If you don't want me to be nice, then I don't have to be nice.”

OpenAI flatly denies using specific user data, including Buckmaster's Codex sessions, while conceding it “cannot rule out” that de-identified data drawn from users' product usage helped improve its models. Its own account says the sprint began after it heard rumors “on Twitter” that other researchers were closing in on Millennium Prize problems; it says it only later learned those rumors concerned Alpöge and Buckmaster. The company has not responded publicly to Buckmaster's other claims.

Mathematicians say the deeper issue is the norm being broken, not the competition itself. “This is clearly a PR victory for OpenAI,” said Oxford's Andras Juhasz, who nevertheless questioned how sustainable the approach is: “Suddenly, 10,000 mathematicians jump on your problem.” Researchers told The Verge the episode could push mathematics — a discipline that runs on an informal norm of trust, where colleagues share unfinished ideas expecting they will not become a race — back toward secrecy. “Even the thought that AI systems might steal ideas from our queries is chilling,” said Carnegie Mellon's Jeremy Avigad. The proof stands as a real demonstration of how fast AI is reshaping mathematics; how the field absorbs that is now the open question.

Sources