AI Breakthrough Tackles \$1M Math Problem as Credit Dispute Sparks Controversy

OpenAI announced Tuesday that its internal AI model produced a Lean-verified proof showing that the Navier-Stokes fluid equations can “blow up”—a mathematical phenomenon where the equations predict infinite velocity, which cannot occur in the physical world.

The result, achieved using approximately 10,000 coordinating AI agents over 88 hours, addresses one of the seven Millennium Prize Problems, each carrying a \$1 million reward from the Clay Mathematics Institute.

However, the breakthrough was immediately overshadowed by accusations from NYU mathematician Tristan Buckmaster, who claimed that OpenAI’s Sébastien Bubeck learned about his and Anthropic researcher Levent Alpöge’s unpublished, related proof and attempted to pressure them over credit before the announcement.

Buckmaster and Alpöge spent nearly a year developing their own approach to proving fluid blow-up, reaching a solution by August 22. According to Buckmaster, he informed an OpenAI mathematician on September 3 about his team’s work, emphasizing its personal and non-corporate nature.

Buckmaster alleges that during a call three days later, Bubeck disclosed that OpenAI’s model had already produced a 100-page proof tackling the same narrow approach Buckmaster says was rarely pursued by others.

Buckmaster claims Bubeck then presented two options: either OpenAI would publish the day after his team did, or Buckmaster would write up his paper alone, excluding Alpöge due to his employment at a rival lab. When Buckmaster indicated he would go public with his findings, Buckeck allegedly responded, “Why would you ruin your career?”

“If you don’t want me to be nice, then I don’t have to be nice,” Buckmaster quoted Bubeck as saying.

Buckmaster and Alpöge ultimately published their research papers independently. While Alpöge received credit in those publications, neither researcher was formally acknowledged by OpenAI—except through a quote tweet suggesting that “de-identified data derived from their usage of our products” may have contributed to improving the company’s models.

OpenAI and Bubeck Push Back

Bubeck, along with OpenAI and CEO Sam Altman, firmly denied Buckmaster’s account of events. In a follow-up post, Bubbeck shared text messages proposing a coordinated release involving Alpöge and offering to share OpenAI’s prompts, asserting he acted in good faith.

“I hope it’s clear from the message that we came in with the best possible intentions,” Bubeck wrote. “I never ever asked for Levent to be removed from authorship of his own work.”

Altman publicly supported Bubeck, stating he “acted with integrity and generosity throughout.” He added that OpenAI initially believed Buckmaster’s team had also solved the full Navier-Stokes problem but later realized they had only addressed the Euler equations—a related but distinct challenge.

According to Altman, OpenAI offered to delay its publication and allow Buckmaster’s team to release their findings first.

In a formal statement, OpenAI confirmed it had no prior knowledge of Buckmaster and Alpöge’s work before its publication and did not access any specific user data. However, the company stopped short of completely ruling out the possibility that general training data influenced its model’s output.

Fields Medalist Terence Tao praised Buckmaster and Alpöge’s underlying mathematics as a “remarkable achievement.” Their collaboration represents the second major AI-assisted mathematical breakthrough involving the same pair of labs in recent weeks, following Anthropic’s announcement that its Claude model had generated a computer-checked proof of Fermat’s Last Theorem.

Buckmaster and Alpöge’s most advanced result—the version closest to solving the actual \$1 million Navier-Stokes problem—remains unpublished pending final verification via the Lean proof assistant. Similarly, no external reviewers outside of OpenAI have yet independently examined the company’s 100-page proof.

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