OpenAI fought dirty on career-making math problem

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NYU mathematics professor Tristan Buckmaster announced three proofs on Tuesday with a preliminary finding on one of the major unsolved problems in theoretical mathematics. The findings, made in collaboration with Anthropic mathematician Levent Alpöge and using both Codex and Claude AI models, are significant in themselves — but they’re also accompanied by an unusual controversy surrounding OpenAI’s attempts to solve the same problem.

“There is another part of this story,” Buckmaster wrote in his statement announcing the proofs, “and one that, honestly, I very much wish I did not have to be concerned with.” According to the statement, a parallel effort by OpenAI built on their work before it became public, leading to a tangle of academic rivalries and conflicting claims.

Shortly after the Buckmaster s statement, OpenAI published a full proof of the Navier–Stokes existence and smoothness problem , which Buckmaster s findings had taken steps towards. According to OpenAI, the proof was discovered by an unreleased next-generation model, which has tackled a range of different unsolved problems over the past week.

All told, the week-long effort consumed 300 billion output tokens — $22.5 million worth of compute, if charged at current Astra rates .

The Navier-Stokes existence and smoothness problem is one of the seven Millennium Prize problems — a set of major unsolved math problems, each carrying a $1 million bounty from Clay Mathematics Institute for the first person or group to provide a solution. The Navier-Stokes equations are widely used in fluid mechanics but poorly understood in theoretical terms. A solution would represent a significant advance in the collective understanding of mathematical physics.

While Buckmaster and Alpöge were finalizing their own results, they learned that “information about our progress had been passed to OpenAI.” When they contacted OpenAI, they were told that OpenAI had already achieved a full proof of the central problem. But when they asked follow-up questions about when OpenAI had begun its research into the problem and how much human input was involved, the answers became more evasive.

“It emerged that an entire team had been working on the problem,” Buckmaster said, and that an insane amount of compute had been used….