NYU professor Tristan Buckmaster announced three proofs on Tuesday, including preliminary progress toward the Navier-Stokes existence and smoothness problem, one of mathematics’ seven Millennium Prize problems. The work, conducted with Anthropic mathematician Levent Alpöge using a mix of AI models including Codex, was overshadowed by controversy after OpenAI published a full proof of the same problem shortly afterward.
Buckmaster said OpenAI’s effort, which he described as involving an unreleased model and substantial computing resources, began only after information about his and Alpöge’s progress reached OpenAI. He noted that the specific approach they had taken was unusual, making it suspicious that OpenAI arrived at the same method independently. OpenAI’s own account placed the start of its effort on September 1, following rumors that the problems had been solved, and confirmed ongoing communications with Buckmaster’s team.
Buckmaster further alleged that OpenAI mathematician Sébastien Bubeck pressured him to remove Alpöge’s credit and discouraged him from making the dispute public. OpenAI stated it had not accessed the researchers’ work before its public release and said its proof differed meaningfully from theirs, though it acknowledged it could not entirely rule out that de-identified user data may have influenced its models.
