OpenAI’s millennium proof dispute raises the question of whether researchers can trust AI labs

After mathematician Tristan Buckmaster accused OpenAI of misconduct, all parties have now gone on the record. The case raises hard questions for open science.

The fight over OpenAI’s AI-generated proof of the Navier-Stokes equations, one of the Clay Millennium Problems that carries a $1 million prize, has drawn public statements from everyone involved. Mathematician Tristan Buckmaster had previously leveled serious allegations against OpenAI. He claimed that after information about his research leaked, the company pressured him, tried to remove his co-author Levent Alpöge from the paper because Alpöge works at Anthropic, and threatened him with career consequences. There’s also suspicion that OpenAI may have trained its models on drafts the two researchers uploaded to Codex.Ad One thing is undisputed. By its own account, OpenAI heard rumors that Anthropic’s models had solved a Millennium Problem and then pointed its own resources at the same problem. On several other points, the stories diverge.Ad Buckmaster calls it “absolute academic malpractice” Alpöge and Buckmaster dispute OpenAI’s claim that its own solution differs significantly from theirs. They say they had entered a similar approach into OpenAI’s systems. As far as Buckmaster understands, that input ended up in the training data. Buckmaster sees this as “absolute academic malpractice.” OpenAI employees say the chance that OpenAI actually trained on the submitted solutions is low, especially if the two had disabled the option to exclude their inputs from training. Whether they did so isn’t publicly known. OpenAI employee Boaz Barak also pushed back on the idea that the model needed outside help at all. “It’s just cope to think that the model would have needed this. It actually started off by proving a stronger claim than they did. Anyone who has seen this model at work would not think it needs ‘hints.'”Ad In its official blog post, OpenAI acknowledges the gap in certainty. “While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models⁠.” OpenAI CEO Sam Altman backed Bubeck on X, saying the team had “acted with integrity and generosity throughout.” He said it had been suggested that Buckmaster and Alpöge should receive the award, but the team was met with “unfounded accusations of plagiarism.”Ad Altman also wrote that the effort started because of “rumors on the internet last week that Anthropic’s models had solved a millennium problem and we were curious if ours could do it too.”Ad Alpöge contradicts Altman on one key point.