Every party to the fight over OpenAI's claimed AI-assisted result on the Navier–Stokes equations has now put its version on the record, and the part nobody disputes is the part that matters. By OpenAI's own account, the company heard rumors that Anthropic's models had solved one of the Clay Mathematics Institute's Millennium Prize problems, which carries a $1 million award, and redirected its resources at the same problem. Mathematician Tristan Buckmaster, who says OpenAI pressured him afterward, calls what followed "absolute academic misconduct."
Buckmaster's allegations, made after information about his research leaked, are four. That OpenAI pressured him. That it tried to remove his co-author Levent Alpöge from the paper because Alpöge works at Anthropic. That it threatened consequences for his career. And that it may have trained models on drafts the researchers uploaded to Codex.
OpenAI's rebuttal runs on two tracks that do not quite meet. The first is that its solution differs substantially from the researchers' approach — which Alpöge and Buckmaster reject, saying they fed a similar method into OpenAI's systems and that, as Buckmaster understands it, the data could have entered the training set. The second is a denial that the help was ever needed. OpenAI researcher Boaz Barak said the system proved a stronger statement than the paper's authors did from the outset, so it required no hints, and that anyone familiar with how that model works would not assume it needed such pointers.
Then there is what OpenAI wrote down. In its official publication the company conceded that the possibility cannot be fully excluded: while unlikely, anonymized data derived from Buckmaster's and Alpöge's use of its products could have helped improve the models. Internally, OpenAI staff consider training on the submitted solutions improbable, particularly if the researchers had switched off the setting that permits their data to be used for training. Whether Buckmaster and Alpöge enabled that opt-out is not publicly known.
Sam Altman backed Sébastien Bubeck on X, saying the team acted in good faith and in the open, that Buckmaster and Alpöge were even offered the award, and that the researchers responded with unfounded plagiarism accusations instead. Altman also confirmed the trigger: the work began after last week's rumors that Anthropic's models had solved a Millennium problem, and the team was curious whether its own models could do the same.
Alpöge contradicted Altman on one detail. Altman said it was difficult to extend him the same offer because he did not want to discuss collaboration or coordinate with the company. Alpöge says he would have been glad to work with OpenAI, that authorship was not decisive for him, that he supports labs collaborating for the sake of scientific progress, and that he finds the episode sad.
The unresolvable question here is being treated as a coincidence, and it is not one. Only one party to this dispute can actually settle whether the researchers' drafts touched the training set: the party that owns the logs. OpenAI has not said whether the opt-out was on. It has instead published a sentence conceding that anonymized data from those users may have improved the models — which is a strange thing to write if the opt-out is the protection the setting is sold as being. The asymmetry is the story. A researcher who uses a lab's product cannot audit what the lab did with the input, and the lab's own denial is the only evidence on offer.
The precedent that concerns me more than the plagiarism claim is the uncontested one. A rumor, unverified, about a competitor's model was sufficient to move enormous compute onto a specific open problem in days, with the aim of solving it first and publishing first. That is a new kind of competitive pressure in mathematics, and it does not require anyone to have behaved badly with data for it to reshape behavior.
Terence Tao, among the most influential living mathematicians, made the same point on Mastodon: even a rumor that someone is working on a problem can now launch a large AI-driven effort capable of closing it before the original project has realized its potential. Tao warned that the incentives push scientists toward not sharing promising directions with the wider community at all.
Which is the actual cost. The Millennium problem will eventually be settled one way or another, by whoever gets there. The habit of telling colleagues what you are working on is centuries old, unprotected by any setting in a product menu, and considerably easier to lose.