Cristiano De Nobili

As a mathematician, the OpenAI/Navier-Stokes story feels genuinely historic and unusually dramatic. Navier-Stokes is one of the seven Millennium Prize Problems, each carrying a $1M prize. These are not just hard benchmark questions. They are among the most important open problems in mathematics, and entire research programs can grow around finding even one plausible route toward them. Buckmaster and Levent Alpöge had spent most of the past year pushing a program started by Diego Córdoba and Luis Martínez-Zoroza. Their goal was to take known blowup constructions with rough forcing and push them to smooth forcing, ultimately toward incompressible Euler and Navier-Stokes. By August 15, they had obtained smooth-forcing blowup results for Boussinesq and Euler. They were using Claude and Codex heavily throughout the project, and Buckmaster says they had been putting their drafts into Codex. Then rumors started circulating that “Anthropic” had solved a major open problem. OpenAI says those rumors triggered a large-scale effort on the Millennium Prize problems. Thousands of agents were launched, first attacking nearby Euler problems before the effort moved toward Navier-Stokes. What made Buckmaster immediately suspicious was the direction: forced Navier-Stokes with smooth forcing. In his statement, he says this was precisely the route Córdoba and Martínez-Zoroza had opened and that he and Alpöge had “quietly chosen to attack.” Almost nobody else he knew was working on it. His reaction: “When I heard ‘forced,’ it was a bright red flag.” He then asked whether OpenAI’s model had been trained on, or otherwise had access to, their Codex sessions. According to Buckmaster, he was told the model did not look up user data, but when he asked specifically about training, he did not get a clear answer. OpenAI denies directly accessing their private work, but its own post says: “While unlikely, we cannot rule out that de-identified data derived from their usage of our products helped improve our models.” And then the story becomes genuinely dramatic. Buckmaster says he was offered publication arrangements, including one where he alone would present OpenAI’s Navier-Stokes result without Levent Alpöge as an author. He says Bubeck emphasized that Alpöge working at Anthropic was the complication. Buckmaster declined. He then says that when he told OpenAI he would make the episode public if the result was released that way, the response was: “Why would you ruin your career?” Bubeck disputes Buckmaster’s characterization of the interaction. Buckmaster is also careful about what he is claiming. He explicitly writes: “I do not know whether our data was used. I am not accusing anyone of anything.” That distinction matters. But I think Tristan’s most important observation is broader than the dispute itself. He calls this a “Deep Blue-Kasparov moment” for mathematics. For a Millennium Prize problem, the scarce intellectual resource is not merely the final proof. It is often years of taste, failed attempts, literature, intuition, and judgment that tell you where the promising path is. If a small group discovers that path, and simply revealing that it is promising can trigger 10,000 AI agents to attack it, then mathematics may be entering a world where identifying the right question becomes more valuable than solving it. And that could fundamentally change the culture of open mathematics. Tristan Buckmaster’s statement: cims.nyu.edu/~tristanb/state…