For years, the leaders of the most powerful tech companies have predicted that AI will displace a significant portion of the workforce. The impact will supposedly vary between industries, we’re told time and again, but none will be totally immune to the coming wave of automation. The much-feared “job-pocalypse” has not yet materialized in the vast majority of sectors. Some mathematicians, however, believe their field has officially entered a new age with an uncertain future, thanks to the rise of powerful AI models.
The field erupted in controversy on September 08, after OpenAI announced it had solved the Navier-Stokes smoothness and existence problem, which had vexed mathematicians for close to a century. Any celebratory mood OpenAI may have felt was largely drowned out by anger from many in the mathematics community, who accused the company of steamrolling two researchers who had made recent progress on another, related problem, which they were preparing to publish. OpenAI has said it acted in good faith by offering one of the researchers, the NYU mathematician Tristan Buckmaster, partial credit for the Navier-Stokes solution. But it also tried to push out Buckmaster’s co-researcher, Levent Alpöge, who works for Anthropic. The whole episode seemed to point towards a grim future for mathematics, one where corporate interests and politicking trump good-natured scientific collaboration.
The controversy heated up even more last Wednesday, when Andreas Thom, a mathematician at the Dresden University of Technology, also accused OpenAI of foul play. In a series of social media posts, Thom said he reached out to OpenAI after noticing that the company’s solution to another math problem (unrelated to Navier-Stokes) seemed eerily similar to work he had recently done with fellow mathematician Gábor Kun. He asked whether that work, which he and Kun had been discussing with ChatGPT, had been directly fed to the model that OpenAI used to solve the problem or used during the model’s training process. According to Thom, the response from OpenAI researcher Mark Sellke was unequivocal, but vague: “that did not happen.”
Photo of Andreas Thom. © Courtesy of Thom
Following the backlash from the mathematics community, OpenAI said in an X post that neither the human researchers nor the AI agents that had worked on the Navier-Stokes solution had seen “any specific user data” throughout the process, though it added that it “cannot rule out that de-identified data derived from their usage of our products helped improve our models.” After the company made that clarification, Sellke’s response started looking more disingenuous to Thom. “When it really gets to [be] a more tense situation, they actually are much more careful in what they’re saying,” he told me. Sellke’s flat-out denial was “not honest,” he said. “You should say that you don’t know.”
Not long after OpenAI published its Navier-Stokes solution, Buckmaster—the NYU mathematician who accused the company of trying to strong-arm him into publishing his results on the company’s own terms—said that the AI genie was out of the bottle, and that the role of human mathematicians had been forever transformed. In an interview with the Australian Broadcasting Corporation, he voiced a sense of grim defeatism. “I think it’s pointless,” he reportedly said. “Like, I think the game is up.”
Thom agrees that a threshold has been crossed, but he doesn’t sound quite so resigned. “I think it will fundamentally change everything,” he said, before adding: “We have to come together as a mathematical community to redefine our subject, to redefine what math students are supposed to learn.”
He also feels that the recent controversies surrounding AI and mathematics point to a bigger, more profound question: As he puts it: “Should these results produced by AI be considered to be the results of the general mathematical community?” In other words, since AI fundamentally depends on the labor and contributions of countless humans—even if those efforts aren’t explicitly credited by the companies behind the technology—can any AI model truly be said to be accomplishing a “breakthrough” in any field, including mathematics? “The whole creativity of the system is trained by human creativity,” Thom said.
It will take time for the tech industry and academia to work out such questions, and to figure out a mutually agreeable solution to the thorny problem of attribution in an age when human researchers compete with AI companies to be the first to publish new scientific discoveries. Three days after it published its Navier-Stokes solution, twenty-seven recipients of the Fields Medal—the most prestigious award in mathematics—signed a statement asserting that “the push by AI companies to solve mathematical problems as a benchmark is detrimental to the science of mathematics, and to the mathematical community.” They also argued, presumably in a nod to the questions raised by Buckmaster and Thom, that the use of AI to solve and publish mathematical breakthroughs “raises severe attribution and plagiarism questions.” On Monday, OpenAI announced in a blog post that it was forming an “advisory group” in collaboration with independent mathematicians, with the goal of giving the broader mathematical community “a voice in how we move forward.”
But for Thom, one thing is already clear: mathematics has now officially entered that new age, even if other industries are still dubious of tech leaders’ claims of impending, large-scale transformation. “You first believe it when the wave hits you,” he told me. “And I think mathematics has been hit now.”