OpenAI's Navier–Stokes Claim Puts Mathematicians in a Reckoning at Heidelberg Forum

Summary

On 13 September, leading luminaries and up-and-coming talents in mathematics and computer science congregated at the annual Heidelberg Laureate Forum in Germany for a week of discussion, networking, and—naturally—wurst. Having attended several of these events in the past, the mathematicians normally focus their chatter on which famed researchers are present, or what interesting problems they have been working on. But instead, every snippet of conversation caught in passing or any debate accidentally overheard was about how AI companies such as OpenAI, Anthropic, and Google are steamrollering their way through mathematics. And there is good reason for these fervent discussions. Mathematics is the perfect testing ground for AI, involving step-by-step logical reasoning and answers that are automatically and objectively verifiable. This has led tech giants to develop their AI mathematical capabilities at a terrifying rate this year, leading to both new solutions to previously unsolved problems and a reckoning within the community as to what it means to do math in the age of AI. Tech Giants Target the Millennium Problems In short order, AI has gone from struggling with everyday research-level problems to solving a whole raft of teasers posed by prolific Hungarian mathematician Paul Erdős, then verifying the proof of Fermat’s Last Theorem, and—most recently and famously—OpenAI announcing it had solved the Navier-Stokes existence and smoothness problem. As attendee and young researcher Ailsa Robertson, of the University of Amsterdam, put it: “AI and LLMs set the math community on fire over summer.” Of the seven extremely difficult Millennium Prize Problems posed in the year 2000 by the Clay Mathematics Institute, only one, the Poincaré conjecture, has been solved by humans so far. OpenAI’s claim to have solved a second, the Navier-Stokes existence and smoothness problem, if verified, represents a watershed moment for automated reasoning. Fields Medalist Jacob Tsimerman, of the University of Toronto, was keen to recognize this achievement during a press conference at the forum: “We’ve seen rapid increases in capabilities, even faster than many people, including myself, expected,” he said. “Is AI doing something new? I don’t know the details, but…solving Navier-Stokes feels pretty definitive.” Since this announcement, rumors have swirled about which of the remaining…