AI Solves a Major Unsolved Math Problem. Not Everyone Is Happy
At the annual Heidelberg Laureate Forum in Germany, which began on 13 September, attendees' conversations centered on how AI companies including OpenAI, Anthropic, and Google are advancing through mathematics, according to IEEE Spectrum.
Mathematics is described as a strong testing ground for AI because it involves step-by-step logical reasoning and answers that can be automatically and objectively verified. The report says AI has moved from struggling with everyday research-level problems to solving puzzles posed by Paul Erdős, verifying the proof of Fermat's Last Theorem, and, most recently, OpenAI announcing it had solved the Navier-Stokes existence and smoothness problem.
Of the seven Millennium Prize Problems posed in 2000 by the Clay Mathematics Institute, only the Poincaré conjecture has been solved by humans. OpenAI's claim, if verified, would mark a second. Fields Medalist Jacob Tsimerman of the University of Toronto said at a press conference that capabilities have increased faster than many expected, adding, "solving Navier-Stokes feels pretty definitive."
At a panel discussion, Fields Medalist Peter Scholze of the University of Bonn characterized such efforts as benchmarks and "some kind of PR stunt." Geordie Williamson of the University of Sydney said OpenAI "behaved extremely poorly." Michael Harris of Columbia University said he trusted mathematician Tristan Buckmaster's account of correspondence with OpenAI that Buckmaster described as coercive, censorious, and threatening. OpenAI did not respond to requests for comment prior to publication.
Williamson raised concerns that measuring understanding against unsolved problems is becoming uncorrelated, requiring the field to reevaluate assessment, hiring, and education. Mita Ramabulana of the University of Cape Town said two of 10 advances OpenAI announced in August overlapped with his work. Ailsa Robertson of the University of Amsterdam said colleagues intensively use LLMs, some spending thousands of euros on tokens, and that some feel they have no choice in order to keep pace with peers.
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Publisher excerpt
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 a