Millennium Prize math problem solved by AI, Terence Tao says the entire discipline is facing a crisis

Millennium Prize math problem cracked by AI in one week, but Terence Tao says the entire discipline is facing a crisis Phoenix Tech Download the app for exclusive early access November 02, 2026 09:43:47 From Beijing Updated November 02, 2026 10:14:30

Phoenix Tech News, Beijing time, November 2 — The New Yorker recently published a feature documenting the dramatic shockwaves that artificial intelligence brought to the world of pure mathematics in 2026. As OpenAI and Anthropic successively cracked multiple century-old math problems, Fields Medalist Terence Tao and several other top scholars began calling on the academic community to hit the brakes, warning that human mathematical intuition and the academic ecosystem are being damaged in the runaway surge of computing power.

"Millennium Prize" problem broken, academia plunged into an existential crisis

On September 8 this year, OpenAI announced it had cracked the Navier-Stokes existence and smoothness problem, one of the million-dollar "Millennium Prize" problems. Three days later, the 51-year-old Terence Tao appeared on a stage at Caltech, uncharacteristically shedding the shirt he usually wears when lecturing and changing into jeans and a black T-shirt printed with "The Great Wave off Kanagawa." "I've just been through the weirdest week of my life," he said, pointing at the crude slides behind him and mocking himself; normally he might use AI to make a fancy presentation, but this time he used only the most basic software.

What made Tao anxious was the loss of control across the entire disciplinary ecosystem. From the start of 2026, large models such as GPT-5.2 Pro and Claude Fable 5 successively cracked multiple Erdős problems and the Jacobian conjecture that had plagued the academic world for decades, and in early October OpenAI released new results on 372 unsolved math problems in one go. But these AI-generated solutions often lack derivation details, rambling on at length about common-sense points an undergraduate could grasp at a glance, yet writing only a few lines at the most critical logical leaps. A flood of AI papers has overwhelmed math journals; those submitting sometimes cannot even understand their own papers, relying entirely on human mathematicians to volunteer free labor to review and verify them.

"We have to slow down; the current pace is insane," Tao said, noting that the math world has moved from the "scarcity of proofs" that prevailed before 2025 into an era of "proof proliferation." In mathematical research, the final answer is often not that important; it is the methodological innovations along the way to the answer that truly drive the discipline forward, and now the slow thinking process on which new problems depend for their birth is being destroyed.

Black-box operations and tech giants racing to publish spark outrage

In August this year, Anthropic mathematician Levent Alperg posted a long string of plus and minus characters on the social platform X, unveiling in one go multiple new solutions to Hadamard matrices that had puzzled the academic world for over a century, but Anthropic refused to disclose the run logs and derivation process in accordance with academic tradition. University of Sydney mathematician Jody Williamson felt the entire garden of mathematics had been sprayed with herbicide; it was like tossing humanity the ultimate answer "42" while depriving it of all the thinking process.

The release of the Navier-Stokes problem in September turned into an even bigger Rashomon-style affair. The day before OpenAI's announcement, New York University professor Tristan Buckmaster issued a statement saying that he and Alperg, using tools including OpenAI's public models, had already made major progress on the problem, while OpenAI, which burned millions of dollars in computing power, claimed to have completed the solution first in less than a week. Buckmaster suspects OpenAI obtained his research data behind the scenes; OpenAI denies it. Buckmaster revealed that Sebastian Bubeck, the head of the OpenAI team, once offered to list him as a paper author on condition that Alperg from rival Anthropic be removed from the author list. After Buckmaster refused and planned to make the matter public, the other party directly asked him why he wanted to destroy his own career.

The controversy prompted Tao and 25 other Fields Medalists to jointly publish an open letter. The letter warned that problem-solving and insight are becoming decoupled, that over-reliance on AI amounts to skipping daydreaming, debate and deep thinking, and that humanity will end up understanding less and less in the future.

The most urgent problem is how to train the next generation

Earlier this year, Tao was called AI's "evangelist" by the media because of a conversation with OpenAI executives and his cooperation in launching an AI math project. But now he has begun repeatedly emphasizing the value of "cognitive friction." He compared the current crisis to the urban transformation when cars replaced horse carriages: cities must keep their sidewalks and cannot turn all space into something suited only to cars, because no one would want to live in such a city.

In Tao's view, the most urgent crisis right now is how to train graduate students. In the past, graduate students needed months to chew through a moderately difficult topic, learning to think like a mathematician through trial and error; today AI can solve such problems in a few hours. He compared learning math to watching the soap opera "Emily in Paris" with his wife: the plot is clichéd but full of fun, and if the audience were given only a few-sentence plot summary, the point of watching the show would be completely lost, and no one could learn to make a show themselves.

This sense of "losing the fun" is spreading through academia. MIT mathematician John Urschel, who once played for the NFL's Baltimore Ravens, spent ten years studying a Gaussian elimination problem. To avoid being scooped by AI, he paid $200 a month to subscribe to GPT-5.6 Sol and Claude Fable 5, fed his research steps to the AI, and finally obtained a correct but extremely ugly proof, which was then polished by hand and published. The result was preserved, but Urschel said frankly that there was no fun in it at all, because the most fascinating part of mathematics is precisely the struggle of groping in the dark; writing out all the answers directly is the most boring part.

Still, the older generation of scholars retains a measure of optimism. Charles Fefferman, a 77-year-old Princeton professor who once wrote the official description of the Navier-Stokes problem, believes OpenAI's proof is most likely correct. He likened doing mathematics to "devil's chess where you can take back moves": even with a thousand stupid ideas, as long as there is one brilliant idea, you are a good mathematician. He believes that in the past some ideas with only a 5% success rate were abandoned because verifying them required a lifetime, and now if it takes only two days to test a result, mathematicians will instead become more courageous and more imaginative. (Editor/Yu Lei)

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