Terence Tao on the Crisis Facing Mathematics as a Discipline After AI Conquers Mathematical Problems

The "Millennium Problem" Has Been Solved, and Academia Has Fallen into an Existential Crisis

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

What made Tao anxious was the loss of control over the entire disciplinary ecosystem. Starting in early 2026, large models such as GPT-5.2 Pro and Claude Fable 5 successively conquered multiple Erdős problems and the Jacobian conjecture that had plagued academia for decades, and in early October OpenAI released new results on 372 unsolved mathematics problems in one go. But these AI-generated solutions often lack derivation details, going 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 mathematics journals, and those submitting them sometimes cannot even understand their own papers, relying entirely on human mathematicians to provide free labor for voluntary peer review and verification.

"We have to slow down; the current pace is insane," Tao pointed out, noting that the mathematics community has moved from the era of "proof scarcity" before 2025 into an era of "proof glut." 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 Giants' Rush to Publish Provoke Outrage

In August of 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 troubled academia 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 that the entire garden of mathematics had been sprayed with herbicide; it was like handing humanity the ultimate answer "42" directly while depriving it of all the thinking process.

The September release on the Navier-Stokes problem turned into an even bigger Rashomon-style affair. The day before OpenAI's official 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 compute, claimed to have completed the solution first in less than a week. Buckmaster suspected that OpenAI had obtained his research data from its backend, and OpenAI denied it. Buckmaster revealed that Sebastian Bubeck, the head of the OpenAI team, had offered to list him as a paper author on the condition that Alperg from the 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.

This 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, and that overreliance on AI amounts to skipping daydreaming, debate, and deep thinking, so that humanity will in the future understand less and less.

The Most Urgent Problem Is How to Train the Next Generation

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

In Tao's view, the most urgent crisis right now lies in how to train graduate students. In the past, graduate students needed months to grind through moderately difficult topics, learning to think like mathematicians through trial and error; today AI can solve such problems in a few hours. He compared learning mathematics to watching the soap opera "Emily in Paris" with his wife: although the plot is clichéd, it is full of fun, and if the audience were given only a few-sentence plot summary, the meaning of watching the show would be completely lost, and it would be impossible to teach people to make a show themselves.

This sense of loss—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 problem about Gaussian elimination. 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 ultimately obtained a correct but extremely ugly proof, which was then polished by hand and published. Although the result was preserved, Urschel said bluntly 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. Charlie Fefferman, a 77-year-old Princeton University professor who once wrote the official description of the Navier-Stokes problem, believes that OpenAI's proof is most likely correct. He compared doing mathematics to "devil's chess where you can take back moves": even if you have a thousand stupid ideas, as long as you have 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 they would take a lifetime to verify, but now if it takes only two days to test a result, mathematicians will instead become more courageous and more imaginative.