A new problem to solve

From the New York Times: Terence Tao is typically described as one of the world’s greatest living mathematicians, but right now he is doing very little math. “I’m on a war footing,” he said while grabbing coffee during a two-day math workshop at the University of California, Los Angeles, that was rife with talk about the existential crisis that artificial intelligence has created in his field. Days earlier OpenAI had announced that it had solved the Navier-Stokes problem, one of seven “Millennium Prize problems” that had stymied the greatest minds in math for nearly a century. “There are no rules any more,” Dr. Tao, 51, said in an interview before the workshop in his modest office on the U.C.L.A. campus, his home since 1996, when he arrived after completing his doctorate at Princeton at the age of 20. ...He was hit by a bigger bomb on Oct. 6, when OpenAI released more than 350 findings in nearly every subfield of the profession, including algebra, number theory, theoretical computer science, mathematical logic and topology. Stunned mathematicians, some who were close to solving problems they had worked on for years, found themselves beaten in an instant by A.I.

Dr. Tao, who has been a tenured professor since the age of 24, said senior academics like himself are not as threatened by A.I. as those starting out. But the math world is looking to him for answers. He has accepted that his celebrated status has made him an unofficial spokesman for the field, a job that for now is consuming most of his time. Until recently his job was as a bridge between the slow-moving world of higher math and the scorching speed of A.I. Dr. Tao, who uses A.I. as an assistant to run calculations, write code, search vast troves of literature and brainstorm ideas, has been experimenting with OpenAI’s models since 2023. He was an enthusiast for a “best of both worlds” future. OpenAI’s releases have now left him feeling used. “As recently as a year ago, I had a pretty good relationship with many employees at OpenAI,” he said in a recent phone conversation ...“At this point, I don’t see a way to constructively engage.”

...At the heart of the crisis in the profession is a menacing question. If solving hard problems is a mission of math, what happens when machines can do it faster? So much of higher math — hiring, promotions, graduate training and acclaim — is based on the difficulty, quality and the impact of papers (the written documents explaining proofs) that a mathematician produces. The consensus is that A.I.-assisted problem solving is the inevitable future, but no one knows exactly what that new world will look like. “Deep uncertainty will persist in these next years,” a draft report by a group of mathematicians meeting at Harvard on Ph.D. education concluded last month...

Full story at https://www.nytimes.com/2026/10/16/us/math-ai-terence-tao.html.