The Year Math Changed Forever
The New Yorker · Rivka Galchen ·
A.I. is solving problems that stumped the field for decades, Rivka Galchen writes. Mathematicians look to Terence Tao for guidance on their altered world.
Terence Tao was ten years old when Erdős visited his home town of Adelaide, Australia, in 1985. Erdős loved children and called them epsilons. Tao, a mathematics prodigy, had started taking college-level courses at age nine. Erdős posed a problem for him and Tao to work on together. A photograph of their meeting, taken by Tao’s mother (who had been a math teacher before having kids), shows the young mathematician and the old one deep in thought, hands at chins, looking at the notepad before them. “I wish I remembered more about the encounter,” Tao recently said. Erdős later sent the Tao family a note, handwritten on Bell Labs stationery, that, after brief wishes of a good New Year, reiterated the problem they had discussed: “Let 1 ≤ a1 < a2 < . . . atn ≤ n be a sequence of integers . . .”
In May of 2023, the mathematician Thomas Bloom began gathering the known remaining unsolved Erdős problems on a website, erdosproblems.com. Their depth and difficulty vary, deliberately. Erdős described some of them as “marshmallows” and others as “acorns.” In a talk in February of this year, titled “Machine Assistance and the Future of Research Mathematics,” Tao quoted Erdős’s characterization of a marshmallow as “a tasty tidbit supplying a few moments of fleeting enjoyment,” and of an acorn as “requiring deep and subtle new insights from which a mighty oak can develop.”
The role that artificial intelligence will play in research mathematics has been talked about a fair amount in the past five years, and a fearsome, unbounded amount in the past five months. Tao—a professor of mathematics at the University of California, Los Angeles, and a founder, in 2025, of the Foundation for Science and AI Research—has been one of the most prominent voices in this discussion. This is in part because he is a venerated mathematician who won a Fields Medal, the highest honor in the discipline, at age thirty-one; in part because, like Erdős, he is especially collaborative and community-oriented; and in part because he was already thinking seriously and publicly about A.I. when many of his peers still thought, as Tao put it, “Oh, it’s a toy, it makes so many mistakes, it’s never going to be useful.” A.I. labs such as Google DeepMind, OpenAI, and Anthropic were trying to demonstrate otherwise. From their perspective, math problems are practical benchmarks to measure the capabilities of their products. Mathematical proofs can be digitized and objectively verified, and the field of mathematics is highly respected. Early on, A.I. tools were conspicuously bad at basic math. When OpenAI’s GPT-4 Turbo was asked to count the number of “L”s in “lollapalooza,” it answered “Five.” The tools have since improved dramatically, but even now L.L.M.s find difficult some tasks that we find easy, and vice versa. “The means by which an A.I. solves a problem is just so orthogonal to the way a human solves a problem,” Tao said, in a recent lecture. A.I. proofs often devote pages to what would be obvious to an undergraduate, then offer only a few lines on what to a human mathematician is a large, cloudy move.
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