AI is getting better at math very fast. In 2025, AI couldn’t beat the top high school students in the International Mathematical Olympiad. But this year, it’s solving open problems that no human mathematician has solved. In response, much of the field has tried to lay out ground rules for acceptable AI use.
In June, following a series of prominent AI proofs, a group of top mathematicians promulgated the Leiden Declaration, which asserted, “Mathematics produces not only a body of results, but also understanding, clarity, and judgment among the communities of mathematicians who have shaped them.” Meanwhile, top mathematicians have been pushing for similar principles in personal essays — math is about human understanding, they say, not just finding the answers.
“Suppose we had a library filled with proofs of every theorem [in mathematics], as well as excellent guides that could, given a question, take us to the answer and explain it,” mathematician Daniel Litt said. “What would a mathematician do in such a library?”
Kai Williams is a writer at Understanding AI who recently reported from the International Congress of Mathematicians and has a new story in The Atlantic called “Math Can’t Go On Like This.” To explore the angsty questions plaguing today’s mathematicians, Williams joined me for a Substack Live conversation.
This debate has implications far beyond mathematicians. It also has a lot to tell us about how to maintain and improve human skills as AI surpasses our capabilities in a variety of fields.
“I do worry about the world where AIs are just better than humans at everything,” Williams told me, “But I think at that point, it’s not just a mathematics problem.”
In our discussion, we unpacked a controversial episode in which OpenAI raced to beat two human mathematicians to a solution, spending the equivalent of $6 million to $10 million in just a few days so it could get credit for an answer.
I also asked Williams, who once considered a career as a professional mathematician himself, what he thinks about the principles of acceptable AI use. While he isn’t sure exactly what sorts of lines the profession should draw, he is very protective of his freedom to do work on his own.
“As an amateur, I have problems I like to think about in the background sometimes when I have trouble sleeping or whatever, and those I very clearly do not want to ask for AI help … the kind of journey of trying to figure that out is where a lot of the fun is,” he told me. “The only way to get as deep an understanding is to stumble through an area yourself.”
