What It Means to Be a Mathematician When AI Does the Math

In the mid-noughties, when music by the Killers and Franz Ferdinand blared out of every pub and nightclub I passed, I spent my days and nights struggling through a Ph.D. in applied mathematics. My research focused on simulating how special light waves interact in liquid crystals and using simple equations to approximate and understand those interactions. When I look back at my thesis now, liquid crystal technology is old hat, and I imagine my work could be completed with AI assistance in a matter of days—maybe hours.

But the same cannot be said for the work of the pure mathematics Ph.D. students with whom I shared a cramped office at the University of Edinburgh. At the time, I felt sorry for these colleagues, who day after day sat at their desks, seemingly tearing their hair out and making no progress. (Though I was struggling too, I was at least always making some headway.) When we finished and went our separate ways, some hadn’t even published a paper.

Now, in hindsight, I finally understand why they toiled for years on abstract mathematical problems that only a handful of people in the world care about. It wasn’t arrogance, as I thought at the time; they weren’t trying to prove their superior intelligence by being the first to solve a seemingly intractable mathematical problem. It wasn’t even a form of masochism (which was my second guess)—penance for some imagined inadequacy. I realized they derived joy, satisfaction, and meaning from the long journey toward understanding.

"Sometimes, understanding just strikes you as being very beautiful. Sometimes it’s a feeling of accomplishment, like completing a marathon," muses Carnegie Mellon University mathematician Jeremy Avigad. "But it’s not quite either of those: It’s just a wonderful feeling when you’ve been thinking long and hard about something complex, difficult, and then—all of a sudden—it just comes together." This feeling has driven mathematicians throughout history.

AI systems are now starting to bypass this slow, deliberative process. Google DeepMind and OpenAI systems have reached gold-medal level at the International Mathematical Olympiad. DeepMind's Aletheia produced publishable Ph.D.-level research results. OpenAI disproved an important conjecture in combinatorial geometry. Additionally, LLMs combined with proof assistants are automating the formalization of mathematical proofs, potentially transforming the role of human mathematicians.