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Many mathematicians approach innovations with caution. It took several years before researchers equipped with computers began transforming entire fields of study, for example. Today a similar revolution could be imminent: artificial intelligence systems, particularly large language models, are beginning to permeate mathematical practice. I sat down with mathematician and physicist Yang-Hui He of the London Institute for Mathematical Sciences to talk about the potential of this technology, particularly for mathematical research.
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An edited transcript of the interview follows
Manon Bischoff: You spent years studying string theory, a field at the intersection of mathematics and physics. But in 2017 your career pivoted. How did that happen?
Yang-Hui He: At that time, there was a new trend in science. Instead of dealing with quantum gravity or the nature of time, suddenly everyone seemed to be talking about machine learning. That was the moment when modern deep-learning architectures really took off. Neural networks showed surprising performance, and many of my doctoral and postdoctoral students were no longer pursuing careers in finance or academia but were looking for jobs in machine learning. I felt that I had to at least understand what was going on.
That year my son was also born. He didn’t sleep, which meant I couldn’t either. I lay awake at night, taking an online course to understand what machine learning actually is. Coincidentally, the [Wolfram] Mathematica computer program had just released a new framework for neural networks. It was barely documented and extremely primitive by today’s standards, but it was enough to play around with
MB: And what did you do?
YHH: I applied this very simple neural network to datasets of Calabi-Yau manifolds. These are high-dimensional geometric objects that play a central role in string theory. I wanted to find out whether the network could recognize the topological properties of these figures
I didn’t have too high hopes. But to my surprise, it worked. The network was able to predict certain features with remarkable accuracy. That was truly amazing! Apparently, neural networks can somehow learn deep mathematical structures even though they know nothing about geometry or topology
MB: What does this mean for string theory?
YHH: Machine learning could advance the field. One of the greatest difficulties in string theory is finding the right version that describes our world. This depends on the exact type of Calabi-Yau manifolds [into which spatial dimensions might curl up]. The question is whether data-driven methods could help us search these countless possibilities more efficiently. Shortly after this insight was published, several other groups began to take up similar ideas. Within a few months, there was a wealth of work in this area.
MB: Despite the new possibilities, you have moved away from string theory
YHH: Once the initial excitement had subsided, I realized that—apart from the physical motivation—I was actually using machines to explore the structure of mathematics. This raises a much broader and more interesting question: Could these methods help us uncover patterns in many different areas of mathematics?
MB: How was this idea received?
YHH: Physicists were relatively easy to convince. They are used to computational tools and large datasets. At CERN [the European laboratory for particle physics near Geneva], they have been working with machine learning since [at least] the 1990s. But mathematicians are much more skeptical. For the past eight years, I have felt like a traveling salesman, going from field to field, asking people, “Do you have data? Let’s see if there’s a structure hidden in it.”
I was able to work with representation theorists, algebraic geometers, number theorists, combinatorists and differential geometers
MB: Many mathematicians do not yet use AI in their daily work. Do you think that will change?
YHH: Absolutely. Mathematical research is changing very rapidly right now and not just because of automation. One of the most interesting effects of AI is that it creates a new common language. Even in closely related areas of mathematics, it can be difficult to communicate with each other. An analytical number theorist and an expert in partial differential equations often don’t speak the same language. But as soon as you start talking about data, patterns and learning, there is suddenly common ground. In this sense, AI strangely makes mathematics more human—it encourages people to talk to each other again.
MB: You’ve used AI as a tool to find patterns in data and to make new assumptions. Are you also trying to use AI to actively prove something?
YHH: That is the crucial next step. Pattern recognition and hypothesis generation were the first phase. Now the real question is whether AI can help solve truly important open problems. I think we’re already close; it’s only a matter of time before we get there
MB: What makes you so sure?
YHH: Because AI systems are improving very rapidly. This is demonstrated, among other things, by projects such as FrontierMath. The aim of this project was to formulate difficult, unsolved math problems and their solutions to test the capabilities of AI. These had to be completely new to ensure that the AI had not already learned the solution in its training data
MB: So you had to come up with new tasks and solutions?
YHH: I was involved in the fourth phase of the project, in the summer of 2025, where 30 mathematicians were locked in a room. There we spent several days thinking up difficult, unknown math problems. We weren’t allowed to leave the room to prevent anyone from overhearing our conversations and perhaps posting [the questions] on the Internet
MB: Sounds exhausting
YHH: At least the food was good, and there was an endless supply of coffee and chocolate. But basically, we sacrificed all publications for the project because the questions with the solutions [were] new results that [could] not leave the room. We all signed confidentiality agreements
We did it because we really believe in this cause: that AI can benefit mathematical research
MB: How did the AI cope with the assigned tasks?
YHH: It was able to crack around 10 percent of the tasks within a month. That’s really exciting. And now the fifth phase of FrontierMath has started, which deals with significant open problems. So it could soon be that the AI achieves a mathematical breakthrough
MB: Does this prospect worry you?
YHH: Not at all. I don’t need to be the one to prove the theorems. I just want to know the answers
MB: What role will humans play when AI takes over research?
YHH: Humans will continue to be indispensable for interpretation, context and evaluation—to decide what is interesting and why. I often compare this to music. I didn’t compose Bach’s music, but I can listen to his music all day long and be deeply moved. It can be the same with mathematics
You can also think of AI as the ultimate mathematical library. One of my favorite examples involves a colleague who asked a very specific question about the monster group—something so technical that even experts didn’t know the answer right away. Using a language model, we were able to find the answer in a theorem buried deep in an old treatise
We would never have come across this work using conventional search tools. But AI has read virtually everything that has ever been published. In that sense, no mathematical work is lost anymore. AI will remember your work long after humans have forgotten it. I think that’s a nice thought
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