Can AI make mathematics more human?

Mathematician Yang-Hui He explains why artificial intelligence is fundamentally transforming mathematical work—and that's a good thing

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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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.

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.

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.