Yang-Hui He: Why AI Will Permanently Transform How Math Is Done
episodePreviously titled “Math Will Never Be The Same Again... | Yang-Hui He” — renamed by the publisher on Aug 3, 2026
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What is the main topic discussed in this episode?
Younghui Hei, welcome to the podcast. I'm so excited to speak with you. You have an energetic humility and your expertise and your passion comes across whenever I watch any of your lectures. So it's an honor.
Uh it's a great pleasure and great honor to be here. In fact, uh I'm a great admirer of yours. You've uh interviewed several of my very distinguished colleagues like, you know, Roger Penrose and Edic Franco. I actually watched some of them. It's actually really nice.
Wonderful, wonderful. Well, that's humbling to hear. So firstly, people should know that we're going to talk about or you're going to give a presentation on AI and machine learning mathematics and the relationship between them as well as the three different levels of what math is in terms of production and understanding, bottom up, top down, and then the meta. But prior to that, what specific math and physics disciplines initially sparked your interest? And how did the collaboration with Roger come about?
So my uh my you know my bread and butter was uh um mathematical physics, especially, you know, sort of the interface between algebraic geometry and string theory. So that's my background, uh what I did my PhD on. And um so at some point uh I was editing a book uh with CN Young, who is an absolute legend. You know, he's a hundred and two, he's still alive. And he's the world's oldest uh um living Nobel laureate. And it's well. You know, Penrose is a mere ninety Three or something. So CN Young of the Young Meals Theory. So it's an absolute legend. He got the Nobel Prize in 1957. So at some point I got involved in editing a book with CN with CN Topology and Physics. And you know, with a name like that, you can just invite anybody you want, and they'll say probably say yes.
And that was my initial friendship with uh Roger Penrose started through working together on that editorial. I mean I Have uh I have um Rogers, a colleague in Oxford, and I've known him on and off for a number of years, but that's when we've really started getting working together.
So when Roger snickers at string theorists, what do you say? What do you do? How does that make you feel?
Um that's totally fine. I mean, I'm not a I'm I'm not a diehard string theorist and you know, I'm just generally interested in the interface between mathematics and physics. And you know, Roger's total chill, totally chill with that. So
you just happen to study the mathematics that would be interesting to string theorists, though you're not one.
Exactly, and vice versa. I I just completely chanced on this. Um, it was kind of interesting. You know, I was recently giving a a talk, uh, a public lecture in Dublin about the interactions between physics and mathematics. And I still find that just, you know, string theory is still a very much a field that gives the best cross-disciplinary, you know, kind of feedback. And it's been doing that for decades. Um it's it's a fun thing. You know, I talk to my friends in uh in pure mathematics, especially in algebraic geometry.
What sparked Yang‑Hui He’s interest in mathematics and physics and how did his collaboration with Roger Penrose begin?
One hundred percent of them are convinced that string theory is correct. Because it it's for them it's inconceivable for for a physics theory to give so much interest in mathematics.
Interesting.
And that's kind of a I think that's a story that hasn't been told so much, you know, in the in the in in media. Um, you know, if you talk to a physicist, they were like, you know, string theory doesn't predict anything, this and the other thing. But there's a big chapter of string theory. You know, mo I to me, more than fifty percent of the story, backstory of string theory is just constantly giving new ideas in mathematics. And you know Historically when a when a physical theory does that, it it's very unlikely for it to be completely wrong.
Yeah. You watch the podcast with Edward Frankel and he takes the opposite view, although he initially took the former view that okay, string theory must be on the correct track because of the positive externalities. It's like the opposite of fossil fuels. But it doesn't give you what you want for your field like physics, but it gives you what you want for other fields as a serendipitous outgrowth.
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Chapters
7 chapters
1
What is the main topic discussed in this episode?
0:00–2:58
2
What sparked Yang‑Hui He’s interest in mathematics and physics and how did his collaboration with Roger Penrose begin?
2:58–52:13
3
How does He define the three approaches to doing mathematics – bottom‑up, top‑down, and meta‑mathematics?
52:13–1:11:24
4
What are complex curves and the trichotomy of curvature in Riemann surfaces?
1:11:24–1:25:13
5
How does the Minimal Model Program connect Calabi‑Yau manifolds, Kähler geometry, and string theory?
1:25:13–1:45:12
6
Why did the author turn to machine learning for algebraic‑geometry data and what did the neural network discover?
1:45:12–2:03:59
7
What is the Birch test for AI in mathematics and how might it reshape future research?
2:03:59–2:15:27
Speakers
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