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New Westlake Chair Professor Thierry De Pauw Finds Beauty in Math

2024-03-28 09:00:37

In February 2024, Prof. Thierry De Pauw joined Westlake University as a chair professor of mathematics with the School of Science.

De Pauw's scientific work pertains to fundamental mathematics, specifically geometry with an analytic flavor. He was awarded the Jacques Deruyts Prize by the Royal Belgian Academy of Sciences. From 2016 until 2018, he was the head of the Géométrie et Dynamique team at the Institut de Mathématiques de Jussieu, Paris. From 2018 until 2022, he was a distinguished professor at East China Normal University.

De Pauw was born and grew up in Belgium. He did his undergraduate studies in mathematics at the Université catholique de Louvain and returned to the university for his Ph.D. degree, which he received in 1998. He has held faculty positions in the United Kingdom, France, the United States, and China. 

The next stop in this illustrious career is with us here at Westlake University. We sat down with De Pauw to discuss his research, why he chose Westlake, and his views on the future.

Question: What was it that initially made you gravitate toward your research field and kept you inspired?

I remember a very specific moment with a teacher. I should say when I was, let's see, 13, 14 years old, something like that. Before that, in the first part of my life, I loved to draw. So, I would create stories on big sheets of paper.

But now something was different. We needed to prove things right for the first time in math. We were faced with giving a reason why something was true. We were trained on little problems from plain geometry and kept our focus on geometry, triangles, and stuff like that. I loved it. So that's when I started to really devote some of the drawing time to math.

I should say I like math, but I also like many other things. I loved reading literature. And so, in high school, the system was we needed to choose our subjects, right? So there was like a Greek and Latin class. And then there was more math, and then maybe more literature. I wanted to take both math and literature, but somehow, in many schools, that was impossible because the classes would be maybe at the same time or something.

So anyway, they were really nice, and they made it possible. I was very, very happy. Then, at university, I actually did some philosophy, too, for the first two years, but then there was no major/minor system at that time. So, I had to give up one at some point.

Question: So, you caught the interdisciplinary bug from a young age. Did you have a preference for classical philosophies?

I'm still interested in philosophy, but I'm not an expert at all. Some of it is a little dry, I would say. One of the classes I really enjoyed was on medieval philosophy. They were interested in proving the existence of god; all that was interesting. But the reason why you enjoy your class when you're young is most often the teacher than the content itself.

Question: What was it that drew you to your field of research? And could you unpack what your research is?

So that's an interesting story. I might be a little bit stubborn. When I was in high school, I participated in the Mathematical Olympiad in Belgium. It's not too hard to be able to compete in a small country and, believe it or not, we didn’t train, there was no pressure, no math camps! I'm very proud because I won a prize for the most elegant proof in that session.

Anyway, so I go down the stairs, and you could choose your prize, right? I guess there was only one thing left, which was a book, and the book was about the mathematics of soap bubbles and soap films and the calculus of variations and stuff like that. So I just took it. I started reading it, and I found it really fascinating.

I go to university. Year one, year two are a little bit hard because it's a lot of learning, right? There's a lot of material. By year three, we have a new teacher. This was not a mandatory class; only those really interested in the topic were still there.

He arrives very late, looking like he kind of stepped out of the shower. He's like: "I'm sorry for being late. I'm taking you to the cafeteria to have a coffee together." Then we go. Then we come back, and then the class really starts. And it was the hardest class I've ever had. He says, "How about this statement? Try to prove it." Then he stops, and he walks around, and looks at our earnest attempts. And then he says, "By the way, on this topic, there's something much harder in this book in the library. And it's also used to study soap bubbles!"

I go to the library. I look at the book. It was like a 600-page book, extremely dry, almost unreadable, certainly for an undergrad. I started reading it.

Question: As a seasoned philosopher, I'm sure you had the palate to digest dry tomes by this point.

And then I like it, right? Because I start reading, I understand a little bit what this was all about. Then I remember this episode from my high school time, and then it's the time to write a thesis, right? In year four, you have undergraduate thesis, right? So then I take this frightening, big book to some of my teachers.

When you're a kid, you like to make soap bubbles. When you have one bubble, what does it do? It includes some volume of air, and there is the soap film around it. It has to enclose it. No air can come out. But it also minimizes its potential energy. That is proportional to the area of the surface of the bubble. That is what makes it a round sphere, right? If you remember some high school math, you can go back home and look at the cube, right? You look at how much volume of air there is in a cube. This supposes you take a cube enclosing, say 1-centimeter cube, right? Of air. What is its surface area? And then you compare that to the surface area of a round ball that would include the same volume of air. The cube has more surface area, right? So that's why bubbles are not cubic! It's not because they're not cubic that they must be spherical, though! That would be a terrible logical mistake; there are infinitely many other possible shapes to rule out.

That's a very old problem that took a long time to solve in math. But when you do the soap bubble, you see sometimes they can gather, right? So they can say, maybe I want to share some of my surface area with another bubble out there, then it costs a bit less total surface area for both of us, right? So then they include one given volume here, then another little one there. What they minimize now is the sum of areas of their exterior surface and one times this interface in between. Does that force anything about the way they meet, about their geometry? The answer to that question is, yes. The two exterior spherical surfaces of the bubbles and the interior interface meet at equal angles, 120 degrees. So this you can actually infer mathematically just from that physical principle of minimizing area.

That book actually is the bible of geometric measure theory. But what's funny is that the teacher who sort of pointed me to the book, it was not his field at all.

Question: Why did you initially choose to come to China and stay in China?

So, when I was growing up, believe it or not, the U.S. didn't have a good image with all my compatriots.

I didn't travel much before except for holidays. Nobody in my family really traveled far away except on holidays. We are from the same place, right? So anyway, the point is, I wanted to sort of check it by myself. Like, let's go to the U.S., live there for a while, and check out what it is really like.

It was the same for my first trip to China. I first came here for one semester to NYU Shanghai to work; that was a very interesting experience. And then I had the opportunity to work for a public Chinese university, which is another different story.

Question: Why Westlake University then?

So, first of all, you get the time to do work and research. We get the time to think. I think...when you're a researcher, that's what you want to do. And it turns out that in many places in the world right now, it's getting more and more complicated for a whole lot of reasons, like, for instance, getting grants, writing proposals, reading proposals that other people write.

And it makes it very time-consuming. I would say, here [at Westlake] we have support like staff support, for instance, which is absolutely fantastic. I must say we have the opportunity to organize scientific events locally and internationally. We have the opportunity to hire Ph.D. students, postdocs, so though it seems like nothing, it really makes a huge difference.

Maybe I tried to convey the fact that I like to be a little bit international and build bridges. I'm from Brussels, by the way. So two languages, right? The country didn't impose one, and so these two communities have kept saying they want to divorce since I was born, but they're still there.

I kind of like that, right? [Unity] makes you stronger. L'union fait la force. This is an international university that sort of has the potential to build bridges with many countries. Generally speaking, I believe that cooperation brings us further along the road than competition does, on the long run.

So, I think it's super important for the scientific community. The point is there are different ideas, right? And these different ideas sometimes come from different backgrounds. So even within mathematics, making bridges between nearby neighboring areas of mathematics is important, but also between people who come from different backgrounds.

Question: Do you have any thoughts on the future of fundamental mathematics? And what would you say to young people interested in this subject?

There is a tendency to understand the world with data and try to find correlations. Mathematics is playing an increasingly big role, I guess, in the way technology interacts with people and things like that.

Why should you learn mathematics? For me? It's because I like it. It's a passion, and it helps me. It's been there forever with me. When I feel bad, I do it. It helps me. There is a beauty in it.

I would tell young people to go back home and work your butt off. It's part of the job. As I said, if you want to write poetry, you need to know the language because you can play with it and improve. Otherwise, it is bad quality.

My advice is: Be ready to fail.

So suppose you can't solve a problem. But that's the story of life, by the way. So you can't solve a problem. So you get gradually more and more depressed, right? So what should you do? Sit down in the corner and cry? Maybe not. Maybe start working on another problem, which is as hard, right? You can't solve it either. But the thing is, it helps you mentally. Maybe it helps you with the first problem. So it's much easier to not be able to solve three problems than just one.

I think math studies the patterns of thought. What you're looking for is a pattern of reasoning. In order to solve one problem, you notice that you sort of made a similar argument to solving another problem. So that means maybe there is a general something behind this, right? That [is what] we find beautiful, and we are attracted to this because of the beauty.