Math Minds: Lê Dũng Tráng

Over the past week, we've had retired Professor Lê Dũng Tráng visiting the Worldwide Center of Mathematics. Born in Saigon, Vietnam and raised in Paris, France, his work in mathematics extends over almost 50 years and across 4 continents. Lê has been a friend of the Center of Math since its founding, and has contributed two research lectures to our YouTube channel (view them here and here). He sat down with interns Tori and Zach for an interview.

What is your current position?

I’m currently retired, both from UNESCO and from France, and I am visiting a university in Brazil. I belong to the Federal University of Ceará in Fortaleza, in the  Northeast of Brazil.

Are you currently involved in any research?

Of course. My most recent research was about Hodge theory. It was research about something already known by other means, so with a friend of mine, we wrote notes about another proof. We implemented Hodge Theory to describe the proof of the theorem.

When did you first become interested in math? Was there a specific moment when you knew you wanted to pursue this field?

There was a specific moment where I thought I should do mathematics. I entered École Polytechnique, a small, elite French university. In those days, the math professor was Laurent Schwartz. He was the tutor of Grothendieck. Now, it’s a military school. At the beginning it was ok, but a lot of the rules were too military. I stayed about 3 months, and then I left.

Now, the moment. So I entered École Polytechnique, and in those days the new students were bullied by the older ones. One week, you have to accept the “bullying.” So I didn’t know why I should go to school during that week! So my father had a good idea- he pretended that I had broken my leg. And during that time, I took a few mathematics exams from the university. I passed all of the maybe four or five exams.  I got better scores proportional to the days I studied. I thought that maybe  I was good at mathematics, that maybe I should do mathematics. Around the same time, Laurent Schwartz opened his Center of Mathematics. I was among the first members. So around then is when I started mathematics. Before then I was leaning towards being an engineer.

What was your favorite math class that you’ve ever taken, and what made it that way?

I must confess, I did not go to class that often. I think I learned much more through seminars than classes. My favorite of those was Hironaka’s about singularities. It was the greatest seminar I ever attended; I learned everything there. It was interesting because I heard the information there, but not until 3 years later did I truly understand. But it was there.

If you could attend a class taught by any mathematician or math professor, living or deceased, whose class would it be and why?

It depends. With my current knowledge, I would like to attend a class by Grothendieck. I know his classes because I listened to his seminars. But you’re not often impressed by them because you just think he’s speaking about something general, and you don’t see the connections. But now I see the connections.

Now speaking about something more interesting- maybe Riemann would have been a person I’d have liked to talk with. He did many things which are deep.

What impact has being Vietnamese had on your career as a mathematician?

There’s two sides to that. On the one side, I feel like I should make a particular effort to study mathematics. Because there were so many people killed by bombs and fires, and I could do something because I was in Paris. So I tried to study well. But it’s not so easy to succeed in mathematics. So during two or three years, I was a bit depressed by the fact that I couldn’t succeed quickly. At some point I was spending my time drinking instead of doing math.

Eventually, I met a mathematician who really changed my life. Haisuke Hironaka was a Japanese mathematician. I met him at the Ph.D. of one of my friends. He organized for us a seminar in the ITS in the South of Paris. We used to spend five or six hours in a row every Friday. And around that time we had May 68 in France. I was involved politically, and suddenly I just gave up on mathematics.

I had some friends at a school in Finland, so I visited there, but I did not study much. A friend gave us a book by Milnor to read about singularities. I read it, and then I was left alone because Hironaka had just gone to Harvard. And then I didn’t know what to do. And I was continuing to drink a lot .

And then I decided I should give up drinking, because I was just wasting my life. All of a sudden I just gave up drinking. And I wrote my Ph.D., in which I solved a problem from Milnor, in 15 days.

What is your biggest contribution to mathematics?

I think in the long run, people will forget about it. But what I did was to build up tools for people to understand how to study singularities. I proved a lot of theorems in the meantime, but mainly because I understood how to study them.

The people who are remembered are not necessarily the most important.

So other researchers and professors working on singularities are building off of your research?

Yes, a lot of it.

When you started out, was there a feeling that you wanted to be great?

No, I just wanted to do something interesting, there was never a desire to be great. I never even thought about making any money at the beginning, I just wanted to do mathematics.

Are there any significant differences between mathematics in France vs the US?

Oh yes. Well the undergraduate level is obviously different. When you reach the graduate level, my understanding of mathematics and knowledge in general  is that most of it you learn by yourself. Not from a teacher. The more you learn by yourself, the higher you’ll be able to go. And I think there are a lot of people willing to do that here in the US.

Any general advice for students looking to pursue a math degree or a career in the field?

Don’t wait for somebody to tell you what to do! Everything you really want to do, you’ll be willing to do by yourself.

_________________________________________________________________________________

Thank you so much for your time, Lê! We look forward to seeing you at the Center again someday.