傳播數學知識．促進數學教育

Interview with Prof. Dong-Pyo Chi

**Interview Editorial Consultant:** Tai-Ping Liu

**Interviewers:** Tai-Ping Liu (TPL), Seung Yeal Ha (SYH)

**Interviewee:** Dong-Pyo Chi (DPC)

**Date:** January 2nd, 2007

**Venue:** Institute of Mathematics, Academia Sinica

Dong-Pyo Chi is a professor at Seoul National University of South Korea from 1976 and he has been working on many branches of mathematics such as differential geometry, dynamical system, combinatorics and quantum computing. Dong-Pyo Chi was interviewed by Tai-Ping Liu (Academia Sinica & Stanford University) and Seung Yeal Ha (Seoul National University) at Director's office of Institute of Mathematics in Academia Sinica.

TPL: The other day, we tried to persuade you this interview, actually I was rather exhausted after your talk on quantum computing, so I said we need to interview you. Take it easy, you say whatever, we would usually appreciate you even more if you don't change the text. Because you are the first one from Korea, this is a very novelty for me. Could we start with usual thing, how did you get into mathematics, your family, how did you grow up and so on. Is something unknown to us?

DPC: When I was in high school, maybe 45 years ago, from 1961 to 64, those days the popular topics was engineering, not pure math, pure science. Chemical engineering was the most popular subject among high school students and then I entered the university, mechanical engineering was most popular. But in those days, I didn't know mathematics, physics, so I just followed what other people did. As soon as I entered mechanical engineering, I found that mechanical engineering was a little boring to me, so I studied physics myself. In those days, not many professors in physics taught us, because engineering campus was far away from the main campus. We didn't have much chance to study mathematics and physics from professors.

SYH: When I was in college, I heard that when you were in high school, you are already very talented in mathematics.

DPC: Well (Laugh), in those days, everybody was talented in mathematics, There was a kind of competition among high school students and I was one of the winner of those competitions. But one of many, that does not mean anything.

SYH: But that's a good start.

TPL: Anyway, you liked mathematics.

TPL: The situations when you grew up in Korea, when you were small, what was the situation in university?

DPC: Only in mathematics, in 1965, there were only seven professors something like that.

TPL: All of them are Ph.D. ?

DPC: No. In those days, to get a Ph.D., you don't have to write papers, if you spend several years then automatically you get a Ph.D. in Korea.

TPL: Some of them get Ph.D. from Japan, or not.

DPC: Yes, some of them, very few, I think all of those people passed away at that time.

TPL: Situation is not that great in academia.

DPC: Not at all, we didn't have many textbooks, we didn't have books either, very poor situation, I don't know situations about the Taiwan.

TPL: That's true, but we have some people educated in Japan, some came from mainland China.

DPC: But in China there are already famous mathematician, like Wang …

TPL: That's true, but we did not have one in Taiwan. Were there any Japanese teachers at that time?

DPC: Not at all, the relation between Japan and Korea was not so good in those days.

TPL: Then you went abroad for a Ph.D.

DPC: Yes, I went to United States to study physics, not mathematics.

TPL: Where?

DPC: Temple university, Philadelphia.

TPL: Then you get a Ph.D. in physics.

DPC: No, I spent one year in physics, then I moved to University of Pennsylvania and I changed my subject from physics to mathematics.

SYH: You told me that in Temple University, your teacher told you to change to mathematics.

TPL: What makes him to suggest to do that?

DPC: He gave many exams, I think I solved them mathematically, not physically. Maybe that's the reason.

TPL: We have to understand Prof. Chi when he said something, we understand he said modestly. So there was exam, you did well,

DPC: I don't know, maybe some impression Then I started mathematics, I have never known much about mathematics, definition of group, definition of continuity, etc.

TPL: Talking about you didn't know about definition, all sort of rigorous mathematics, but in your research, you have been working on quantum computing, and quite a variety of subjects, and people who switch from engineering and physics to mathematics, I know a number of them, but there became very pure, but you are different. you actually stay in physics, your heart is still in physics, so in this rigorous mathematics, you must have an opinion about that, "Are we mathematics department spend too much on this rigorous mathematics?".

DPC: Yes, that's the impression that I got, especially major theory of all those things.

TPL: We overemphasize them.

DPC: That's my impression rather than physical meaning.

TPL: We don't emphasize enough those things.

DPC: I think so, in some sense, I am bilingual in physics and mathematics, but I am more or less more close to physics, that's reason why I liked to emphasize more physical meaning, anyway, that's my opinion, rather restricted.

TPL: People in the 18, 19 centuries, most people are like you. Right?, mathematics is a central tool in understanding nature.

DPC: Yes, even they didn't differentiate mathematics and physics. They are just one.

TPL: So in this regard, you are in the department of mathematics, and you teach mathematics courses, so you must have some suggestion about teaching in mathematics.

DPC: Next year, I am going to teach for senior students. It's a special topics in mathematics, the subtitle is physics and mathematics, half of them will be quantum mechanics, really quantum mechanics, but it's a part of linear algebra actually, the other half will be general relativity from the differential geometry point of view. But it is very elementary I think, I hope students will like it but I don't know.

TPL: I will be happy to be your student.

SYH: Actually, I am thinking to attend it.

DPC: Oh, no, quantum mechanics and general relativity are very exciting, I think every mathematician have some understanding, some of it. It's not very difficult. If you read physics book on quantum mechanics, but I think we can understand those things by spending semester.

TPL: Maybe you should write down notes.

DPC: I wish I could, but I am not good at personal computer and Tex.

SYH: I think you assign some student to take a note.

DPC: O.K.

TPL: That's true, I would say that I really mean that, after you talked about quantum computing, I was quite excited first time I understand, I was quite exciting, so I couldn't sleep so well.

DPC: I am sorry about that. I could spend more time, but those four hour lecture is not enough. I think, but I cannot make it four hour lecture.

TPL: So after your Ph.D. in mathematics, you did not go, you stayed in pure mathematics. What was your interest at that time?

DPC: Differential geometry.

TPL: Then you came back to Korea.

DPC: Oh, I just spent one year in US as an instructor.

TPL: Now, when you were in Korea, over so many years, how many years?

DPC: More than thirty years.

TPL: But at that time in Korea, there was not a lot of academic research in mathematics. Right? How did you keep yourself ? It must be not easy.

DPC: I didn't do well, but I taught a lot and I spent much time to students. Actually I produced around 25 students. I don't know how many master students. I had a big group when I was young, maybe around 100 master students all together.

SYH: Actually he is one of the popular advisors in my department.

DPC: Maybe in those days, I might be only one young professor in my department, not these days.

SYH: You said you produced more than 25 Ph.D and then most of them are in Academia?

DPC: Mostly, but some of them are not.

TPL: How did you deal with students, because students come in different size and different shape? You take them all.

DPC: I let them do whatever they like to do in the way they like. I haven’t forced them to do, actually I don't have much energy, I just suggest something to them.

SYH: But very impressive.

TPL: You have a broad interest.

DPC: That's why I have many students.

TPL: Do you have a student who learn things and teach you? or do you learn by sending students to new field first?

DPC: No (laugh), that's a good policy.

TPL: I see, so you have very broad interests.

DPC: I just let them do. Some are doing combinatorial thing, some are in dynamical system or something like that.

TPL: So what are the topics of dissertations of your students? Can you just tell us few topics that your students have done with dissertations?

DPC: These days, most of them are quantum computation, symbolic dynamics, differential geometry, harmonic maps, etc.

TPL: I suppose it is always difficult to change topics. How about for you?

DPC: I just do that seems to me exciting. When I got excited, I start with some books and papers. (laugh)

SYH: Some days ago, I asked the same question how he can change subjects/ Originally most of time, he studied by himself. He does not learn from taking class, so he does not have psychological barrier. Whatever he is interested in it, he can go there.

DPC: If I could understand them, most of them are too difficult for me.

TPL: How did you get into quantum computing?

DPC: Oh, It was 1997 I guess, there was a conference in number theory in Minnesota. IMA. The topic was emerging application of number theory something like that, the Topic was actually on quantum chaos. It deals with chaotic system quantum mechanically. Given a classical chaotic system, quantum chaos is the study about the quantum phenomena of a classical chaotic system. That is very interesting subject. It is closely related with number theory, especially Riemann Hypothesis and a number of people in Princeton are doing that kind of things. It was a two weeks long conference, and last two days, I think there was special topic on quantum computation by Peter Shor and some other people. What I got impressed was a number of audience. Before Shore, it was maybe forty something like that, but in Shor's talk, there was more than maybe a hundred or two hundred audiences. So I was so impressed, what kind of subjects it was.

TPL: You did not know before you came.

DPC: Not at all, so when I came back home, I looked at the book and archive something like that. Because I don't have much obstacle like quantum mechanics.

SYH: So in 1997, that was a beginning stage of quantum computation. But Peter Shor's work was 1994, and Grover's work was 1996, that was very early stage. Many people got interested in it.

TPL: I guess, beside the fact, you have no psychological barrier to go into a new field and you also knew quantum mechanics.

DPC: Yes, that's why I can do.

TPL: You knew quantum mechanics all the way back. Right?

DPC: Yes.

TPL: You know physics and then you learn mathematics. Of course physics uses a lot of mathematics and now suppose you have your complete control of undergraduate studies of Seoul National University, What would you do?

DPC: Yes, make math and theoretical physics in one department. I think in Russia they do, Department of mechanics and mathematics, and maybe Oxford and Cambridge, theoretical physics and applied mathematics. I think we should do that. That's the way we learn physics and mathematics. How about in Taiwan?

TPL: Well, there was actually few years ago, we have so called theoretical center of physics and mathematics. There was a talk about having center of excellent on this. That's not easy. In Chinese saying, you should have Budda before you build a temple. Instead of building temple and then look for Budda.

DPC: Same situation in Korea.

TPL: So come down to another question may I explore, which is because Korea and Taiwan have somewhat similar situation in the sense of academia and we are both economically so called newly rich countries. Academically we have few decades of experience, and yet we all came from very ancient intellectually cultural heritage, so we all try to do well in intellect that we value that, yet modern sciences we have short experience. So what do you think to improve science and mathematical science?

DPC: I don't know. I don't have any idea, actually I haven’t had any that kind of leadership at all. Yes, I spent two years as a department chair. That's all.

TPL: The leadership as a department chair seems not an important leadership, the important one is that you are having doing which is in seminar room and Ph.D students, so on. Let me put the question little differently. That was a bad question. Let me try another question. Suppose you have to advise young people. Say like Seung Yeal for example, what does he should he do? He has just came back from United States. Based on your experience, because to improve the academic situation is up to people like Seung Yeal. What would advise him to do?

DPC: Nothing to advise him. He is doing well. Actually, I haven’t given any suggestion to people, sorry about it.

TPL: We have here in Taiwan and I think in this part of world except Japan, government try to give money to academia. There are many debates as to where money should go and how much money, what should we do. I am sure you are aware of that.

DPC: Yes, in Korea, there are many physicists and chemists who have close relationship with government. So physics and chemistry have much more fund than they should get. I think they waste money in those fields compared to mathematics. I don't know exact amount. Relatively very small amount goes to mathematics compared to physics and chemistry. It's very difficult to get a research fund from Korean Research Foundation these days.

TPL: There are people who say that we should have more communication with other scientists, but you seems to survive by yourself quite well. All you need is just one conference to set up. For the next few years, you will continue to research quantum computation.

DPC: Nothing else to do.

TPL: (Laugh) I think many people wish to say that.

DPC: Seung Yeal knew that in Korea we have to spend quite percentage of energy to do some paper works something like that. So people could not concentrate on research. That’s the real problem in Korea. That's why some people want to leave Seoul National University.

TPL: But is it clear that those who go to private university and research institute with no teaching, do they do better in research? My general impression is that busy life is necessary .....

DPC: Yes, I agree with you. Mathematics is a personal, human thing, so we should contact to people.

TPL: These days, people are talking about interdisciplinary research.

DPC: I think it is not easy to do that. Two people from physics and mathematics do research together is difficult.

TPL: So you are suggesting that young people should be educated more broadly. If you have to do interdisciplinary research, yourself have to know both fields.

DPC: So undergraduate training is very important. You should have very good undergraduate training.

TPL: Now theoretical physics is a one field that gives us so much research opportunities. How about other fields?

DPC: I don't know other fields.

TPL: People are talking about biology.

DPC: I haven’t read any paper from biology.

TPL: Last December, I tried to have some biologist to come to give a talk, but I must have to say I still have not a personal fond of field of biology and chemistry I feel comfortable go into it.

DPC: That's the problem. We usually think mathematicians can not communicate with physicist or chemist, that’s not easy.

TPL: So about undergraduate education, right now one can think of theoretical physics and mathematics. Then people are saying that this is a biology, but how does it is not clear how to do it.

DPC: I have no idea. Just do what you like if you like it, biology, then take a course about it. That’s what I can suggest.

TPL: Going back to yourself. The thing what you do here in your career so far, you mostly read the paper by yourself.

DPC: Yes, these days student present what they read in the seminar.

TPL: In your department, all these thirty years there, that is a common trend, or you are exceptional I imagine.

DPC: Come on, we usually study by ourselves, no?

TPL: I know study is by yourself, but branching out to another field with students. Because I know this is very difficult for the people who came back to Taiwan. One can always think about how I continue research so on.

DPC: Same problem. Probably.

TPL: But of course now Korea has a lot of communication with outside world.

DPC: Yes, these days. It used to be very isolated but because of internet, we can easily access to Archive at least what’s going on. It could be behind several month.

TPL: Now In Taiwan, most people have a degree from USA, that’s also the same in Korea ?

DPC: Yes, these days, but good news is that domestic Ph.D. are especially very good in mathematics. Recently we hired several young faculties and several of them are domestic Ph.D., maybe three.

SYH: Yes, somehow, I think in Korea good universities do not much care about overseas degree as long as your research is good.

TPL: I see, but domesticlly produced Ph.D., some of them are quite good. This would seem to me that you have a good domestic advisor.

DPC: Maybe yes.

TPL: So the situation is now good.

DPC: How about Taiwan?

TPL: We have good domestic Ph.D.s like C.C. Chen. But my impression from you, you have more good students domestically produced.

DPC: These days, many good domestic Ph.Ds.

TPL: I see, also Korea in general because of economic situation and political freedom and so on. Everybody talk about that Korea has so much confidence.

DPC: Oh, No. I don’t know. Economic situation is not good, Income is increasing but the price is more increasing something like that.

TPL: I can see you two live rather well, but Korea and Taiwan are in terms of living standard, we are quite doing well whatever you measure it. It’s nice to hear that among domestic Ph.Ds , some of them in Korea are good.

DPC: That’s good news.

TPL: Now in Taiwan, we are facing similar kind of situation. There are people who go abroad, but the total number of going abroad is now less than ten years ago.

DPC: Same in Korea. Less people go abroad.

TPL: So how to concentrate on producing a good domestic Ph.D is an important issue. We have several universities with Ph.D. programs but none of them has a lot of Ph.D. students. So how many Ph.D. students in your Seoul National University in mathematics ?

SYH: Each year, maybe less than 20 students in Ph.D.

TPL: Each year 20 Ph.D. new students ?

DPC: But some of them leave after one year something like that, go United states or Europe. Some quit mathematics of course.

TPL: But in any given time, you have therefore about maybe seventy …

DPC: Ph.D. student?

SYH: I don’t know exact number of Ph.D. students, but the total graduate students is more than 100.

TPL: That includes master students?

DPC: Yes, he (Seung Yeal) should know. He is charge of allot fund to graduate students.

TPL: What are the strong subjects in mathematics in Korea ?

DPC: Maybe, nonlinear PDE.

SYH: Yes, nonlinear PDE is one of the large communities as a single subject.

TPL: That is also true in Taiwan. But what are subject good students go into ?

SYH: I think still many students are in algebraic geometry, topology, etc.

SYH: My impression is that still many graduate students are interested in pure math like topology, algebraic geometry, algebra.

TPL: Now this might be related the way students are educated. Because they are educated in those subjects in depth. Yes, we have students in US, students sometimes cross from another department to this department and so on. This is not happening so much in Taiwan. For example, you cross from physics to mathematics, although this is not happening in Korea. This happened while you were in US. So in Korea is it easy to cross from one department to another?

DPC: Many good physics students in undergraduate changed to mathematics in Korea.

SYH: These days, in my university, in undergraduate, students can have double majors. So good students major in mathematics and physics. Those students can cross it.

TPL: So quite a number of them cross subjects in graduate school.

DPC: I know one example who give up the medical science to get to mathematics department. Maybe ten years ago. He got a gold medal in math Olympiad something like that. His parent forced him to do medical science to earn good money.

SYH: Two or three years ago, I interviewed one such a student. His parents want him to be a medical doctor, so he went to medical school and finished two year internship and then he want to switch to mathematics. I think it is crazy. He is now in US to study mathematics.

TPL: Sometimes one has to be very carefully. Because so many years passed.

DPC: Yes, mathematics is a young man’s subject. Should be under 23 or 25 something like that. (laugh)

TPL: This sounds very familiar in Taiwan too. In US, if you study mathematics, and then you decide that you don’t want to go academic. Mathematics major is easy to find a job in high tech or some other fields. How about in Korea ?

DPC: Used to be very difficult in non-academic, but these days this is changed. Some go to bank, financial company, etc.

TPL: I don’t know about in Taiwan.

SYH: I heard that in Korea, if you have some education in financial mathematics, then it is easy to find jobs in financial company. So at this moment, financial companies are trying to find good people in mathematics. But I don’t know how long it will last.

TPL: My general impression is from talking to you is that education in Korea is not as rigid as we have here. I think people cross departments more.

DPC: I do not know about Taiwan. It’s not easy in Taiwan?

TPL: It is easy but people do not have a habit. They go to mathematics, study mathematics. There is no law prohibiting that. But it’s not a habit and it’s not a culture. This is something one need to do.

DPC: Maybe because Korea has chaotic periods. Korean war,…That’s the experience.

TPL: We have a political situation also a little bit too lightly now and that may have some positive effects now.

DPC: Yes,

TPL: In old China, every time dynasty is changed, then chaotic then new art formed.

DPC: Yes, new culture …

TPL: So in this regard, Korea and Taiwan are very close. There are political changes a lot in Korea and Taiwan. Well, let’s stop here.

DPC: Thank you.

- Tai-Ping Liu is a faculty member at the Institute of Mathematics, Academia Sinica.
- Seung Yeal Ha is a faculty member at Seoul National University.