Prof. Sun-Yung Alice Chang was born in Xian, China on March 24, 1948 and grew up in Taiwan. She graduated from National Taiwan University in 1970 and earned her doctorate in 1974 from the University of California, Berkeley. She has been a faculty at University of Maryland, UCLA, and since 1998, at Princeton University. Her research interests include classical analysis, geometric analysis and partial differential equations. She is a member of the National Academy of Sciences and Academia Sinica, and was awarded the Ruth Little Satter Prize in Mathematics of AMS.
Prof. Paul C. Yang was born in Changhua, Taiwan, in 1947. He graduated from the University of California, Berkeley in 1969 and earned his doctorate at the University of California, Berkeley in 1973. He was a faculty at Rice University, University of Maryland, Indiana University, USC, and, since 2001, at Princeton University. His research fields include differential geometry and partial differential equations. He has made important contributions to conformal geometry on the extremal metrics and on scalar curvature and Q-curvature.

TPL: Let’s get started. We would like to be in English because in the future we would like to publish this in English version. It is much easier to talk mathematics in English I think, at least for me.

SYC: Yeah, because education in Taiwan we learn mathematics in English. In China, they now learn mathematics in Chinese.

TPL: One time a person called Yamaguchi in Japan said that we should make English a scientific language. English is an international language. I think that makes sense.

SYC: Actually, I was told in Korea nowadays that if you teach a course in English, they give you extra pay. Try to encourage.

PCY: 50 dollars per lecture.

TPL: You know that 50 dollars Yuan in Taiwan is enough for a Bento. (All laughing)

TPL: Okay, so let’s get started. First, I just want to say that it’s very nice of you two to spend the rather extended period recently here. Usually we have a standard question to start. But perhaps we do it a little bit differently, which is “How did you two meets?”

PCY: How did we meet? We were graduate students together.

SYC: Yeah, at the Berkeley.

PCY: I was doing algebraic topology. But I couldn’t do the problems, I asked her. (All laughing)

SYC: Haha… I didn’t remember that.

CCC: That was a very good strategy.

TPL: This is like a Chinese story about 青蛇 (green snake) and 白蛇 (white snake), about this umbrella. He deliberately forgot the umbrella.

SYC: But in our department, we have another couple, Manjul Bhargava. He and his wife got married because he asked her questions in symplectic geometry. They started their relation because he went to ask her a question. I didn’t know you ask me a question. (laughing) Spanier, perhaps, graduate course. Maybe the first year I was a graduate student. I took Spanier.

JHC: So, you were in the same class?

PCY: No, we were not in the same class, but there were some questions I could not do. Educated in Taiwan they knew how to compute this spectral sequence very well.

TPL: So, in fact that you two were not in the same part in mathematics at that time. You were student of Chern, right?

PCY: No, no, I was a student of Hung-Hsi Wu. (伍鴻熙)

SYC: Paul also had his undergraduate in Berkeley.

TPL: Berkeley has changed quite a bit since then. Wouldn’t you say?

SYC: Most of our teachers from our graduate school had retired.

TPL: At that time when you two were students at Berkeley, I seem to have an impression that Berkeley was very much on top of the world, academically.

PCY: Yeah, it was a very active place.

SYC: Very active place. Lot of graduate students. Actually, it’s a loss of the math society now that Berkeley has so few graduate students now. I was told that Berkeley has 20-30 graduate students per year now. When we were graduate students, each of the year they accepted about 100 students, new graduate students. And some of them were foreign students. Many of them were supported by National Science Foundation. And some of them even self-supported. They had looser standard of accepting students. So, lots of students went there and it turned out that they had some very successful cases. For example, I was told that Thurston, he was not the top student. But somehow, he was admitted to Berkeley and he ended up very successful.

TPL: They played the law of large number.

SYC: Yeah, because you have such a large number so sometimes you can take chance, accept some students who are special. And now they lose their freedom.

PCY: Even then they stretched the dollar. Each graduate student takes two quarter courses and the third quarter you don’t register. The department saves money this way, even then.

SYC: Yeah, when I was a graduate student. The policy is after you pass your qualifying exam, and you become something called teaching associate and then you don’t have to register consecutive courses, consecutive semesters. So, the policy was a quarter system at that time. You register for two quarters, and the third quarter you do not register. So, you don’t have to pay tuition.

TPL: So, it’s the conscientious effort on the part of the faculty.

PCY: Yeah

SYC: That way they can support more students.

TPL: At the time Berkeley was a very liberal place. It was to educate the mass in a way.

CCC: As a comparison, how many students do you take in Princeton per year?

SYC: Princeton is exactly the opposite; the tradition is to accept very very few students and this still is the way. Each year we accept about between 12-15 students. It has been that way in the last 20 or 30 years. Very small number of students. How about Stanford?

TPL: Actually, I don’t know. But I think altogether at any given time we have maybe 60 students which means each year we have 15.

SYC: Yeah, very small number of students. Because it’s very expensive to support graduate students and the university charges you tuition, so that means each of our students would have to make sure we have grant, enough grant to cover their tuition and living expense. It’s actually a lot more expensive to support a graduate student than to support a post-doc. We computed and found that 2 post-docs equal to 3 graduate students. But these 3 graduate students are already under your grant. The university only charges you 50% tuition. If you are going to support students fully without using your National Science Foundation grant, it is terribly expensive.

TPL: The life of graduate students is quite different then because you have so many graduate students although Berkeley has quite a large of faculty. But still with so many graduate students, a lot of graduate students are supervised very loosely, no?

PCY: Yeah, yeah…

PCY: Mainly it is the more senior students teaching the more junior ones, right?

SYC: I think of my adviser, depending on advisers. Since I was a graduate student, my advisor is Donald Sarason. He must have 6-7 graduate students at the same time. So basically, we formed seminar group and learned between ourselves. It’s very nice. It is also because of the large number. There was this atmosphere, like I remember it used to be the colloquium talks in Berkeley. Each graduate went to attend colloquium talks. The room, the very big room was all packed and we always sit on stairs. People who came late did not have any seat. It’s always like that. So, In this atmosphere everyone somehow seems to learn mathematics, this is the most important thing. That has something to do with this large number of students.

TPL: You two have been in a number of institutions. Since your PhD days and there are state universities like Maryland where we were together, then UCLA which is another big state university. And now you are in the fancy private university. So Paul, what is your impression?

PCY: I think we did it another way around. We went to very big public places or very big private places in the earlier stage of our life, career. Usually people would do the other way when you finished your PhD, you have famous advisor and you got good important position. But I think we did it in the hard way.

SYC: We also did the wrong direction. I think it makes sense to go to the west coast when your life is better and more comfortable at least for people from…like in our background. We move to the east coast, the much colder place.

TPL: We talked about Berkeley. How about some thoughts on Princeton?

PCY: Princeton is a very competitive place. So, every day you go to work, you feel the pressure from your colleagues whereas on the west coast, there’s basically no such pressure.

SYC: You don’t feel it. But when we were students there, there’s no difference. Yeah, in UCLA there’s more relaxed.

PCY: I think in the way moving to the east actually was very helpful to us mathematically. Otherwise we stay on the west coast, we would probably be much more relaxed people.

SYC: Have a better life…

PCY: But I am not sure if we are healthier. I think the severe cold weather and the change of seasons make you work harder actually.

TPL: And maybe good for the health.

PCY: Yeah, good for the health.

TPL: You two look great overall, I can say.

SYC: But I like Berkeley a lot. I enjoyed the years at Berkeley a lot. But I was a graduate student, so there was no comparison between when you were student and you were faculty.

TPL: Somewhere I read that Princeton department of mathematics and also theoretical physics for that matter are very prominent. There seems to be some conscientious efforts on the part of university and institution to keep this strong. And then I also heard that Lefschetz was very instrumental in building up the department of mathematics. Is there something to that?

SYC: Yes, of course. I think Lefschetz really built up the department of mathematics…for historical reasons, people are very conscious. You want to keep the math department very prominent, one of the best departments in the world or within the university. People are very conscious about that.

TPL: You mean within the math departments?

SYC: Yes, within the math departments and also within the universities. It’s just a tradition. Math and physics departments.

TPL: So besides everybody’s putting pressure but also is there anything that has been done in terms of hiring policy? Every year we talk about how you should do in hiring to make this a prominent department. Is there such a discussion?

SYC: How do you think, Paul?

PCY: Actually, I think I disagree with you slightly. I think that’s what they want you to say to the public. But I don’t think the university gives us much support now to math and physics than it was 20 years ago.

SYC: Paul represents his opinions.

PCY: Yeah, it’s my point of view.

SYC: Because I have been the chairman and need to be more careful.

TPL: But perhaps this is overall trend in the U.S?

PCY: Definitely we see that everywhere. So, the university now is basically run by MBA type. I think this is true everywhere. Now if you happened to have an excellent tradition in math and physics, they would like you to keep in that way, but spend as little money as possible to keep that way.

SYC: Marketing is a little bit different. Comparing the experience of what at UCLA versus in Princeton, I feel that the university gives more support to the math department and honor the math department a lot more than comparatively speaking than in UCLA. So, for example in UCLA, it’s even rare for a chair to have a chance to meet with the dean of engineer. You have to make an appointment and it’s an important event if the chair is going to meet with the dean. And in Princeton because it’s a smaller university, it’s very easy for the chair to meet with the dean. I just call him up if I want to talk about something. Even to see the president, it’s not unusual if I have things I want to discuss. I can try to make an appointment to talk to the president. In UCLA it’s almost impossible. I have been there for more than 15 years or something. I don’t think I ever met the president. And in Princeton every new faculty is invited to the dinner at the president’s house. And the president would say, “Hello, Paul! How are you?”

PCY: Yeah, that’s certainly so.

SYC: She knows everybody, every faculty. It has something to do with scale, too.

TPL: But in Princeton the department of math is the leading department. While you are the chairperson…

SYC: We try to emphasize that to the university. We are number one ranking or number two ranking. Every time we saw that, we tried to push this into their mind. We are top department.

TPL: This is true. To keep it prominent is not an easy thing.

SYC: Not at all. So constant effort. Very conscious. We are aware we are competing with Chicago, with Stanford, with MIT, Harvard and so on. The competition is almost every faculty we fight and we try. Not easy at all. Every recruiting, every retention case.

TPL: You are the chairperson, so what are the things you do? What are the efforts you made in hiring? How do you succeed?

SYC: First the faculties have to contact with… The reason people come to your department of course because there are many factors… salary, your treatment and but most people look at the contacts. For example, in the department if we want to hire someone in number theory, it’s relatively easy because we already have a very strong number theory group. And in recent year we try to hire someone in probability because we think that’s important field. But on the other hand, we don’t have faculty already in that field, and that makes it much harder. So, the No. 1 factor is you already have strength and build around the strength, and that’s much easier. So, for probability we were discussing now maybe we should have a group hiring 2 or 3 people to build a strong group at one time. And the other factor which is more and more important than before is dual career, husband and wife team. Princeton is a small town. There are not too many other job possibilities for the other partners. In old times, in mathematics it is no doubt that 99% of hiring are men. In old time, the wife followed the husband because it’s a nice town to bring up kids and so on. And nowadays, wives also work. So the job possibilities of the other half is very important.

TPL: So, the hiring now is not just within the department of mathematics. It involves other departments.

SYC: Yes, yes. We have to consider the possibilities of the other half and many factors. Almost every of our hiring is younger generation of people. This becomes more and more important factor. Maybe Stanford has the same problem.

TPL: We have the problem that housing is expensive. This has become a factor.

SYC: Yeah, yeah, in Stanford I can imagine the housing problem. That’s right.

TPL: Some years ago, Donaldson came and looked around and found that houses were expensive.

SYC: But in the case of Stanford, Stanford has lots of lands. The university has lots of lands. So, if they want they can build houses for faculty, is it?

TPL: But if you build houses for faculty, that are the university’s houses. On the one hand, people don’t want to pay so much. On the other hand, they would like to reap the profit when they sell the house at higher price. You see the difficulties.

SYC: But in Taiwan you probably have the same problem like in National Taiwan University (NTU, 台大). In the brief stay I have noticed that housing nearby this area is terribly expensive. Would that become a problem when you are hiring young people, new people? It does so? This must be more and more important considerations.

CCC: Last year we considered Chan Chi-Hin (陳子軒) but finally he went to NCTU. I think housing was a factor.

TPL: Yes, It’s an important consideration.

SYC: But NTU has lots of land.

TPL: Again, that’s the same problem. Either you provide this as a renting property… so this is what happening now. But a lot of people say that “I would like to own my own house.”

SYC: After you retire, you still need a place to live?

TPL: Yes, and usually they don’t allow to stay beyond retirement. In old time, it allowed that but not anymore.

PCY: But Princeton takes a mixture of both. You get a discount from the market price when you buy and you get a discount when you sell. So you partially make some profits when the market goes up…

SYC: And we have a different type of housing program. The one point I had is we own 85% of our house and we pay 85% of the market rate. But when we sell it, we also have to sell it to university people at the market price where we get 85%.

JHC: How did you start to work on conformal geometry? I thought originally you were not in conformal…right?

PCY: Conformal geometry? I guess we started working on the Nirenberg problem.

JHC: Is your first problem…

SYC: We describe Gaussian curvature.

PCY: Yeah, Yeah. She just finished her work with the Carleson on the Moser-Trudinger inequality. So it’s very natural to try this Nirenberg problem. So that’s how we really got started and we learned more about conformal geometry.

SYC: Paul, in graduate school years, you worked on complex geometry. It’s that alright?

PCY: Yeah.

SYC: It was a very geometric problem. I worked on very analytic problem. And then he began to ask me some questions, some analysis problem and geometry problems. Conformal geometry is sort of in between geometry and analysis. It’s natural for us to discuss the problem.

PCY: About 1985.

TPL: You have your PhD at what time?

PCY: 74. But that was very natural. She had this Trudinger- Moser inequality, right? There was a feeling that okay if you know how to control the spectrum so well, maybe we can do some problems together.

SYC: But I think it’s actually an advantage to us…we started out a bit differently. His thesis and my thesis are in different direction and later converge. If we started from the very beginning, I don’t know what would happen. A little bit advantage we started from different directions. I think by the time we do joint work together, people already knew that each of us is independent. If from the very beginning we did joint work, especially for women, people would think maybe you are under the shade of your husband or something. I don’t know. I think in any case people may still think I don’t know much about geometry which probably is true, but on the other hand, at least we already did independent work before we do our joint work. Paul has his field and I have my field. There’s more confidence about our joint work.

PCY: But awareness of each other, I think, has influence on the choice of problems. I think we purposely choose problems, at least in my mind, so that I knew she’s is very good in that kind of analysis. So purposely we choose to move in that direction. That’s an effect.

CCC: I read your paper on the Nirenberg problem and also other papers related to higher dimensional cases. Due to the conformal group of the standard sphere, the solutions of the problem lose compactness. To solve the Nirenberg problem you use some scaling constraints and use the scaling group itself define a degree and eliminate the Lagrange multipliers from the constraints. Those ideas are very fantastic for me. How did you come out those ideas? For me, not so standard. I never saw such beautiful idea.

SYC: I think the idea nowadays has been widely used in different settings, it looks more natural now than when we first started. When we first started looking at the Nirenberg problem, we did talk a lot. It’s that all right? There was a year where we were in Zurich spent the year. Without teaching, we talked every day and talked about the problem. I still consider that piece of work, our early work on S2, on the sphere, probably one of my best works. Because, really we spent a lot of time thinking, discussing every day, talking about that, and doing nothing else.

CCC: So roughly speaking the idea is that you have a PDE problem which you cannot solve. Then you put some constraints to modify the equation and make it solvable. Then you use the conformal group to remove the Lagrange multipliers so that the solution of the modified problem becomes the solution of the original equation. This is very amazing.

SYC: That’s a piece of work we were very proud of. Although later on when people cite our work that’s relatively less mentioned, but still that’s the foundation of our work, our first joint work.

PCY: Yeah, neither of us knew much about calculus of variations.

SYC: We learned from scratch. We were not influenced by other people. So we actually thought about what’s going on. Also, we didn’t know anything about fully nonlinear PDE. Had we known that, maybe we would be influenced by other people.

PCY: I think now the solution of the same problem…becomes much easier if use the present technique. But called our method the fishing for a solution; cast, fish, and try to catch it. Yes, we invented our own method. I think it’s no longer used. It was very efficient.

TPL: When was that?

SYC: That was in 1980s…Is that right?

PCY: 88, right after the Zurich visit we finished…

SYC: 85, 86… Our daughter was born in 85, the year we were at Zurich… published in 87.

CCC: So, it’s very good for a family having two mathematicians, right?

SYC: It’s plus or minus. That really is plus or minus. That means… for example, we can travel together now and go to visit places and have same schedules. That’s one plus because we are in the same circle. Of course, that also means the circle of your friends are all limited in one area. My daughter constantly complained to say that our life is too narrowly focused, which is true for people working in the same field.

TPL: To have such a full career in the family, when the children were small, that’s not easy huh? Both of you have worked hard.

PCY: We were very lucky, right? Alice’s parents came to help us at the crucial moment. Otherwise, I don’t think we can finish…

SYC: Very difficult…

TPL: They came for how long?

SYC: For 5 or 6 years. They took turns coming to help us raise our kids. I think without them, we probably would have only one child. We have two children because we have lots of help from our family.

TPL: But this is very Chinese, right? Here in Taiwan grandparents come to help…I guess.

SYC: More common…

PCY: Yeah, it works. Also, it is very good for the children. My son and daughter keep coming back to visit their grandparents because they remember them.

TPL: Paul, you went to U.S when you were in high school?

PCY: In middle school.

TPL: In middle school. So you actually had learnt your Chinese language securely by that time.

PCY: I’m not sure about that.

SYC: The speaking language is okay. But Paul likes to read Jinyong’s novels (金庸小說), Wuxia novels (武俠小說). That’s the way he kept up his way learning Chinese.

TPL: But in Jinyong’s novels the Chinese is not trivial. There is a lot of classical Chinese.

PCY: Nowadays it’s much easier to read. You can look it up on Google.

TPL: In this series of interview, before Li-Wu came to help us, we asked post-docs or graduate students for help. They would ask the Google to translate the English text into Chinese. That was incredibly bad. First, we made the mistake to correcting the Chinese. We should have translated ourselves because to correct the Google translation is impossible. It’s so incredibly bad.

SYC: Somehow the grammar is a little bit different. When you translate, as sometimes I see articles in Chinese translated from English, it doesn’t read like Chinese. It’s that all right? It’s different organization of sentence. It looks awkward. But gradually I feel that sometimes when I speak Chinese, it’s also awkward. It’s a bit like English translated into Chinese.

TPL: In any case, the translation which is initially done by Li-Wu is really great, and then Hsuan-Pei and I would go over, particularly the mathematical parts. Can I ask you about your undergraduate study? There was an article on傳記文學. You must be aware of that article, talking about the coming age of women mathematicians.

SYC: It’s Professor S. S. Chern. I think Professor Chern had the idea of an article of me. And the person who writes each article is the wife of Chung-Tao Yang (楊忠道). She contacted each of us and we provided her some information. And eventually she edited the article… the final form of the article is written by her.

TPL: It’s all about 5 of your classmates, right?

SYC: Yes, I think that including Wen-Ch'ing (Winnie) Li (李文卿), King Chung Graham (金芳蓉), myself and Chuu-Lian Terng (滕楚蓮), and then Jang-Mei Wu (吳徵眉).

TPL: I have heard some of your former male classmates said something like that: “Although we are not as good as the ladies, but still we are good students.” So how was your undergraduate life?

SYC: I think I have a very good undergraduate life. One reason could be… at that time I didn’t realize it but later when I was in Berkeley I realized that there were so few women mathematicians. That our class was special. There had about… I think at the beginning 10 and later on 1 or 2 more transferring students. So we had a class about 35 but about 10 to 12 woman students. So we formed a good group.

TPL: Strong group.

SYC: Very strong group. And we studied together. We formed 5 of us and studied together. Formed a study group from our freshmen year. One scene I remember vividly is we used to have calculus by Professor Miao (繆龍驥), and then what he did is we used Apostol, a difficult textbook. And the homework assignment usually was odd number problems at the end of the chapter. But for our study group, we did every problem. Each of us did the work at home and then on every weekend, Saturday afternoon or something, we studied together. We went to one of the family, one of the homes of the classmates. Took turns and we studied together. We went over the homework. And we would say something. Someone would say, “This problem I only see the first step and I have got stuck.” And the other would say, “I saw the other point. But I didn’t see your point.” And then sometimes we discussed the problem and then the problem was solved. There are many experience like that. So eventually every one of us did every homework of every chapter. But it’s not all work. We also had dinner together, went to see movies together, to parks, and hiking together, 郊遊. It’s a lot of fun. That experience is very helpful to us. And later on I can see many people in my study group somehow all continue to graduate school and stay in academics. I think it has something to do with our experience. We think math is fun and the group activities were very helpful to us. So in my class, we had 李文卿, 金芳蓉, 吳徵眉, and we also had 胡守仁, and also 劉小詠, who died young. 吳徵眉also stays in academics. We also had 梁潤葵. She is a Professor in University of Malaysia. She’s the僑生. So we have a lot of people stay in academic. Very unusual, very unusual. This has something to do with our forming study group which encourages each other.

CCC: So there’s a name for these ladies called 台大五虎將

TPL: 五俠客?

CCC: Something like that.

SYC: Even we have been in U.S. for a long time, we still contact with each other.

TPL: Paul, you didn’t know all those undergraduate stories of your dear wife, do you?

PCY: I heard about this. Of course, that’s very important for young people to learn. Learn from each other. It’s a much better way to learn than to figure things out yourself.

TPL: Once you get a taste of it, it’s joyful.

PCY: You know someone can always see things different from you.

SYC: But this has something to do with our group of people being all strongly motivated, so each of us did our homework. Before our discussion, there was the fleeing that “I don’t want other people to feel that I know less”.

TPL: So, everybody contributes.

SYC: Yeah, everybody tries to contribute. Has something to do with that.

TPL: Paul, your undergraduate year was a little bit easier?

PCY: Actually, I didn’t learn much mathematics from my undergraduate. That was during a very active period in Berkeley. I learned most of my mathematics in graduate school, even the undergraduate stuffs.

SYC: I think for boys maybe it’s a little bit less important to have a study group than for girls because in graduate school you met so many other boys. You have chance to socialize and interact with other people. For girls, for women, there are so limited numbers and experience, so it is important that we had the study group from the very beginning.

TPL: So, in your undergraduate class you had this critical mass.

SYC: Critical mass is one of the key words. That’s right. So, you don’t feel that you are very isolated. Our group is so strong and we are the loud group in our class. The others are very good but we are united. That’s true. I think one time one of the boys told us, there’s a joke like “You all are on top of the class now, 20 years from now you will stay in kitchen.” There were things like that. There were childish remarks like that at that time.

TPL: But the other day you two told me this, a very nice thing to say, namely, you two like to cook dinner together.

SYC: Yeah.

TPL: Here in Taiwan a lot of young couples don’t eat at home at all. You know that.

SYC: I like to dine at home. Simple food.

TPL: Jih-Hsin (日新) has several other questions. He brings us back to more serious topics.

JHC: Some standard questions. One of them is “How do you choose research problems?” You choose the problem because of its important or because of something else?

PCY: Most process is trial and error. Somehow you like to do an important problem but you are not sure, right? So you begin by taking maybe similar version of the problem you want to do, but you are already familiar with. I think it’s a matter of trial and error. For example, moving into CR geometry, right? That’s exactly this idea. This conformal geometry successful? So look for something similar, you know completely well. So in the beginning we tried something very basically but it failed. And then eventually Jenn Fang Hwang (黃振芳) he showed us how to do this basic problem and then we made progress. And you moved on and more. It’s very hard to say how to choose the problem. It’s a matter of luck. In the beginning it’s trial and error.

SYC: Yes, also a different type of problem is a famous problem. You tried and you knew that somehow for one reason and the other you can approach it so you stop. Like when I was a graduate student, the famous problem is the Corona Problem of one complex variable. It’s well-known problem for one variable and several variables. There are lots of efforts so I jumped in and tried. And eventually I realized that I didn’t go anywhere. And there’s still much progress at this problem. So maybe the machine is not mature yet. A little bit of work but it’s far away from complete. So tired and failed. Still try it’s alright? I mean there’re different types of problems. One is your search direction and the other is famous, challenging problems sitting there, everybody takes a look.

PCY: In the back of your mind, you have certain direction you want to push, so that’s the main motivation. But then you want to make things easier. So try to make it possible. You don’t want to work on a problem and for 5 years there’s nothing to show.

CCC: I think that Prof. Yang has several papers on minimal surface in different geometric settings like CR geometry and Heisenberg group. Some of them are joint with Prof Cheng.

PCY: That has joint with Cheng and Jenn Fang Hwang.

CCC: Yes. As we know that minimal surfaces are very important in Riemannian geometry, and how about the importance for minimal surfaces in other geometric settings?

PCY: Well, this equation is special, right? This is more like conservation laws. It’s more elliptic and it’s not hyperbolic. It’s very degenerate so this area we move into is basically studied by Italians. We are the first group of outsiders who come in. I think we are very lucky we make some progress. Once you make some progress you gain more confidence. And now it becomes a real subject.

TPL: Some Italians joined you guys.

PCY: Yeah, yeah, yeah. We have an Italian guy. Malchiodi, who’s part of the group.

SYC: Yeah, I think to work on a problem is sometimes a matter of luck. You’ve searched for direction but a certain moment something certainly clicks or you hear some other things, and that matches with what you were searching for. This happened to our Q curvature. For a long time we didn’t understand this Q curvature and its Laplacian scalar curvature part, and then its quadratic curvature part. We didn’t know what that means. We stayed at the region for a long time. But one day after we reached Princeton we heard a thesis defense of a graduate student, Viaclovsky, and then we realized it was connected with the things we were working for.

TPL: So it seems to me that the important thing is that you have to keep thinking of it.

SYC: Yeah, that’s true. That’s always the case. You are thinking about it and then it clicks.

TPL: But what makes you keep thinking about it, I guess it must be something what Jih-Hsin said that you think it is important. That’s why you keep thinking about it.

PCY: Oh, yeah, the equation is very simple, very nice. Very nice. Very simple equation. But then these things at least for me, we know it has to do with Gauss-Bonnet. So that’s the important thing so you keep looking for connection, eventually find it. We want to use PDE to study geometry. So the important quantity should be the quantity that controls the main topology. It’s just a very elementary reason. You just want to find something that fits.

SYC: The connection to Viaclovsky‘s work is that he was studying the symmetric function of the Schouten tensor, and when we looked at it, we realized this other part is the symmetric function of the Schouten tensor in these special cases. So this is the part we were looking for the structure. That’s the click.

PCY: May I correct…I would say Chern-Gauss-Bonnet…

SYC: I looked at瓊瑤小說. There’s a 小說. Its name is 心有千千結(The Heart with a Million Knots)，心裡面有一千一千個結。I always look at that and think that’s how we mathematicians always wondering about something…

TPL: What kind of person is Chern?

SYC: Oh, Chern is an amazing person. You know we both were graduate students at Berkeley. Chern is an amazing person, is that all right? Because I was a person in analysis at least at the very beginning and nothing to do with his research field, but he talked to me very often. We bumped into each other in the campus. We walked together and chatted. Sometimes he invited me for lunch. He really took care of everybody passing through Berkeley. I wish I had learned more mathematics from him. I did take one of his classes. But at that time I thought I am going to be an analyst, not a geometer. So I didn’t really learn mathematics from him.

TPL: Paul you are close to Chern mathematically.

PCY: But I think he really taught us how to be a scholar. I didn’t learn much about mathematics directly from him, but the way he taught students, the way he interacts with friends and colleagues. I think he taught us how to live as a scholar.

TPL: So how to live as a scholar?

SYC: Enjoy good food.

TPL: That’s only necessary, not sufficient.

SYC: 心很寬he makes friends very easily with other people. One thing he said really impressed me… I think because of different cultural backgrounds and because of limited language ability, many of us Chinese people in America or foreigners in America sometimes feel discriminated, or feel that people may look down upon you. I am sensitive. But Chern once told me he said he didn’t understand it. He said for his life he never felt anybody has ever looked down upon him. He always felt comfortable. This is so, considering that he studied in Germany and then he moved to IAS from China because of the war, and so on, also considering his move from China to IAS.IAS has a very elite environment. He was educated in German. So I don’t know how good his English was at that time. He could have felt he was being ignored or looked down upon by other people if he’s sensitive. I don’t know. But he told me that’s one thing very far away from him. He felt comfortable in any environment and didn’t feel people have looked down upon him. I think it’s something for us to learn.

CCC: I think he had confidence. However it should be more than that. I mean he knew how to be comfortable in a new environment.

SYC: So my way of interpreting is he is more大度的人. 度量比較大. It affected his ways how he looks at things and the ways he feels about things. That’s my way of thinking.

PCY: Well, he’s a very positive person. Whenever he could help you in any direction, he would do so.

TPL: Carleson, you collaborated with him. He of course is a great analyst. So, can you say something about him?

SYC: Carleson is a great mathematician, a really deep thinker. He works so hard. He wrote very few papers. But for example, he used to visit UCLA one semester every year. He is the person who works in his office more than 8 hours a day including all the Saturday and Sunday. He works all the time. He thinks all the time. Not only for any problem he think very hard, he’s very knowledgeable. He wrote very little. But he’s very different from Chern. He holds very high, strict standard. So in his early days he offended many people. Because he tells you what he think. By the time I knew him, he’s already in his 50s and 60s. So he already mellowed a lot. But on the other hand, he still holds his high standard if you really talk to him. So we were in a seminar with him and there’s a very famous French mathematician coming to give a talk. After 20 minutes, Carleson said, “After all this smoke, where is your meat?” So when you talk in front of him and you need to be very careful, give him some meat.

TPL: Some meat…

SYC: Yeah, yeah, yeah, so each time I went to talk to him I am very careful. I was very scared I told him something which is on the superficial level. He wants to know what the critical point is. And he thought about it over after you met him. After you left, he would think how to do. And next time he would continue. So when I did joint work with him, we were both looking for something which we think is right, but the answer turns out to be either negative or different from what we both initially thought. We worked very hard, did one example or another. I went to school at 10 a.m. He was there at 8 a.m. When I arrived at the school he was already walking outside my office and wanted to talk to me. And Carleson would say, “So last night…” It’s very intense working experience. At that time he’s already probably 55 years old or something. Very intense working experience.

TPL: Carleson was in Taiwan for the IMU membership of Taiwan and China. He was the president of IMU, so his trip of coming here from China through Hong Kong delayed by one day because China somehow tried to block the trip. For some reasons I was the host though I was not the faculty here. It was in mid-1980s. We went to Palace Museum and had a little bit chat. And he said Kolmogorov is the greatest living mathematician. He said that one of the things had direct contact with Kolmogorov was the Fourier series for the L1 function. Kolmogorov found a counter example which is divergent.

SYC: The famous one.

TPL: Yeah, the famous one. Kolmogorov was very young when he did that, maybe in early 20s. And then Carleson said that he worked for 9 years to try to find a counter example for L2 function and only at the 10th year he said to himself that it could be convergent and it took him one year to prove the convergence. We reserved a suite with two rooms at Grand Hotel for him because he’s an important person, president of IMU. He could not understand what the use of another room, the meeting room, as nobody would go there to meet him. During the banquet, he said that when one works on a problem, it is important that one has some feeling whether it would work or not.

SYC: If you look at his vitae, he probably has 30 or 40 papers in his life. I think he has worked on… probably 4 subjects, each he spent 10 years. He really is a deep thinker.

TPL: He said his advisor is Beurling. He has this admiration of Beurling.

SYC: Yes, Beurling is the other opposite, also has very few papers. Beurling goes to the extreme. He had many papers, but when the result is not complete, he didn’t publish. So has many papers in his drawer. Carleson at least published. Yeah, that’s the Swedish tradition, living in this very cold place there’s this analyst who worked day and night.

TPL: That’s what it takes. Analyst is not for place like Taiwan. It’s not cold enough.

CCC: Yes, it is not cold enough.

PCY: But in winter Taiwan can be quite cold. There’s no heating…

TPL: Yeah, no heating and damp. It’s not comfortable actually, not to mention that summer is less pleasant than winter. So I can see that when you two came back here, you two have quite different activities while you are here in Taiwan. Alice you went to Tsing Hua and gave many talks, and Paul you have collaborators here day in and day out.

PCY: Yeah, yeah, we try to work hard. I feel very fortunate to have some colleagues working here in this environment. It’s very nice.

SYC: Yeah, we now meet a number of other young people whom we try to establish contacts.

TPL: Yeah, you’ve told me. It’s very impressive… First, you work so hard. You gave so many lectures. And then there are quite eager audiences.

SYC: At Tsing Hua what the idea is I gave talks in the morning 10:30 ~12:00. And they have 3 TA post-docs and then a study session with groups of … maybe master or PhD students learning groups for another 1 hour and 30 minutes, 2 hours each afternoon. And then 3 TA came to my office to talk to me often. So this my activity there. I feel that if maybe one or two of them gets interested in one of the subjects, that’s already quite good. For general students, I only want them to have some concerns. Some clicks are already good. Also there is another thing nice to see. I used to visit Tsing Hua and I worried that there were not too many connections between the National Center for Theoretical Sciences (NCTS; 理論中心) and Tsing Hua. My impression used to be that people in Tsing Hua didn’t go to attend talks in NCTS. I’m not so sure, but felt that it’s not a close connection between the two places. This time I do not feel so. For example, the students are from Tsing Hua and there are a number of faculties from Tsing Hua also attending my lectures. The lectures are all given in NCTS, and the students are from National Central University (NCU; 中央), National Yang Ming Chiao Tung University (NYCU; 交大) and National Tsing Hua University(NTHU; 清華). So that’s good. I like to see the more interaction.

TPL: Yeah, But maybe this is not the interaction between the two institutions. It’s interaction with you.

SYC: But still everybody was sitting in the same room.

TPL: So it’s important for the institution to get good people to come to visit. That’s the key thing, right?

SYC: I’m glad it happens. At first I worried about this because I didn’t have close connection with people working on there.

TPL: Also, you must have prepared for the lectures. That was a hard work.

SYC: Yes, it’s fine. At first I wasn’t sure what level of courses I should give. I adjust the content of the course after the first week. And people will tell me if that part is covered too quickly or the other part we should do here more. I adjust the content. That’s good. There’s a former student of Gursky who’s now a post-doc here. He talked to me a lot.

PCY: Yeah, I met him.

SYC: Yeah, he’s in Taiwan now. He’s my former student. He has another student who is a PhD student. He got PhD in 2012 and now works in Tsing Hua, as a post-doc.

TPL: You two wrote paper with Gursky.

SYC: Yeah, we wrote lots of papers with Gursky.

PCY: Gursky has two students from Taiwan. One already finished his year and there is another woman student.

SYC: She’s going to finish this or next year.

TPL: Princeton has many great mathematicians there. Can you tell some interesting stories about some of them?

PCY: It’s a dangerous thing to do.

TPL: We heard all kinds of rumors. One is, Beurling was in IAS, right? Peter Lax one time told me the story that at one point Beurling received a letter but he did not reply. He usually didn’t reply and that letter happened to be an offer of professorship from Harvard. And he did not reply. Okay, let’s go to your colleagues. Shimura has retired.

PCY: Over ten years.

SYC: He retired a long time ago…But still shows up once in a while. He’s physically still very healthy, he and his wife. He has a recent book about porcelain china in certain area of Japan. I am not an expert. There is a period, at the bottom of the bowl there would be a character, talking about a story or something like that. He made a systematical study of that. And he had published a book. If you google search, there will be a book by Shimura about this.

JHC: I have one more question but it’s not important. What’s your attitude…this question we asked before… when you get stuck from some problems?

PCY: That’s easy to answer because you just go to another problem. But we usually come back to it later.

SYC: One problem I’d like to return before I retire is corona problem. Well, I’ll see if I can get anywhere.

TPL: Maybe you can tell us a little bit about the problem and why it is so difficult.

SYC: I think one complex variable is so well developed. There are many fine machines. So you use a very detailed knowledge. You know the structure of the zeroes of analytic function on the disk. But for C2 domain basically you do not know.

TPL: This is a very basic question. So therefore, it’s an important problem.

SYC: Yes, it’s an important problem.

TPL: You have a problem you want to go back to, Paul? Not the corona problem?

PCY: Not the corona problem, but actually I have some ideas about this corona problem.

SYC: Paul is the idea person.

TPL: Talking about Paul is the idea person. How do you two work together? In what way you work together usually? Is it possible to describe that? Because everybody admires you two so successfully collaborate.

PCY: Well, I will draw a picture and said, “This is the way it should be.” And she said, “Well, write it down!” I cannot write it down. I just draw a rough picture of what should be going on.

SYC: Sometimes grossly wrong. Sometimes there is something behind it. And we try to pin each other down from very scratch, try to adjust and pin each other down.

TPL: But when I told to Paul, I had the impression that he respects analysts a lot. Is that so?

PCY: Oh, yeah. I mean you either very strong algebraically or you really know how to use equalities.

SYC: Actually, in my career I would say Paul gives me encouragement much more than other people. By nature, I think maybe because I am a woman, sometimes I doubt about myself and so on. More doubts than my colleagues. My colleagues go on very confident mathematicians. So they don’t have many doubts. Maybe they have doubts but I cannot tell. But Paul always tells me I am a good analyst and a strong analyst and so on.

TPL: You were involved with the American Mathematical Society.

SYC: Long time ago, one time… I was the vice president.

TPL: How was it? A lot of work?

SYC: At that time, it was just a name. The only thing you did is in the conference you went to introduce speakers. Very little work. But later on I did serve on various committees. I still serve in some committees in AMS. I am taking an attitude differently from early generation of Chinese mathematicians in America. In early generation, maybe the generation before me, I think some of them do not try to get involved. I try to get involved whenever there’s a chance. So if they ask me to serve for committee, sometimes of course I have to count my ability to do certain works or my energy or my time. To the extent possible, I am serving. I try to accept. For that reason, I do serve in various types of committees. I serve on AMS committee to evaluate prizes, select speakers and so on. I also served on… for example, committee on society and something in New York area, they have some prize for scientists in all research areas. They ask for people to volunteer to evaluate this, to read files. I serve on that. And I also serve on a variety of committees. Some of them are just community work. It’s a different attitude. I try to get involved. But there are also things I will say no. People try to ask me to run AMS president. Then I think okay it’s an important work. It’s very time-consuming. It’s a work you have to speak to a large audience. My English is not that good. Not good enough for me to do that type of work. I am not going to be effective in that job so I say no. On the other hand, in general I try to get involved. I’m also serving on university committees, undergraduate admission committee and committee to evaluate people’s promotion.

CCC: Was it a very heavy job when you were a department chair?

SYC: In our department, chairman is something everybody shared because we are a very small department. Paul and I went to Princeton about 14 years ago, 1999. But when I look at colleagues who have reached Princeton longer than I, most of them have been chairman before. So it’s not special that I am being chair. It’s almost like my turn. That’s probably in Stanford, too. When the number of colleagues is very small, everybody takes turns.

TPL: But the Department of Mathematics at Princeton is bigger than the one at Stanford.

SYC: We have about 30 full faculty. FTE is probably 225. We have too many joint appointments. 25 FTE full time. And then we have another probably equal number of instructors, post-docs. Is that the same size as Stanford?

TPL: The number of full-time faculty seems to be something like 22, 23.

SYC: It goes up and down a little bit too in our case.

TPL: Stanford has more mathematicians outside the department of math than inside the department of mathematics. But Stanford is a big university. Some mathematicians are in OR departments, in computer science, statistics department and even EE has a lot of serious mathematicians, or in economy.

SYC: Oh, I see. We have something called PACM, Program of… I cannot remember…

PCY: Program of Applied and Computational Mathematics.

SYC: That is a program, but it is associated with us. They have 8 faculties, each is joint with one department, and 4 out of them have joint appointment with our department.

TPL: So Peter Constantin is in that program.

SYC: Yes. Ingrid Daubechie used to be in that program. Weinan E is also an example.

TPL: In Princeton department of mathematics the main stream is pure math, right?

SYC: That’s true. Very old-fashioned. Sometimes we would think about what we should do, but we are one of the few departments which is really completely dominated by pure mathematics.

TPL: So what is the major strength in Princeton in the department of mathematics?

SYC: I think it varies with respect of time, different time is different. Still basically…number theory is very strong. Analysis, different type of analysis, depending on how you count analysis.

TPL: Harmonic analysis…for example.

SYC: Harmonic analysis used to be very strong and now people are moving in different type of PDE.

CCC: In Taiwan do you think that the students in math department are not as good as before?

SYC: How do you feel? I know that the percentage of students’ going to college has dramatically increased. So, the general level has been going down, but how about top students?

CCC: I think the same situation happens because before in each year we have 2 or 3 very good students. They can get admission from good university in the U.S. But now, we have this kind students only every 2 to 3 years. So that’s quite different.

SYC: So, it’s not in each undergraduate class you see 2 or 3 exceptional students.

CCC: No, some of them are really good but not so outstanding.

SYC: Each class perhaps has 35 students?

CCC: No, no, we have 55.

SYC: So, you have 55. How many of them will continue to graduate school?

CCC: You mean for PhD program or Master’s degree?

SYC: Uh, PhD and Master’s program.

CCC: Maybe 15~20. Most of them stay in Taiwan. Only few of them go to U.S.

SYC: So, in each class of 55, would 5 of them go to abroad?

CCC: Yes, around that or even less.

SYC: Okay, I see. So, the same concern of you is the level of 15 students.

CCC: I think even the level of this 15 are not as good as before.

SYC: I see, I see.

TPL: It’s very puzzling to me because now the number of active researchers has increased. And one should be able to play what Berkeley did. Law of large numbers, right? And you admit not just math major or related physics majors so on. Perhaps the problem is when students come to graduate school, do they see the future? Do they provide the good education that the smart guy can prevail? Perhaps that’s the key question. Some people go to graduate school just ask themselves “what can I do after the graduate school?” But in Berkeley, if you also ask the question, some of them or many of them actually don’t go to academic, since for them there’s a possibility of doing well outside of academic. But here there’s not that possibility so they don’t get excited. I don’t know.

SYC: What you have mentioned we do not observe in Princeton. Actually our students are getting better. Students try to compete to get into math department. We have to raise our standard to allow people to admit. We have more math majors than ever before. So I am surprised. I also heard in China now that mathematics and physics return to become第一志願 (number one choice) enrollment.

LWC: Professor Chang, I would like to ask: You just said that in Princeton more students want to study math. Don’t they worry about the employment? For Taiwanese students when they choose their preference, they will take employment into consideration. But for those in math major, if you don’t be in academics, people don’t really know what else you can do with mathematics. So usually that won’t be their preference.

SYC: Okay, I know that math majors have increased a lot, not only at Princeton but also in Michigan and a number of other places. Math majors all dramatically increase. It’s because of the job market.

LWC: Oh, really?

SYC: Yes, in the America nowadays, all the finance markets and stock companies, many of them hire mathematicians to do the traditional jobs for the MBA or economic majors. Many of them prefer to use mathematicians as analysts because nowadays the data is large. To analyze data needs more scientific training.

LWC: But wouldn’t they prefer students in actuaries or statistics?

SYC: Actually, one of the difficulties of our department is when our undergraduates in their third and fourth years, many of the companies send mails to them, want them to be interns to work in the summer and when they graduate they try to recruit them. So, job is not the problem. Actually, in the contrary, people sense that in this difficult economic time to be a math major is assurance you will get good jobs. So that has something to do with the math majors’ increase.

PCY: Why this is not so in Taiwan?

LWC: As far as I know, it’s not really the case.

SYC: Remaissance Technologies (Simons foundation) is a stock company. Of course their business is trading, buying companies, selling companies. The analysts they hire and all math or physics Ph.D.

TPL: I suppose in Taiwan also you need a lot of people who can do quantitative analysis. Because this is just a natural thing. You need to be able to analyze things rather precisely, quantitatively. So perhaps the question is that education in department of mathematics actually enhances your ability in this.

SYC: Yes, it’s also important to become broader. You have a lot of flexibility to choose what to do later. In our undergraduate students about 50% went to market immediately after they graduate, about 1/2 go to graduate school. But the graduate school they go to can be a different types of graduate school. Our training provides them the ability to go to pure mathematics department, applied math department, economic department, and some of them go to statistics and engineering schools. Some of them go to law school. Our students are very desirable in law schools. Top law school wants students with science background. If you are good students in our department, it’s very easy to get into a top law school. Students know that this education is very valuable to them. Actually, in good economic time students at Princeton usually would like to major in liberal arts such as the appreciation of arts, more enjoyable things. In harder times they want to be in science. Math is one of the favorable majors. We notice that enrollment in all these hardcore science courses shot up, every student try to be prepared.

LWC: How did you let students know about this? Because I don’t think Taiwanese students they are aware of this kind of information, right?

PCY: Must be the markets, right? I think in the U.S is also the market. The students know coming to mathematics department they will have better jobs. We don’t have to tell them.

LWC: So, the companies will release this kind of information to them?

PCY: They learn through their friends I think. The company comes to us. They come to grab our students.

SYC: Yeah, they have this market fairs and they try to attract our students. That becomes a threat to us in a sense. For our graduate students in the summer, Goldman Socks would come and then say, “How about going to internships for three months?” Something like that. They try to lure our graduate students away. Part of it is the job market. The other message is your education need to be broader so the students have more choices later.

PCY: When we were at Berkeley, the Harvard Law School always set a table in front of the math department, recruiting students.

SYC: The same happens at Princeton, for math and physics department students. To get into a top law school, if you are English major or History major, tough competition. But if you are math and physics majors, it’s relatively easy.

LWC: That’s really different what I heard from students here for mathematics major students.

SYC: Maybe math department should also propagate such information, telling you that how other societies evaluate math major students.

LWC: But there are students go on for the graduate education because they think one way to be employed is to be a student. They go for further study not because they want to further their education but because they can’t find a job. So, there’s no job market for their employment. Really strange.

SYC: I cannot tell.

TPL: We just provide them the good education and hope that they will acquire rather broad perspectives, and certain flexibility in their thinking. So they can prosper in many directions.

SYC: Yeah, some of my students even PhD students work in Goldman Socks. I do not consider that a failure. He is very happy there. He found the work challenging. Maybe he’s a useful message to the community that the mathematical training is very valuable.

TPL: Yeah, and also useful message to incoming high school students. That’s how we try to attract better students.

SYC: Yeah, that’s right. The small percentage should go to academic research if they are interested in. But broader students should do a variety of things, go to different fields.

TPL: Faculties need to have this mindset, say going to the Goldman Socks is not a failure. It’s a success.

SYC: If the students are motivated.

TPL: We all have PhD students going to industries, right? I have two. One of them actually got the gold medal of Math Olympia or something. I later learned.

SYC: Secretly I hope my students can stay in academics but on the other hand, if he is happy with whatever his doing, I feel he has a very valuable education. We have good relation.

TPL: If he stays in academics we will be in contact and this becomes more constant friends. That’s true.

SYC: That’s right. But you can also try to tell students you enjoy your life. Things like that. Like you have a good life, you let students know. To provide the role model in our profession is very satisfactory.

TPL: You say every year you have 50 undergraduate students, incoming undergraduate students.

SYC: We only declare majors in the third or fourth year. So, each year we only declare between 40 to 50 students wanting to major in math. This is a dramatical increase than 20 year ago. 20 year ago, each year we had about 15, and now we have double or triple.

TPL: How many of them actually eventually become mathematicians? 5? 10?

PCY: Maybe 10, maybe a year more than 10.

SYC: Yeah, maybe 10.

TPL: That’s incredible. But still those are top students actually.

SYC: We also have top students go to work in Goldman Socks.

TPL: Yeah, that’s what I mean.

SYC: Very smart young man.

TPL: Still there are maybe 35 of them go to non-academic jobs by their own choice.

SYC: Yeah, some of them become professors like this very well-known applied mathematician nowin Stanford in statistics. What’s the best known person in statistics in Stanford? What’s his name?

TPL: Donoho.

SYC: Yeah, he was our undergraduate student. He said the only reason he wants to be a top mathematician is he wants to be comparable to Milnor, who happened to be his roommate. At that moment, he decided “Okay, I am going to do something else.” He succeeds as a statistician. What’s wrong with that. You can do a different thing and be very successful.

PCY: The main problem seems to be the financial markets do not hire mathematicians in Taiwan.

SYC: Probably they didn’t know that.

TPL: There was a study by Eugene Wong (王佑曾) who is in Berkeley. He said that Taiwan really needs to develop that section of service economy.

SYC: And analysts, based on data.

TPL: They really initiate certain financial package of certain program. Not to copy and just use it from someone established abroad because Taiwan should be in good position to do that.

PCY: Maybe the math department should talk to the business school people, right?

LWC: Actually, it is the actuary degree that would be hired.

TPL: I think one of the things is financial math is actually not easy math. It’s rather sophisticated. You have Ito Calculus and so on.

SYC: I have another student, not my student but in Princeton. He said that since he was in financial math, he is computing heat kernel every day. In that finance market computing heat kernel every day…

TPL: Yeah, yeah, that’s right. Because it’s stochastic induced dissipation and so on. So, you need a very strong undergraduate program to prepare your students to be able to compute the heat kernel at the right place…

SYC: Yeah, to have the feelings.

TPL: It’s not easy to have that strong undergraduate program. There are serious mathematics and stochastic process and so on.

SYC: Yeah, stochastic PDE is very interesting. The only thing I know about it is from the book, An Introduction to SDE, the undergraduate textbook by Evans. I read his stochastic PDE and I found it very interesting. It’s very different.

TPL: So maybe it comes down to the point that undergraduate education needs to be strengthened.

CCC: Actually, once there was a manager of an investment department of some famous bank. He gave a lecture in our department. He mentioned that he likes students from math or physics department. So, he encourages students to come and get an interview in his department. However, I think the job market is not so supportive as a whole.

SYC: In America, for example, there’s James Simons who did joint work with S S Chern. Later on he has this investment company, and uses some computation science and becomes so successful. So that somehow influence the point of view.

LWC: When I talk to students about this, they all say I am ideal because I got different educational background. So they think my thinking is different from Taiwanese students. I am just too idealistic. It’s the foreign way of thinking about job markets. It’s not the actual job market here. So, the students really hesitate to try and the parents will discourage them from taking mathematics. We run a core curriculum program in Academia Sinica and sometimes we get calls from parents asking about the core curriculum program, and they ask what kind of help the program would bring to their kids? Because they will apply for their children, I’ll need to do a little bit persuasion and explanation to the parents. As doing this I found out Taiwanese parents and students don’t really know what they could do with their Bachelors or even Masters.

TPL: The students shouldn’t have the mothers called.

PCY: Maybe the market is too small.

SYC: Maybe we offer in stochastic PDE and so on since students will feel interested in. Actually, I think one of the reasons is that we do not have many people in the field of probability. So, they cannot offer such kind of courses. I pointed out in my other interview the difference; in some sense you say the students’ level is low. But in Princeton and in America we fight and we struggle to have students. That is, we have to justify our department. Of course, we have service courses. But the other resources depend on how many math majors we can attract. Students compare different departments and choose their majors. And your systems, you have students there. You don’t have to fight for these students. So, in some sense, …

TPL: So, the situation here is better because you don’t need to fight for the students. So, whatever I offer, you have to take. And therefore, I offer anything. The obvious downside is that faculties feel no need to change the curriculums according to the changing society.

SYC: So, we constantly adjust our curriculums to see how to attract the best students. We are competing with economics department for students, and why should the students choose mathematics we have to justify. We constantly change our curriculums and look it over to fit the needs of students.

TPL: That’s why there’s no sense of crisis now. Because whatever I teach whatever I offer, there will be always so many students coming to my department of mathematics.

SYC: And also in the case of National Taiwan University, you always have the best students from Taiwan. Is that alright? For us, it’s not the situation. We have to fight with other departments to make them the math majors.

TPL: Now some of the mechanism needs to be introduced. Otherwise, people are just not thinking hard, not making sufficient efforts to improve undergraduate education. If we say that probability is important, you and I can teach probability, right?

SYC: So, for us the number of faculty we have, the number of junior faculty we can hire all depends on how many students take our class. Each year we have data, how many undergraduate students take our service class, how many math majors we produced. That’s the base of the number of the faculty. So if our math majors go down, that means our math resources go down. So, it’s very important for us. For you, you have this number of students always there.

PCY: That can change too.

SYC: Princeton of course is special. It’s a small elite school. If you teach in other places of America, like UCLA, sometimes you have students, the math majors. Sometimes Calculus is a class you have to take. Everybody has to take Calculus, a service course. The level of students is very low. I think some people maybe prefer to go back to Korea, to China because they have better students. So that’s the situation you are in. You’re teaching students in NTU. Already higher level of students. In America, sometimes you have to teach those students which you do not want to teach. You have to. It’s part of your service.

PCY: But I think Tai-Ping is right. If you don’t watch out, maybe in 10 years students would become even worse, and you don’t to teach them. You are in trouble.

SYC: I looked at the college exam problem this year on the newspaper. A number of them are probability problems. It’s interesting. The problems are not easy. The English part looks very easy to me. But the mathematics part of the college entrance exam this year each takes some thinking.

TPL: I am really impressed with you. You really care about what happen here. You two should come back more often. You two have very positive impact on us, bringing in very positive thinking. So, we get together no more than 5 years.

PCY: Definitely, yeah, yeah.

TPL: Then we have our progress reports and we chat again.

PCY: Yes, yes.

TPL: Thank you very much.

PCY & SYC: Thank you.

• Chiun-Chuan Chen is a faculty member at the National Taiwan University.
• Jih-Hsin Cheng and Tai-Ping Liu are faculty members at the Institute of Mathematics, Academia Sinica.
• Li-Wu Chen is an editor at the Institute of Mathematics, Academia Sinica.