傳播數學知識．促進數學教育

Interview with Prof. Clifford Taubes

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

**Interviewers:** Tai-Ping Liu (TPL), Jih-Hsin Cheng (JHC), Chung-Jun Tsai (CJT)

**Interviewee:** Clifford Taubes (CT)

**Date:** December 12th, 2012

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

Prof. Clifford Taubes was born in 1954 and grew up in Rochester, New York, USA. He had a bachelor's degree in physics from Cornell University and a doctor of physics from Harvard in 1980. He has been a professor at Harvard University since 1985, and now he is the William Petschek Professor of Mathematics there and works in gauge field theory, differential geometry, and low-dimensional topology.

Prof. Taubes explores geometry and topology in three or four-dimensional space by gauge field theory of subatomic particles in physics. With the unique analytical ability, he obtains meaningful theorems in geometry or topology at each stage. Being one of the few first-class mathematicians, he has received many mathematical awards. From the interview, we can learn about his personality of focusing on thinking. As an old saying goes, “if you keep your mind on something, you can reach Tao”. Does that mean someone like him?

TPL: First of all, thank you for coming this long distance to give the lectures . We should have charged entrance fee to your lecture. It was packed. People were really eager and looked forward to your lecture. Let’s start with a very standard question, which is “What experience do you have in growing up and how did you get interested in mathematics?” But you actually got your bachelor’s degree and Ph.D. in physics.

CT: I didn’t get interested in pure mathematics until I was in graduate school. It’s kind of a long story. I wanted to be an astrophysicist. But I was an undergraduate at Cornell University, and one couldn’t major in astrophysics; one had to major in physics. So I majored in physics. The only mathematics I took was engineering math, differential equations and things like that until my senior year. I took an introductory topology course in my senior year, which I found fascinating. I went to graduate school for a year in astrophysics, and I hated it. It might not have had anything to do with the graduate school but a lot to do with me. So here is the interesting part. I decided that I didn’t want to have anything to do with people any more during that year. My plan was to leave astrophysics and go to forestry school. In northwestern America they have vast forests, and they have what they call fire towers, which is basically a house on the top of a tower in the forest with windows on all sides. The person’s job is to live in that house, away from all human beings. They just have to keep an eye out for forest fires; then they radio that there is a fire so it can be put it out before it does too much damage. So my goal was that I would live in a fire tower and never have to deal with people any more.

TPL: As a hope that there’s no fire, so you don’t have to contact people.

CT: Right. So towards the end of my first semester as an astrophysicist at Princeton University, I applied to a number of forestry schools. And I got accepted to the forestry school of Washington State University, which is in Pullman, Washington. I was working with Larry Smarr , who did computer simulation of colliding black holes. He was coming up to Harvard, and so was another professor named Bill Press , a very amazing applied mathematician. Both of them were going up to Harvard the next year. So Bill Press said to me, “Look, why don’t you apply to the Harvard physics department? I had a fellowship, so there would be no problem. And your grades are really good, you should get in. You can always go off and live in the woods, but it’s really hard to come back and go the other way.” So I said “Well, alright, I will apply.” So I got accepted to the physics graduate school at Harvard. That summer, I was back home with my parents, and I had bought a car. As I was driving out to the driveway, if I turned to the right, that was to the west, I was going to forestry graduate school. And if I turned to the left, which was sort of to the east and to Harvard, and then I was going to physics graduate school. The question in my mind as I got in the car and drove off was “Was I going to turn right, or was I going to turn left?” Finally Bill Press’s advice that “you can always go into the woods” came in to my head, so I said, “alright, I’ll turn left to Harvard because I can always go off in the woods.” At Harvard I had a common delusion, which is that if you know enough math you’ll be able to understand the workings of the universe from first principle, and you’ll never have to get your hands dirty with experiments. This is, I think, a complete delusion. Now I think the opposite. I don’t believe the universe is based on the group E8 or some such; the fact is that I would be disappointed if there’s some mathematical underlying symmetry that explains it all. But at the time, I had the delusion that if you just knew enough math, like Einstein or Dirac , you could, without ever getting your hands dirty, be able to find the first principles behind the workings of the universe. (It may be that the whole enterprise of String Theory is based on this delusion.) In any event, I thought, gee, if I just learned more math, I would then become this brilliant physicist. So I started taking math courses. So two things happened. One is that I got seduced by the beauty of mathematics. The other thing has to do with the physics department and the math department in those days. It might still be true, I don’t know. In the physics department they had a Monday afternoon colloquium, and in the math department they had a Thursday afternoon colloquium. In the physics department they would serve tea and cake before the colloquium, but the cake was this kind of really dry, sort of panned cake that I used to get in high school, stale and awful, and it was basically horrible stuff. And then the math department, they would get their cake from this gourmet bakery in Harvard Square; the icing was thick, and the cakes were really great. They would have this great food in the math department, and in the physics department it was this horrible stuff. It was like; gee the math department seems like a much nicer place than the physics department. Also, the people were friendlier, to be honest. In the math department people would ask what you were thinking about, and they would give you advice, and in the physics department you never told anybody what you were thinking about because they would publish it the next day. So I was sort of happy in the math department and being a mathematician.

TPL: This is a great story.

CT: The people are nicer; the food is better. What else could you ask for? And I was intrigued by what I was doing.

TPL: So you have been there since then, right?

CT: Well, I spent two years at UC Berkeley, and then I came back.

TPL: Back to forestry, you said you would like to be alone.

CT: It’s still true.

TPL: I see. Which one of physics and math allows you to be left alone more?

CT: I couldn’t say. I don’t know. Right now I’m pretty much a hermit. I don’t go to parties or functions. I ’m not that comfortable in certain social gatherings. I don’t make small talk. You sat next to me at dinner the other night. I sat there eating my food. You know, okay, that’s over, I am going home. I mean it was great, but I would rather think about mathematics.

TPL: Yeah, one needs to focus. Many years ago there was a Japanese mathematician called Yamaguchi , and he had many good students, for instance, Nishida , Mimura , Matano , and many others. He asked me one question all the way back then in late 1970s and early 1980s when he first visited Taiwan. He said, “Are there any hermits in Taiwan?” And that gave me a very strong impression. Indeed, a society needs hermits, otherwise what kind of society would it be? Of course, during the Culture Revolution in China, one was not allowed to be a hermit. One was not only not allowed to say what one wanted, one was not even allowed to keep quiet. I could not answer his question “Are there any hermits in Taiwan?”

CT: Well, you know, I interact with my students. I’m in my office almost all day. It’s just that it’s doing mathematics or talking about mathematics that interests me, not so much talking about what the latest movie is, or sports, or things like that. If you want to talk about mathematics, I’m happy to talk about that.

JHC: This is a standard question. Can you tell us about the mathematicians that have influenced you the most?

CT: I would say Raoul Bott .

CJT: Did you take his class?

CT: Yeah, I took his class. But it wasn’t necessarily his class as much as it was just being around him because we were colleagues. He was such a generous and gentlemanly, self-effacing person. He was so generous with his mathematical time. He was also the opposite of arrogant. He was very humble. When he went into a lecture, he would always ask the simplest questions. He was never afraid to ask what you might say is a really dumb question, like “how could you ask that!!” I learned from him that there’s no such thing as a dumb question. If you don’t understand something, ask. Don’t sit there and pretend that you’re so smart or you already know it. There’s a tendency for people to pretend they know something when they don’t really understand it. Raoul Bott would ask these very simple questions. He had this very profound way of thinking. He would also work very, very hard at understanding things. Of course, his writing and his mathematics were beautifully elegant. And you wouldn’t have any hint from his written work of how hard he worked to get it into such an elegant form. I coauthored some papers with him. I was fortunate enough to work with him. He would struggle like everybody else to understand something. It wasn’t just a matter of understanding; it was a matter of understanding in the right way. When he wrote it, it was very, very elegant; it was the correct way to say it. And he demonstrated the right way to behave. To be generous, to be open, and to be supportive of other people, to ask questions, not being afraid to ask, try to understand the certain elegance of something. It was everything. He was really a role model for me in so many ways, not only in mathematics, but in life. He had the most influence on me.

JHC: There is another standard question. Among your own research work, which is the most satisfying?

CT: It’s interesting. Each problem I worked on, in some ways, I found to be harder than the previous one. So I can’t say which one I’m most satisfied with because for example, if I solve the problem I’m working on now, I would say “this one.” It’s always what I’m working on now or just finished that I find most satisfying. Once it’s done, it’s done, and I never want to see it again. Once I understand something, I want to move on.

TPL: It’s the process.

CT: It’s the process that’s the most fulfilling, not so much solving the problem; this is what I find. Once I’ve solved it, in some sense I’m very self-critical, I would look back and say, “Gee, why did it take me so long to solve that one? That’s obvious; I should have seen it right away instead of spending two years struggling. If I had been smarter, I would have written that paper in six weeks instead of four years. ” It’s a process of learning and uncovering things, seeing things and understanding things you never understood before, you never imagine you would understand, and all of a sudden you see how it works. There’s sort of a good feeling you get from that, but then once you’ve understood it, where is the next mystery?

TPL: This reminds me about my experience in reading Ahlfors’s Complex Analysis book . Sometimes he says “obviously,” and I beat my head against the wall. I don’t understand it, not to mention that it is obvious. And then after understanding it, actually it’s obvious. And then the next day, I’m lost again.

CT: I’ve learned and tried very hard not to use in my papers “it’s obvious that” or “it’s easy to see that” because in some sense that’s telling the reader “you’re dumb if you don’t see it.” In fact, where I tend to make mistakes are parts of the proof where I say “it’s easy to see that” because I don’t necessarily check it. But the other thing I realize is that it’s not fair to students and to people learning. They would say, “Yeah, it’s easy because you’ve been a mathematician for 30 years. You can see it; you know exactly what to do.” But it’s not easy to see if you’re a graduate student or somebody else. So I really try to avoid using that phraseology “it’s easy to see that,” “it’s obvious.” I mean, you might as well say “and you’re an idiot it you can’t see it right away.”

JHC: So what is your attitude when you get stuck on solving a problem? Have you ever got stuck?

CT: Yeah, that’s the life of a mathematician, to get stuck. You’re fortunate if you get unstuck every couple of years. What I’ve learned, in some sense it’s my philosophy, is that there are only a few, maybe only a handful of people I think of as being truly brilliant. In a sense, they really come from another planet. For instance, Witten , Simon Donaldson , and Atiyah . These people are, to my mind, a different level. My way of doing mathematics is that if I think something is true, let’s assume it is, if I have some compelling evidence, or an argument that something is probably true, if I think about it long enough, just by trial and error, I will eventually find the proof if it is true. Long enough is, well, who knows. It’s not the brilliance itself that will find the proof. It’s just that if I just keep trying different things, just by the laws of probability I’ll hit on the right thing sooner or later; that’s sort of my philosophy.

CJT: This is also what I learned. You should tell the story about coming to your office and work every day. You mentioned in one of your talks that you just try to play with an equation the whole day, or something like that.

CT: Right. You try different things because you believe it is true. Of course, it might not be true, and eventually I get frustrated and force myself to think about something else. But then on occasion, I go back and say, okay, well, maybe I’ve learned some new tricks, let me try them out again on this old problem. So I never really give up on anything. Just well, okay, I’m burned out, and I don’t really have any new ideas of things to try, so I’ll work on something else for a while and come back to it. Maybe in the meantime I’ve learned some new tricks, and I’ll try them out and see if it works.

TPL: May be some people look at you and say, Cliff Taubes. He comes from another planet.

CT: Maybe that’s because I can sit in my office all day and try things out and not get frustrated. Maybe that’s sort of the talent I have. I’m not plugged into some extraterrestrial knowledge, but it is just that I don’t get bored sitting in my office staring at something and not succeeding for days and days and days. What I talked about today, the theorem about SL(2;C), I started thinking about things like that a long time ago when I had no idea how to do it. To some extent it was only after I kind of stumbled on these papers of Han, Hardt and Lin , about Almgren’s function. I thought maybe this Almgren’s function will help me, and I figured out how to use the Almgren’s function. I learned something new; then I went back to this old problem and saw that this new stuff would actually work on the old problems.

JHC: How were you aware of Almgren’s function?

CT: I knew that there were these problems about nodal sets of eigenfunctions, and these problems had certain similarities to what I was looking at. I saw this paper by Han, Hardt and Lin and I followed their references to learn more about how Almgren’s function can be used. I habitually look at the math archive. At least I read the introductions to papers in principle, that have nothing to do with gauge theory, because I think, Gee, I might learn something, some technique. I’m not necessarily interested in the problem they’re working on. I’m not interested in nodal functions of eigenvectors of Laplacian per se, but on the other hand, when I see somebody writing a paper about the heat equation or Laplacian, or some nonlinear equation, or statistics, or whatever, path integral, something, and it looks like they have some new technique, I think, well, let me try to understand the technique. I think of it as a tool; I have a tool box, I put this tool in the tool box, maybe it’s just the kind the tool that would work on the problems I’m interested in. So I do make a point of reading a lot of papers that are very far from my research just on the off chance that I’ll see some new way of doing something. One of the things you have to avoid as you mature as a mathematician is getting wedded to the same technique. If you just have a screwdriver with one kind of end, there are only so many different kinds of screws you can use it on. But there are lots of different kinds of screwdrivers. I do make a point of reading a lot and trying to learn a lot of different ways of thinking and types of mathematics. Not so much that I have any interest in working on those problems, but I keep them at the back of my mind as a possible approach to some problem I’m actually interested in.

TPL: Is it possible for you to describe certain things, a certain core subject that is at the heart of your research. This is something I want to understand.

CT: I would love to understand the structure of the universe. From the point of view of physics, I think it’s a very interesting, fascinating question. As I said previously, I am not of the mind that the universe is based on mathematics. Even so, it is undeniable that mathematics is so effective in describing the physical world. I think there are two answers to why this is. One is, it’s basically Taylor’s Theorem. The other is that we develop our mathematics after the fact to describe what we learn.

TPL: In your intent to understand the structure of nature, is there something mathematically you can state?

CT: In mathematics I would love to understand the classification of smooth four-manifolds or even simply connected four-manifolds. You know, there is this joke. It’s a version of a joke I heard about this faith healer who claims to be able to cure people by these Christian principles. His name was Oral Roberts , and he came from Tulsa, Oklahoma. I won’t tell you the Oral Roberts joke, but I’ll tell you the mathematics version of it. There are certain jokes that I think of as classic, and the Oral Roberts joke is one of the classics. So I’ll put myself in the Oral Roberts world. So Cliff Taubes dies, and he goes up to Heaven. And there’s Saint Peter at the gates of Heaven. And Saint Peter tells you your fate: whether you’re allowed to get into Heaven or whether you suffer eternal punishment for your sins. In my case it’s pretty obvious what will happen.

TPL: To Heaven.

CT: No, I have way too many sins. I can’t even hope for that. But anyway, so this mythical Cliff Taubes dies, and he goes to the gates of Saint Peter, and Saint Peter says, “Okay, tell me your name.” “My name is Cliff Taubes.” “Cliff Taubes? Not THE Cliff Taubes?” “That’s my name anyway.” “Cliff Taubes the professor from Harvard University who studies four dimensional manifolds?” “Well, that’s what I do.” “Oh my God, this is THE Cliff Taubes.” And he sees Angel Gabriel, one of the angels, flying around. And he says, “Gabriel, come here, come here.” The angel flies down next to Saint Peter. Saint Peter says, “Gabriel, guess who this is.” “I don’t know. Who is it?” “It’s Cliff Taubes.” “Not THE Cliff Taubes? The professor from Harvard University who studies four-dimensional manifolds?” “Yeah, it’s him, Gabriel, it’s him.” “Holy mackerel, we have to tell the man.” So they grab Cliff Taubes and drag him into God’s throne room. It’s a big alabaster building, gleaming; there’s a throne that’s golden, you can hardly look at it because it’s so brilliant. And sitting on the throne is God. Gabriel says, “Hey, God, guess who this is.” “Who?” “It’s Cliff Taubes.” “THE Cliff Taubes? The Harvard professor who studies four-dimensional manifolds?” “Yeah God, it’s him! It’s really him.” “Hey Cliff! So what’s the classification of four manifolds anyway?” Not even the heavenly host knows the answer.

TPL: You thought you were going there to check.

CT: I thought I’d go to Heaven and find out the answer, but in fact, Heaven was waiting for one of the mortals to figure it out because Heaven didn’t know the answer.

TPL: Not even the Creator.

CT: The Creator doesn’t even know the answer.

TPL: I have heard a similar joke, but not about the classification of four-dimensional manifolds but about turbulence.

CT: You can tell it about almost anything. Like I said, I heard it about Oral Roberts.

TPL: So we are still quite far from that goal.

CT: I don’t know, there might be some brilliant youngster who figures it out. It might be just around the corner, but we just can’t see it. We don’t even know how far we are from the goal. That’s the problem.

TPL: Could I ask a very ignorant question? So what has been achieved so far? Of course we have not reached the goal, but we have done something.

CT: We know a lot more than when we did before Donaldson’s invariants. Of course it’s the work of Michael Freedman which basically solves the problem at least for small fundamental group for topological manifolds. In differentiable manifolds, Donaldson’s work and the Seiberg-Witten equations basically increased our knowledge by a factor of a million. All of a sudden, we knew a tremendous amount more than we ever knew. But we don’t know how much we don’t know. We don’t know how close we are. In some sense, we have no idea what these invariants can tell us. But we have no idea whether they tell us everything, or whether we know just this tiny measure zero amount of the four-dimensional story, or whether we know most of the four dimensional story. We have no idea what we are missing. The fact is that there are no viable conjectures even. It’s not like three manifolds before Perelman , there was a geometrization conjecture, and everybody believed it must be true that there were no known potential counter examples; every three-dimensional manifold that everybody can write down, you can basically tell what it was. But in four dimensions, even for the four-dimensional sphere, there are potential counter examples that nobody can decide, and there’s no viable conjecture for four dimensions. So we have no idea how close we are and how far we are. All it takes is to stand on your head and see everything slightly differently, and all of a sudden you know what the whole answer might be, or you never know the whole answer.

TPL: Is four-dimension important because of the three space dimension and time?

CT: You could say that it sort of makes it relevant for physics. Although I think the right way to think about it is, you know, physics in the guise of cosmology has as it goal to discern the structure of the particular universe we’re in. Meanwhile, the four dimensional classification question asks for the list of all possible, four dimensional universes. The question asks for the possibilities that are allowed if you make an assumption that the universes are modeled by a smooth manifold? This is relevant to physics to the extent it tells them what the options are. But it is likely that any answer that we come upon would not be interesting to physicists because the physics question is not so much what are the possibilities but what is this one particular universe that we live in.

CJT: In your thesis, basically you studied those vortex equations. Meanwhile I guess everybody thinks you are a great geometric analyst. I’m very curious about how you learned all those partial differential equation techniques and analysis. Usually it’s very hard for a geometer or a topologist to learn analysis.

CT: I guess if I have any talent at all, it’s with analysis. My way of looking at these things is this. And this is maybe a bit of an exaggeration, but there are basically only two theorems in analysis. There is integration by parts, fundamental theorem of calculus, and there is the maximum principle. The first derivative and the second derivative. That’s it. Then there’s complex analysis. There’s Cauchy integral. Basically, if you know that, then there’s just the question of figuring it out how to use it right. If you can figure out a new principle, there will surely be the great things you’ll be able to do. But as far as I know, there are basically only the maximum principle and the fundamental theorem of calculus, and there are the Cauchy-Riemann equations. So everything reduces to that. It’s sort of universal. So you don’t really have to know more than that. You just have to play around, and eventually, if you work hard enough, you’ll figure out how to use it on a problem. But how do I figure out how to solve the vortex equations? I don’t know. I don’t understand something unless I understand it at the level of derivatives and what’s actually happening, you know, the term “meat” of it. A lot of people understand these things at a superficial level, as a tool. But they don’t distinguish between what is fundamental and what is just kind of convenient. Somehow I like getting to the bottom of things. So we’re taking derivatives, what does it say about derivatives. So maybe that’s just how my mind is put together.

JHC: Your thesis advisor Arthur Jaffe wrote a book about quantum physics with Glimm .

CT: He wrote his book with Glimm, yeah.

JHC: It’s all rigorous mathematics in the book. So how do you look at it? What’s your opinion of using rigorous mathematics to study quantum field theory?

CT: I think quantum field theory should be made rigorous. I don’t think that’s necessarily something physicists would be too interested in. But from the point of view of some sort of mathematical problem, I think that’s a really interesting problem, how to make rigorous sense of quantum gauge theory. I mean, there is an interesting physics problem there because we see quarks as confined. So everybody believes that SU(3) gauge theories describe quarks. I don’t think there’s any rigorous proof or an even halfway rigorous argument that SU(3) gauge theories really end up in having quarks confined. I don’t think anybody would believe that if you could prove, construct a rigorous SU(3) gauge theory, that it wouldn’t end up confining quarks. This is because all physical evidence points to the things being described by an SU(3) gauge theory, and also the physical evidence is that quarks are confined. Therefore, SU(3) gauge theories should confine quarks, but you should have some sort of mathematical proof. I think that’s an interesting problem. And to be honest, I think a lot about how to describe a quantum SU(3) gauge theory by taking geometry into account more than the physicists. They do it from a very perturbative point of view for the most part, or argue by analogy with problems that have similar symmetries. Maybe if you thought really hard about the geometric structure, you could define a rigorous quantum field theory that jumped over a lot of the problems that stymie the physicists. So I think about this in my spare time, but I cannot claim it any success. But sometimes I do it in my spare time. I think it’s an interesting problem.

TPL: Do you do something else besides mathematics during your spare time?

CT: I read history, actually. I’m interested in history. Recent history. I’m interested in the 1900s. It was such a horrible time. There were these horrible wars, WWI, WWII. Of course, all that happened because of what happened in the previous century. I’m interested in how people think, why do people come to conclusions they do, why the United States is in this kind of quagmire in Afghanistan, why do we keep making the same mistakes, why did we make the mistakes we made in Indo-China and Vietnam, why are we so stupid when we go out into the world.

TPL: Never learn.

CT: Nobody ever learns. I think that’s very common. I don’t think this is endemic to Americans, but certainly Americans assume that everybody wants to be like them, and everybody thinks like them. So everybody ends up hating Americans, like in Afghanistan. So we go to Afghanistan, and we always say “rescue them from the Taliban,” which I think is sort of appreciated, actually. And then we end up staying there, and they end up hating us. The point is, we dump billions of dollars, trillions of dollars, and where does it go? It goes to these corrupt people who then ship it to bank accounts in Europe. The people end up hating us because without even knowing it, we are disrespectful to their culture, to their religion, to their beliefs without even knowing it because nobody knows anything about what other people think. And so we walk in there, and everybody ends up hating us. We would have got much more from money if we had taken that trillion dollars, in five-dollar bills, and flown over the country, and just dump it out of the window of the airplanes. All the local people would have gotten money instead of the warlords and corrupt people around them. And they would have been delighted; they would have been able to better their lives because they would have been able to buy things with the money. So we should have just flown over. If you think about it, a trillion dollars, you could fly over the whole country a couple times a year, hit every single square foot, and just throw the money out of the airplane.

TPL: You could cover it with five-dollar bills.

CT: And the people there would never actually meet the Americans, so they wouldn’t have any chance to hate us. And they would actually like us because we throw money out of the windows of our airplane.

TPL: It’s U.S. dollar.

CT: Yeah, sure. Absolutely. And they wouldn’t hate us because they wouldn’t have the opportunity of meeting an actual American and realizing what jerks Americans are.

TPL: I can see that you say this thing with a passion; I’m moved.

CT: So, I want to learn history. When I travel, for example when I go to Taiwan, I don’t want to insult you guys without even knowing it. I probably did. I probably insulted you five times at dinner the other night without knowing it because I don’t know the culture of Taiwan. I don’t want to go there and have people whisper behind my back that “well, he might be a good mathematician, but he sure is a jerk.”

TPL: Clearly this was not the case. But as a general principle I understand what you say.

CT: As a general principle, I don’t want to go to places and insult people without even knowing it. I want to know how people think and their history and culture. One thing I learned as a mathematician and teaching math is that everybody’s brain works differently. What seems obvious to me is not obvious to my students and to others. And when I say something, and I think I say something that’s as clear as a bell, when they interpret it, it’s not as clear as a bell. It has many different interpretations. And what’s to my mind really fascinating and interesting about people is that everybody’s brain works differently. And trying to learn what it is, you know, somebody who grew up in some mountain village in Afghanistan, how do they think. They’re not dumb, it’s the same human species. They just think differently. It’s interesting to me, and I want to know why they think the way they do. So that’s one of the reasons I read histories. I wish I could speak different languages. I wish I could speak Chinese.

TPL: Like your son.

CT: My son, yeah. My son speaks Russian, Chinese, Tibetan, some smattering of various Central Asian languages. I wish I could speak Russian, Chinese, all these languages, so that I could actually talk to these people, hear what they think about and say, what do you think, instead of just going there and insulting people without even knowing it.

TPL: That’s a good point, without even knowing it. You say, why, I have been trying to be so kind to you. And they hate you.

CT: They think, you’re an ingrate, and alright, I’ll just drop bombs on you instead.

TPL: Following along your line, the mathematical community of the U.S. is somewhat different from some of the important centers, like Russia, in the 1960s, 1970s, even to the 1980s, and France, in that the U.S. is a big country, and there’s also this immigrant mentality. It seems to me that in the U.S., because of that, diversity of opinion is allowed.

CT: I agree. For example, I had some experiences in France when I was just starting out. This was certainly true in PDE and analysis: in order to get a good job in France, it seemed like you basically had to impress a few people at Collège de France. In some sense they were these king pins, so everybody basically worked on the same problem, everybody did what these few people at Collège de France were doing because if you worked on something new and different you might not get a job. I started out working on non-abelian gauge theory and nobody had worked on it before; Karen Uhlenbeck and I were the first to work on this subject. In France we would never likely have gotten jobs because this was not the stuff that big shots at Collège de France did. It was very centralized. In the U.S., for some reason it’s not. I could work on something new and different and get a job too. There was such a need for mathematicians at least in those days. The job market is horrible now because of budget problems related to the financial crisis, but in those days, I didn’t have to impress one person to get a job. It was somehow much more tolerant of thinking about different things. There wasn’t a sort of centralized power.

TPL: It is a healthy situation.

CT: Yeah, it makes it much more interesting and diverse, like a cauldron of soup, bubbling, and lots of different things coming up instead of just one flavor, and everybody does the same thing. If everyone does the same thing, then things become in-grown. As an example, there is the Yamabe problem. At this point, what else is interesting to say about the Yamabe problem? Even so, you have a whole generation of people in certain places still working on the Yamabe problem.

TPL: Now it’s more global, right? So for example, here in Taiwan, if you want to promote someone, at least at this institute, we would not ask only local people for assessment. We ask the global panel.

CT: I think that’s made a big difference. Things are more diverse now everywhere. Mathematics is truly much more global.

JHC: I saw an interesting picture on your webpage, a drawing of some figures in Journey to the West , one of the Four Great Classical Novels of Chinese literature.

CJT: It’s your son’s drawing. I think he has a website.

CT: Oh yeah. He has a couple of websites, actually. He does write, and he’s an artist.

JHC: I’m curious about your motivation of putting such a picture on your webpage.

CT: I read Journey to the West, which is a wonderful read. My son was making a comic strip of Journey to the West, where the characters are American ones. In any event, I see the Journey to the West as a metaphor of my own search for the truth in mathematics. In the book, at least in the translation I have, the Tang Monk is completely hopeless. So I see myself as the Tang Monk, the totally helpless guy. And there’s the Monkey King . It’s a very subversive story. When you get to the end, Heaven basically plays a trick on them. It’s a very subversive story; I was sort of surprised.

TPL: That’s great literature.

CT: Yeah, it’s truly great literature. One of the things I make a point of is trying to read some of the great literature, like The Odyssey , some of the great epics of the world, stories of different cultures because you get a feeling of these cultures. It’s interesting. So I see Journey to the West as a metaphor of my search for truth in mathematics.

TPL: It’s a long journey.

CT: It’s a long journey, and there are many dangers ahead. I see myself as the Tang Monk, the completely helpless guy that’s constantly rescued by other people.

TPL: But you cannot find better companion to go along, right? The Monkey, the Pig …

CT: The Monkey is wonderful.

TPL: Well, Your journey to Taiwan this time has been a little bit short. Maybe next time you can really experience more local culture. Next time you can come here, enlighten us with some lectures, but mostly, take easy and enjoy it. Let us find a time that’s good for you. Not during summer, it’s very hot in summer.

CT: I like hot weather, though.

TPL: Then Taiwan is good all four seasons. Thank you very much. Please do come back.

- Tai-Ping Liu and Jih-Hsin Cheng are faculty members at the Institute of Mathematics, Academia Sinica.
- Chung-Jun Tsai is a faculty member at the National Taiwan University.