Interview Editorial Consultant: Tai-Ping Liu
Interviewer: Tai-Ping Liu (TPL)
Interviewee: Cédric Villani(CV)
Date: January 12th, 2016
Venue: Institute of Mathematics, Academia Sinica
Prof. Cédric Villani was born in Brive-la-Gaillarde, France on October 5, 1973. He received his doctorate at Paris Dauphine University in 1998, under the supervision of Pierre-Louis Lions, and became professor at the École normale supérieure de Lyon in 2000. He was the director of Sorbonne University's Institut Henri Poincaré from 2009 to 2017 and Vice President of the French Parliamentary Office for the Evaluation of Scientific and Technological Options (OPECST) in 2017. For his contributions in the fields of kinetics theory, probability, analysis and geometry, he has been awarded Fermat Prize in 2009, the Fields Medal in 2010, and a member of the French Academy of Sciences in 2013. He was elected to the French Parliament in 2017.
TPL: Your first two talks on Landau damping are great. I suppose that you could sense the enthusiasm from the audience. We look forward to hearing more. How did you find this problem of Landau damping?
CV: I started to work on Landau damping after a conversation with my former student Clément Mouhot. Both of us were discussing in Lyon and actually we were working on Boltzmann equation, trying to attack problems of irregularity of Boltzmann equation. There’s some point in the discussion that we got interested in the effect of averaging, and we did a few calculations and there was a conjunction, it was really a miracle in the conversation. The conversation reminded me of the conversation that I had had couple of years before in Princeton with the post-doc. And for Clément, it reminded him of the conversation he had with Yan Guo in Providence. And we put together everything and Clément had discussed with Guo about the Landau damping. Then Clément said that there has to be something, we should carry out this idea for Landau damping. Actually the conversation was so important that I put it as chapter one in my book on this problem. I published this book Birth of a Theorem, and chapter one is about this conversation which I compared to a fecundation because there’re two people discussing, and from the interaction it’s born something and started something which is neither belongs to one or to the other, but share the fruit of the interaction. By the way, the book is now translated in Chinese. I received the news just today.
TPL: I see. I was just aware of the English version only past few days.
CV: Yes, the English version was a big success in Great Britain, but it didn’t do too well in the U.S.
TPL: You gave a talk in MSRI.
CV: I gave a series of talks across America, maybe 6 or 7 talks related to the book. All the talks went very good but somehow the media did not catch the book in the U.S. while it did in the U.K very strongly. It was all you could imagine about people in the U.K. and I even was on the BBC, on the talk show, on the news.
TPL: Okay, so let’s go into this a little bit. Now you are busy and I want to say thank you for taking your time off to visit us. So you go around to give talks, Aoki told me that there’s a Japanese magazine and you are one of a few people featured in that magazine. So you are, let’s say, in the spotlight. So how is your life these days?
CV: After 2010, I went into a lot of projects. And indeed I wrote the book, the French version appeared in 2012 and it was a big thing. And then I wrote another book after that and also another book. I also went into designing some courses and give hundreds of lectures etc.. So indeed I was in the spotlight quite a bit. It came with enormous amounts of work. I think I work even harder these past few years than it was when I was working hard on Landau damping, for instance. Already it’s six years and it’s more tiring, very very tiring. The main difference being that this is much more secure. I mean if you are a researcher, you work hard, you never know you shall succeed. If you are in communication project, if you have a good product and so on you will succeed, if you have a good personality, good project, good work, you will do it. So now my life is divided between numbers of projects. Most important is the extension of Institute of Poincaré. It’s the biggest project for Poincaré since it was renovated in 1990 because we will double the space which is available to researchers. We will get a lot of companies as partners of the project. We received bunch of millions of euros for doing the work and we are creating a museum of science incorporated in the Institute. So all these will cost more than 15 million of euros, and I am in charge of these, so hiring people, defending the project in front of the politicians. And there’s usual activity of Institute of Poincaré, so finding the people and so on, and the program and the science. Then there’s an activity of writers, so writing books, also caring for the translation, and there’re the interviews. I am spokesperson for a few projects, including the application of France for Universe for the World Fair 2025, and application for International Congress of Mathematicians 2022, and some European federally think tank and I am presidents of some of the associations, we have to find money and funding and place and whatever, and going cooperation with Africa. So every year I go there for teaching and administration of research two weeks per year. And I have been sitting in the board of some of the institutions. Also, I am in part of project for recording some of my lectures to give a cycle of public lectures that to be as DVDs on various subject, also for this one has to get the money. And also I am just hired in the scientific board of European commission. It is 7 people for all over the Europe so I am the only the French and the only mathematician on the board. So it’s a lot of answering and pushing going these projects, writing writings, interviews, writing texts. And one has to keep everything in mind. It is funny the way and it’s a lot of work.
TPL: You remember your first visit to Taiwan and Peter Lax was around at that time? He said to me, “Oh, I thought the scholarship is dead; then I see the scholarship is still alive after I had a talk to Cedric Villani.” Okay, so it’s still alive. I think many people are impressed.
CV: Your comments on this, first it brings back the memory of my first stay in Taiwan. I stayed here for a whole month. So this was a timing which I had this beautiful long trips. If I compare to now, it’s such a big change. Everything now’s so fast. For instance, I went to South America recently. I spent three days in Uruguay, three days in Chile and three days in Mexico. During these nine days, I took like nine planes and gave seven lectures or something like this, and met hundreds of people. And hu~ I was back. So it’s quite a complete change of pace.
TPL: It’s that like most time of the year?
CV: Yes, a lot of times, for instance, after this I am going to Beijing for two days and Singapore for three days, and then back in Paris. In February, I will go to Nigeria, then Vancouver then Cameroon, then March I will be back in China for ten days again to three different universities. So it’s very very quick. It’s special training in some sense, but I would never recommend such a life for young scientists. When you are building your career and in the beginning learning it’s important to stay long, long period and learn quietly from the people.
TPL: Not for the all scientists if only for their health.
CV: Yes, yes, it’s this also.
TPL: But you look just fine. One time when I got a degree in 1973, I happened to stay in the same hotel with Jacques Lions. He told me that he’s traveling all around. So the time on the air plane is the time to do mathematics. Of course I think his pace compared to other people is very intense at that time in 1973. But compared to your pace now, I think his pace may be more relaxing.
CV: Yes, because in 40 years the whole world is accelerating, of course. Also much more places to go now than in the time of yours because now the whole world is trying to emerge, mathematics and sciences.
TPL: Yes, so I suppose that people would like you to be around and with the basic mentality that science and technology are important for the development of the economy. That’s in the back of mind of all your hosts, I imagine.
CV: Yes, for instance, when I was in Uruguay, they wanted to use this as a way to promote for the politicians the importance to the development of science. In Chile, it was even bigger operation. It was like a conference of Nobel Prizes that were like 10 guests, all of them either Nobel Prize or Fields Medalists, I was then with them, and Atiyah was supposed to come but he canceled in the last minute. And many people…and it was a big operation and we met the president of Chile with much publicity among all the schools, the newspapers and televisions, etc. So they want to do this, use the people who are as spokespersons as we to promote the science among the society and that’s the concern in all the countries now.
TPL: Let’s talk about Africa. I remember in the 1970s, Africa has a lot of commercials about spending some time in Kenya with wild life and so on. But we don’t hear much about Africa. The whole continent is not as safe, as say, during the 70s. That’s just my general impression. So what has happened to mathematics in Africa now? You must have some impression now.
CV: Yes, first thing is that it’s not only the science development which is lower than expected. It is the economy development which takes so much time. One first thing is the political organization in Africa. It’s still so complicated, played by corruption and dictatorships and wars and so on. Take a country like in South America or Asia, they are well-organized with strong power and some strong governments in many cases. In Africa, war and war and war, for instance, western Africa Ivory Coast should be very strong in science by now if it had not been for the war which has destroyed everything. As we know, it takes much longer to build higher education system than to build economy. You can change completely your economy in ten years, but you cannot do this for science.
TPL: Build the culture.
CV: Yes, it’s in the culture, it’s in the schools, you need like 30 years. All the time war is destroying everything. Algeria is now a good example. All the mathematicians in the 90s they died or they could not go out. The whole system was wrecked. Then of course on top of that, you have the corrupt governments. When you have money, it’s not spent on the science, etc. Now the war is even there. You know north Cameroon you cannot go, Chad you cannot go, south of all the Sahara you cannot go. There are the Islamists here and there, and Libya of course, to talk about it. So it’s still a big issue about that. And then they also have to handle the problem of the numbers. You have these huge universities in Egypt, in Nigeria. But there’s a tendency to act pure bureaucratical way, just giving diploma, not actually caring about who’s the good student and not. The notion of who’s excellence and that is a big problem in the whole system, so lots of difficulties. On the other hand, even in spite of that, whenever you go to Africa, you feel there’s a lot of good feelings on the ground. Good atmosphere, every time I go there, I came back to Europe full of joy, you know, because of the people having such a positive attitude.
TPL: They want to do well.
CV: They trust they are moving forward. They are handling all the difficulties often in good mood. Certainly, there’s more stress in many big developed cities than in many cities in Africa.
TPL: Okay, I see.
CV: So many initiatives are starting in Africa, also another thing I experienced was it’s so damned difficult to find the right managers, in particular the right directors, so difficult. And it’s a question of culture in large part. And in some cases for instance, what I saw in Cameroon was wonderful, new institute starting from nothing. Good scientific director, good administrative director, they get along very well and really sense a good atmosphere and good progress, amazing! But it’s a rare case and in many other situations I saw how difficult it was. So I am involved in the initiative of Neil Turok, director of the premier institute, called African Institute for Mathematical Sciences. He received the google prize few years ago for his work on developing the science all around Africa. I’m also involved in the initiative by the World Bank which is based in Benin. Benin is in the Sub-Saharan Africa. It’s the strongest country in mathematics. It has traditions. It’s a very small country but with strong respect for science and some very good mathematicians. The project come little substantially improvement, then anyway it takes a few long years before Africa rises. In the long run, Africa has some enormous assets, it will be reservoir of young people for the whole world. They said that there would come the time that half of the youth of the world would be in Africa. It will be reservoir for students. People would compete together with African students and so on. In terms of economic development in the long term, they have so much agriculture and minerals and so on as the reserve in the South America and Asia for minerals are getting decreasing and maybe people will turn to Africa and China hasn’t been doing very well and invests a lot in Africa.
TPL: I see, so maybe in the future the major universities in the West will look for talented young people from Africa.
CV: In some ways as they are looking for Chinese now.
TPL: Chinese are now going to finance.
CV: Yeah, I remember hearing Lax already anticipating the trend. Now the young Chinese going to…
TPL: At that time, he was proposing looking for some Albanians, but now Albania may be a bit too small. It goes to Africa. But you’re talking about…
CV: This is important, by the way, you’re raising. Immigration is always important in science.
TPL: Yes, I immigrated myself twice. But let’s go back to your statement of difficulty to find a scientific manager. So I would like to guess that this realization make you put more effort as a manager, is that so?
CV: Yes, you know in the developed country, in France is much easier than in Africa because the institutions are here to support you. It’s like you have all this invisible arrays of things and commitments. And you know there have to be representatives of this institution in the board and there’re other representatives of other institutions. You have to give reports to this and that. Sometimes it’s very frustrating because there’re so many things to handle. But it kind of supports you, and you don’t spend such big amount of time in politics as in countries which are less developed. You have to get the support of individuals rather than institutions. You spend lots of time, you spend such big amount of time in politics in Africa, countries like Senegal for instance, talking and making alliances and so on. It’s important but if the institution was stronger, it would be less time spent on this. But to come back to the Institute of Poincaré, it was a big experience for me. So when I took the job in 2009 after long hesitations, it was clear to me that it was just for 5 years. But at the end of the 5th year, it was clear to me that it was just starting. I could not leave the institute at that point, that I needed to continue for the next round of five years. And indeed it took six years to get the right amount of money from raising the support from the political institutions for everybody. And I could see how much we have to be projecting in the long term, thinking of the communication of making things like we made the books, we made some movies, we got into all kinds of events, we organized exhibitions, we built the network of journalists to discuss with, and now I came to the radio to record some interviews: “Oh, you’re here! Oh, it’s good to see you, etc.” And people would say that “Why don’t you come in my show next month? We can do something about this.” But I have no time. It would be crazy I might as well die on the spot. But now I know the people and they know Institute of Poincaré. But also I saw how difficult it is to handle the people. Simplification is I don’t have to handle colleagues, which is a big source of difficulty when you are handling science institutions, but I have to handle the people who are in the administration, and so there’s always something. You know in 6 years I think half of the staff at some point or another was in tears in my office because of some disputes, some problems, some big things . In this case, you always have to remain stable and clam like: “We will solve this out. Don’t worry!” And couple of times I have to tell people “Now, you have to leave because it’s not your job.” and “You are not doing good.” and “You are making enemies here, etc.” This was an interesting experience, so difficult.
TPL: Talking about something that definitely not difficult for you. It’s to write an article or to write a book. You seem to have a particular talent in this. You take out a pen and then sentences one after another flow from your pen.
CV: It’s true. Both of my mathematical activity and other activities…I like to write. I really think writing books is what I am best at, doing synthesis and so on. It was always a need like I had to. In spite of that, the books I always wrote on…I mean like for instance, I wrote this big book on optimal transport 1000 pages. Each page has been written at least three times because I write and I rewrite. The first draft usually is handwriting, then there is typing and retyping. At some point, I don’t know, there were some days in which probably I spent 13 or 15 hours in a single day writing on the book. It became complete obsession. But I’m very proud of the result. As my first book I wrote, I started to write when I was maybe 26, something like this.
TPL: You were visiting Georgia Tech.?
CV: Yes, during visiting Georgia Tech. At about the same time, I wrote my big synthesis on kinetic theory and I started the book on optimal transport, the first one. The recurrent theme is that all the books that I wrote or most of them as I started were the ideas of somebody else , let’s do this course, and I write the note for the course and the guy would say, “This notes are beautiful, why don’t you make a book out of it?” So I make the book, etc. Very often the book was rebranded into different categories than the one it was supposed to. So my first book on optimal transport it was supposed to go into the lecture notes series of courses of whatever of American Mathematical Society. In the end, they put it in the graduate series because they thought it would be good for wider category of graduate student who are not specialists. My second book on optimal transport it was supposed to be a lecture notes which were notes for a course, and they said, “Let’s put it to Grundlehren because it will appeal to many people.” And my Bodley Head book “Birth of a Theorem” it was supposed to be first at the time as a science book, but they said it should be a literature book because really it was a more general book. So it happens to all these projects that in the end, it was delivered to be broader gender than the one it was first thought to be. I think it’s a general pattern and as you see, reflect the fact that I love writing these books and always try to think which would be the wider audience who can profit it by the book.
TPL: That’s very nice. This reminds me the statement I once made “creativity is a way of appreciating others’ work in your own way. “
CV: It’s not just this, but in the large part it is this.
TPL: You like to write books. I suppose that it is the urge that you would like to put this into an organic whole so that people can appreciate it, can understand it. And this organic whole sometimes keeps growing because otherwise it is not its natural whole.
CV: Yes, first thing, the book is growing and somehow it’s out of control at some point. The book lives its own life. But also when you put it, if it’s right it makes the subject grow. My two books on optimal transport I think they have big role in inflating the subject, let it grow. And always writing the books I discuss some big pictures, I put open problems so people have problems to think about. Also, I write them for the people but also for me. When I wrote the book, I know the subject much better afterwards, so much better. Several of these projects are…I did not have time to fulfill and one day I will have to go back to this. One is undergraduate lecture notes. I wrote something like 400 pages of undergraduate lecture notes, including an attempt to capture all these senses in the book by Brezis of functional analysis, and reput it in more modern language and without the Axiom of Choice, at some point I decided I will never use Axiom of Choice again. So I wrote maybe 70% of the book which is about Lebesgue integration, functional analysis and Fourier integration. And I did not touch it for the last 8 years or so. At some point, I was really working for my students in my course. I have this project that one day I will write with Clément a big book on the Vlasov type equations. I have in mind to write a book on geometry of surfaces, just surfaces. It’s a big area with long past, and somehow it was a bit out of the fashion. But I’m sure there is a re-erect and is coming back in fashion again, that was my impression. These are the three biggest mathematical projects for books that I could not complete. When I was here in 2002, I gave a series of lectures on Boltzmann equation. And I did with handwriting some lecture notes at the time and I recently saw it again. I remember it was how happy I was to have this opportunity to write down these notes.
TPL: Your trips to the east coast of Taiwan was unfortunately all during the raining days. I remember that. I remember you have a baby. All the young ladies loved the baby.
CV: This must be amazing. They always say absolutely, first words of Chinese, we kept hearing: 「好可愛! 好可愛!」(how lovely! How lovely!) everywhere, everywhere as we moved to the cities, the girls want to photograph with her and so on because she was blond, very cute. By the way, after we were back in France and few days later, we went to the public park or something with the kid. There’s one Asian kid in all the group. He went directly to her, to play with her.
TPL: Very good, that’s very nice. You’re one of us. The small child, very small child… they know much more and can sense much more than we could ever realize.
CV: Yes, very small children they communicate very easily. Later age is more difficult. The very little ones before language and so on, they can feel things very well and communicate with each other without words.
TPL: You said that you wrote your first book when you were 26. Now here in Taiwan in particular, what do people do at age of 26? They may be in graduate school and so on. People say that mathematics is a game for the young people. I think that’s a truth. Also, scholarship is also a game for the young people. You need the energy and you need to be able to work for a long time. So people started too late in many part of the world. I remember when I was a teenager, my brain was very lively and can think of many things, a lot of nonsense, that’s true. But I thought in any case intensively. So what do you think?
CV: I think it’s very true. People should not wait if you go in higher education, you should not wait too long before you do some research projects. Even if you are not knowing everything, mastering lots of things and so on. Also, in the high school, you can do projects which there’s some research even if you don’t know much. I saw there were experiments in Great Britain about children of 10 years being involved in research projects, about the bees and so on, something about the environment. So I think this is very good. Also, I like to recall that when I was in École Normale Supérieure, at the end of my first year of study, I essentially skipped all lessons because I was busy with socializing and so on. I started again working on second year but then again at the beginning of the third year I did not do anything because I was the president of the Student Union, organizing events and a lot of things and zero mathematics for maybe 6 months or so. The only thing I did during this time was to read the Cercignani book without understanding really about what the thing was. My PhD advisor was very worried about me, by the way. But then I started and when I started to work, etc…So as a result of this whole, there was one area of PDE I did not know at all. I have almost no training in classical elliptic theory. There were a bunch of areas in which I did not know, but you learn again by yourself, and the importance is you have the energy to go for this. And then if you continue to learn, you will catch up the things you did not see before. Writing is a very instructive activity. I remember very well writing my first research paper. What a big mess! I spent so much time working and trying and putting it to shape and then looking for advice of my advisor for the writing. In the end, the result was not a good paper. When I saw the paper again, I wish it was deleted from my list of publication. But it’s very much learning when you are making this paper, how to organize this, how many sections, etc.
TPL: You one time told me that your parents like to take you to the museum, and you have a brother and you two took this a little bit differently. You actually didn’t mind going to all the museums. So maybe you are born a little bit differently. You are born as a scholar. People are different, right?
CV: People are different. And the difference you can see from day 1 after birth. The kids may be very different. Some people say that it’s because parents raised them differently, but this is false. Education plays a role but also people are different. And yes, from the start, very eagerly concentrating as a young child, reading a lot, a lot, a lot. A lot of novels, books and so on. My parents are both in literature. The house was full of novels and things. I read a lot. Part of the fact that I am working in writing now on non-mathematical texts is due to my classical training in French literature.
TPL: I see. You’re talking about people are determined on day 1. And education can only do that much. This reminds me of Mark Twain’s saying. You may have heard this. He said, “I never let my schooling interfere with my education.”
CV: This is a good one. I always like with Tai-Ping. He always has some good quotes for every situation. In the case of Mark Twain, this also comes in the context of American education which was much less rigid than in European. Much later than Mark Twain, some of the best American mathematicians are also some of the originals. Maybe they are not changed or shaped by the education. If I look at myself, I can see that I was much shaped by the French system. It was there. And there were also some of my personal features, but I went through the classical elite curriculum of French and this shaped me a lot. But if you take guys for Bill Thurston, Bill Thurston for sure he was not shaped by anything. Or take John Nash, he was completely unshaped also. These are two purely American mathematicians not imported. So their education certainly did not influence them much. That being said one has to counterbalance this by the fact that during the middle of the 20 century. And I discovered this by reading a book on the history of Bell Labs. The whole of American research was done by people like who were born in small villages with no particular scientific environments, but then some teacher supported their talent and their potential, and gave them particular lessons and sent them to universities and so on. And the whole story of the innovation of America in 40, 50, 60’s was done by these people. Somehow the system has disappeared. Now the talented American kids do other careers in science in most cases. And it has been replaced by a system much more based on immigration. But in those days, education was playing a big role for the science.
TPL: Richard Schoen said the same thing out of his personal experience. He came from a small town in Ohio, by the way. He was also interviewed. I interviewed him for this series. He came from a small town in Ohio. Then there was a high school teacher and so on. But now when he goes back there, this is not there at all.
CV: No, that’s not there. It was said that people like in China do exactly this, and many of the people I read their biography, there’s same kind of pattern, as the one Schoen described. It’s very interesting. And yes, it has disappeared. The whole education, one thing particular, you can see was there’s a sense of duty. The teacher they had and also the kids, this idea that education is the way for something better, for achieving dreams and whatever.
TPL: And the teachers take this as their duty.
CV: Personal duty, yes. Some cases are doing extra hour lessons, you know in the evening just for one student, etc.
TPL: But in the classical Chinese society, it was like that. They value education a lot. But then of course later on, the government became corrupt. If you are smart, you may not prevail and so on. Then that destroyed the system. But in the old time, there was an old saying which can only be said in Chinese, called (In fact, I heard this in Taiwanese.) “There’re 狀元student, but no 狀元teacher. “ 狀元 is no. 1 in the hierarchy of examination. Of course, this is a tautology if the teacher was the first in the examination, he became high officer. He would not be stuck in the small village to nurture the new generation.
CV: Yes, I see. That’s one big thing. Nowadays all countries worry about their education systems. And there are all the ranking and international tests which of course do not in fact reflect the whole truth, but it’s interesting to look at. The countries which play best like Korea or Norway, Finland, countries in which teachers are extremely respected by the society and also have some freedom in what to do. I think that’s the single most important thing in education system, respects society gives to the teachers. If you look which are the best students, how well they go and so on, and like maybe the top this amount percent gives the teachers, like the teachers are higher in the top, top percent. The smallest amount is in Korea, like really elite who become teachers, like you, the no. 1. Then of course, education depends so much on culture that many other factors coming to play.
TPL: I would like to ask you the typical question, which project, I mean in research, give you most headache?
CV: In my career?
TPL: Yeah. Some of the projects must be…you really think hard.
CV: Really the Landau damping, the project was the biggest headache. Also because we really have to think about what should be conjectured. We are not really sure what we wanted to prove, and the techniques and the core of the proof we discovered in the working, the fact that was linked with the Kolmogorov-Arnold-Moser theory, the fact that there was critical regularity which was of Gevrey type and not Sobolev type was something we did not expect at all. So it was really really a headache. Most of my book, Birth of a Theorem, is about recounting this headache. It was the first time in my career that I ended up working on one project at the time. I mean during all the rest before it was always looking on 2, 3, 4, sometimes 5 projects at the same time. But this was so hard that I had to focus 100 percent on it.
TPL: For how long?
CV: The focusing period was not that long. But I think there was two years and the half between the first conversations and the paper being accepted. It’s not that long. I mean there are other projects. One paper I started to work with Felix Otto in 1999 was published ten years later. But it was more mild, and this one is the real massive headache, the Landau damping. There was the hyper-quasivity direction of research and so on. It was quite some headache. Another real big headache was some particular work on the optimal transport. In optimal transport, there were big surprises. I will comment more on the developments of the subject. But of all these problems, the biggest headache on the problems of transport type I had was the certain problem which was mixing the regularity of PDE and non-smooth geometry. And the paper I worked with Wang and Loeper, I will tell you the result. (I am trying to find nice words.) So when you do optimal transport, with the transport cost which was the square of the distance function like one you need for the mass transportation the cost is the square of distance. And it is known since about ten years that in general the optimal transport in the surface on the manifold in the geometry is not smooth even if the densities are super smooth. There’s no smoothness of the transport functions. The transport function can even be discontinuous. These were the works like people of Trudinger, Wang, Loeper. There was certain geometry condition, complicated geometry condition that ensures the smoothness, some smoothness at least. And I had this idea, this smoothness, this geometric condition which was just of curvature type should entail a strong geometric property on the shape of cut locus in the manifold. Cut locus is a very subtle object to handle, it’s where the geodesics cease to be minimizing, and it was real real tricky this thing. I did this with Wang , Loeper, but we had to really find a way to think of the problem with some iterative procedure which was a kind of continuity method but in non-smooth setting , and the parameter which was growing was the radius of a ball which we were considering inside all the tangent spaces at the same time such that the tangent cut locus remain convex . Anyway, here I am a bit confusing, but this was real tough. And the only time in which I first let out a preprint which was false. Because the first version of the proof was completely false, then we had to rewrite it completely. It’s false because subtlety of something which was not smooth and we did not notice it first. This problem about the shape of cut locus first started to haunt me as I was in vacation doing some hiking in Australia after some time. You know, they always say in creativity, there’s first the preparation in which you think and think and think hard. And then there’s your illumination later. And I had first spent 6 weeks working with Trudinger and Wang in Canberra. And then I was on the hike and so on. At some point when we were camping, I had this idea, this should imply this. And then I thought about it long time but could not find the proof and it took quite some time to get the good proof.
TPL: Actually when I listened to you, I was thinking about something else. You are trying to explain cut locus and try to find the right word to say it. At the end, you said and you still claimed you are not satisfied with your explanation. So what have come to my mind is following: You told us while you are very young, your parents have lots of books and you read this book. So I suppose that reading all these literature and other non-scientific books help you organize your thought, or help you find ways to express yourself. And that by itself is actually rather scientific in the way. And that’s one of your strengths. Could I say that?
CV: I think so. Always I am very careful about the expression on radio, television, etc. constantly in my mind which is the word that I have the right use, etc. And which are the words people understand. Also, as for scientists, mathematicians, let’s see. I remember my colleague in Lyon in physics he used to say that I was the only mathematician with whom he could discuss because I choose the right words for them to understand. Indeed, this way of communicating is literally skilled and is not so related to scientific skills. You can be great scientists and be completely unable to communicate, to explain in speech you are doing. For writing books, it’s important, which are the right words and so on. By the way, when I read my first book again, my first book on optimal transport, I am always embarrassed to see how I was writing in mathematical statements in slightly informal way. So as I grew older, I became stricter on the writing. So I cannot recover this style which was highly informal.
TPL: Okay, you talked about the quoting. So let me offer another quote this moment. I was interviewing Ambrosio also for the series. He said an interesting thing. He said that De Giorgi said that he would never offer his students the intuition. He just state the plain truth. And he said that it’s up to the audience to come up with whatever intuition that you think you can relate to that subject. So Ambrosio said that De Giorgi really sticks to that point.
CV: That’s interesting. If the student is named Ambrosio, certainly it works.
TPL: Is a mystery where did De Giorgi get the intuition, right? And De Giorgi said that no, as a teacher, he doesn’t offer you the intuition. He offers you just the plain truth.
CV: For my students, I like to offer intuition. One thing I always say is that you should never help too much to students because they have to find things for themselves. That way they will become autonomous.
TPL: I see.
CV: Students played very important role in my career, most importantly Clément Mouhot who became my collaborator on Landau damping and other subjects. But also for instance I learn a lot discussing with Figalli, and my other students also. There’s a Chinese proverb I know about…”I learn things from my teacher and more from my colleagues and even more from my students. “ something like this.
TPL: I am searching for my memory bank because Chinese history is long and Chinese culture…
CV: And there’s other very important proverb which is in Chinese, and which applies very well to research, saying that when you travel, the importance is not the goal but the path you travel. And in real travel you will never know the road you are going.
TPL: This sounds like Daoism not Confucianism. So now the importance is the path you travel. So what do you see for yourself in the near future? What would be your path you think?
CV: It is so arranged that somehow about all the projects I am into currently should all come to a kind of an end around 2019, 2020. Institut Henri Poincaré I will end my term there 2019 or 2020. But also the conference cycles, the work at the European Commission, and other associations which will be okay as well. So somehow I am focusing now on all these projects, make sure that they can continue them to the right term. Then I will have to find some new cycle maybe, starting from that. When I have more time for my research project, for sure the first things I am going to write is books because that’s the way to really be immersed again. And I know exactly which are the books, which are the list.
TPL: You mentioned the Chinese saying about teachers, students and colleagues. I can now recall this saying: Learning, then you realize that you don’t know enough, Teaching then you know you are limited. 學而後知不足,教然後知困Writing books sounds like a good way to make yourself hungry again.
CV: It was already like this. Around 2000, 2005, I had a kind of crisis in which I felt I had not much motivation again. It was maybe a sequel of my stay in Berkeley which I had been frustrating in some respects even though it was the root source for important thing in my career. There have been some frustrations. I sensed that my motivation was really low. What put me back was starting to write the book, the big book on optimal transport, which were St. Flour summer school lecture notes at the beginning. And writing and writing the book I felt the motivation coming back and next thing I knew I was full of projects and things I wanted to do.
TPL: That’s remarkable. Your capacity is remarkable. I am sure a lot of people can have such a dream. But you carry it out.
CV: A lot of energy, mainly. So once I had an interview with…joint interview with an artist who is famous in France, he does shows with horses. His name is Bartabas, not his real name, that’s the name he chooses. He says whenever he starts a new project with other people in his troop and so on, he can convey only doubt and energy. These are the two things as a master he can transmit.
TPL: Very good, very nice, doubt and energy. I see. So you are thinking of writing another book.
CV: Yes, in the past one of the most rewarding experiences was I wrote comics together with a graphic artist. It was a great experience also because we like each other so much, with that artist. And for sure we will try and write another one with him also in the coming years. Again one thing I will do as common because we talked about activities in my mathematical research, extra-mathematical activities. There always were some similar patterns. Like I told you, always it starts with a conversation, then let’s do some projects and let’s go back and forth. A lot of…for instance, some of the way we worked with Clément on Landau damping, I found again in the way to work on the comics with the artist. With the main difference that we see in the two is when we do research, it’s very risky because you never know you may get it or you may not get it. Even if you are very good, maybe you don’t get it. You miss one important point, maybe there’s just chance sometimes.
TPL: Of course, you have a better chance if you are prepared.
CV: If you are prepared and if you try many things, you have a better chance.
TPL: We’ll work you hard tomorrow, and the day after tomorrow. So maybe I should not work you too hard today. You come back to Taiwan in the future?
CV: Of course.
TPL: So maybe let’s stop here and let’s go for the dinner.
CV: Very good.