Cédric Villani on Living Theorem, Pop Culture, and the world of Mathematics
Interview conducted and condensed by Avra Kouffman
Q. Which aspect of preparing this TedxOrangeCoast talk did you most enjoy?
A. It’s hard to say. I’ve prepared many talks — literally, hundreds — since my Fields Medal, but I prepare Ted talks with special care and this one in particular. Ted talks are very well set in scene; they’re viewed by many, many people, so you have to be extremely careful how you present things; and they’re so short that you need to situate everything as perfectly as you can. This was the first of my three Ted talks that I really had some time to prepare. This, in itself, was enjoyable — being able to prepare and think for quite a time about how I wanted to present things. I knew I wanted to include a few allusions to songs. I’m in frequent contact with the translator of my book, Living Theorem, so I asked, “Could you translate a few lines from an Allain Leprest song?” It was hard because it’s a French song with plays on words, so to render it in English was quite tricky. It was fun! The other fun thing which I quite liked and mentioned in my talk: I really was sitting in an armchair, thinking about how to present the idea that mathematics is everywhere, when I noticed the table next to me was a definite mathematical shape, a Reuleaux triangle. This was a very exciting moment. I saw it and wondered, “Is it really what I think it is?” and rushed to get a ruler to make measurements, so it was quite fun. It was very interesting to me that during the preparation of this talk, some mathematical adventure came.
Q. Tell us about Living Theorem, your book.
A. I wrote it for the general public. It was quite a hit in France and it has been translated into about ten languages. The English version will come out in spring 2015. It’s a very special book. I will not say it’s the best book you’ve read, but I’m sure you’ve never read a book like this! It’s a story of mathematical discovery, but viewed from the inside and viewed in the moment. It’s presented as a diary of the adventure, so to speak. It spans about 2 ½ years on three different continents. A lot of it is in Princeton, by the way. It tries to put you in the scientist’s head when he’s working, with moments of doubt, moments of joy, moments of frustration and of doing anything else and then coming back to it and so on. I think this is the first book ever that shows you what the life of a mathematician is — not trying to simplify things, but putting you directly into the mess. It’s not a book that conveys science and explains it to you. It’s a book that tells you about the life of creating or researching. You can see when you communicate science that you simplify things, as I do in my talk. When you explain to your little daughter, for instance, what you do at work, it’s using words she can understand and simplifying your work. But another way to put your daughter in contact with your work is to take her to work with you. She’s there and she can see all the agitation, the worrying, going this way, that way, moments of tension, how people really speak and think, what they like to do and so on. That is what you will find in my book — no explanations, but the atmosphere is exactly what it is to be a researcher. It covers 2 ½ years, but just one theorem. It’s one of the theorems that got me the Fields Medal, so it was a very important moment in my career.
Q. Your talk implies that beautiful minds are kind, rather than condescending.
A. At least, that’s the way I think they should be and that’s really how they have to be if they want to earn the title ‘Beautiful Mind.’ When you think of something beautiful, it’s an interaction between somebody who sees and finds the person or the mind beautiful and the person or mind that there is. It’s totally meaningless to be a huge power but without anybody to see it. A beautiful mind is somebody who somehow finds this beauty, sees things in different ways, puts them in perspective and is able to share so that other people profit by this. I use the image of the reflector, getting the light and reflecting it to the other people. That is the condition to become inspirational, to continue to live in the hearts and minds of the people who admire your work.
Q. You show how a few minds, like Einstein or Mozart, become shared cultural references. If you were to become a shared reference, who would you most like to reference you in a poem or a song?
A. Let me see. I quote two songwriters in my talk, first Melanie Safka and then Allain Leprest. I would certainly have loved to be quoted by him, but now he’s dead before I ever even had a chance to meet him! My favorite French singer is Catherine Ribeiro. Not only does she know me, but we exchange regularly emails or phone calls, so definitely her reference, when it comes to scientists. Let me just say, it’s great luck, with the kind of distinction I had and the publicity, that I’m in the position to connect rather easily to almost everybody in the culture world. For instance, I made contact this year with my favorite French graphic artist, Baudoin, and now we’re collaborating on a project that involves comics and history and science. It will take a good six months of production; you’ll see what it is when it’s out!
Q. You feel you’re doing the right thing when you make people feel smarter, since then you’re sharing the light. Spreading light is also a religious concept.
A. For us mathematicians or researchers, light is the symbol of the idea that is appearing. Think of the image of the light bulb. That’s the light we receive. When we see the light, in our context, for us, it’s just the light of understanding. In my book, there’s a passage in which I’m walking back home and crossing a very dark part of the forest. It’s at night before light appears, and I compare this in the book to the process of mathematical discovery when you understand nothing and then, a faint flickering of light and then, all of a sudden, it’s “ah!” –light everywhere and illumination and so on. For us, this light image is definitely not in the religious sense, but in the sense of the Enlightenment, the feeling of understanding … or maybe that is our religion!
Q. As a parent or mathematician, what words of encouragement do you have for parents who stress over helping kids with their math homework?
A. There’s no fixed rule. You have to know what your child is up to, what he or she wants and so on. That’s one thing to keep in mind. Some children need to be taken care of very closely; others just need to live and not be bothered. It depends, a lot. I think, for parents, my main advice would be that the most important thing — maybe more important than helping on a subject that maybe you haven’t mastered — is preparing an atmosphere of work, of work that is joyful. The best thing may be to work nearby the child while he or she is working. My children, I almost never help them, but they’ve seen me, since they were so young, working, reading, at home in the evening when they’re doing their homework. They grow up with the idea that working is normal, it’s natural, it’s peaceful; that one has to concentrate and reading is natural. And then, Poincaré used to say that the most important thing in educating children was to make them marvel about the beauties in the world, the natural wonders, to show them how beautiful nature is and let them find [out] for themselves, on their own.
Q. If you could help the public understand one thing about math, what would it be?
A. Mathematics is alive. That’s the one thing. It’s changing, it’s dynamic, it’s moving faster than it ever has, it’s everywhere around us. It’s more important in our world than ever before because it’s so omnipresent nowadays with the advent of computers, etcetera. The second thing is that mathematics is a tool that is a way of reasoning and learning how to reason in a logical way. This, in itself, is one reason why it’s so important to learn mathematics at school, even though you can then forget everything. It’s the one opportunity that you have of learning the art of logical reasoning. There is no other course that allows you to do this. That’s why it’s so special and that’s why, also, sometimes it’s so dreadful! Why would we learn this thing, the art of logical reasoning? There are remarkable quotes by Abraham Lincoln about when he wanted to understand what ‘proving’ means, when he was a lawyer. He found the best he could do was to study mathematics. For a long time, he read and reread the Elements by Euclid until he could master all the proofs. He explained, “That way, I understood what it means to prove something.”
Q. In closing, what do you find valuable about the Ted talks series, personally?
Several things. First, Ted talks are a good way to touch many people because they’re short, they’re very much seen and so they’re a good means of transmitting. I know my first two Ted talks have been very much viewed and shared. Preparation is also a very interesting moment because you really think about how to make the story you want to cook up; it’s a very interesting creation moment. Third are the people, the other speakers and lecturers you meet. It can be extremely interesting. At this particular TEDxOrangeCoast, for me, a very illuminating encounter was with the skateboarder Rodney Mullen. It was really a magical moment for me. We had dinner together and we saw each other again and so on. It was really a great encounter. And I don’t see any … Really, where on earth would I have met this guy, if not for this event?!