A Conversation With Edward Frenkel, Mathematician & Filmmaker

By Zara Raab

Professor of Mathematics at University of California, Berkeley, and author of more than 80 articles in scientific journals, Edward Frenkel has published two monographs on his mathematical research, most recently Langlands Correspondence for Loop Groups, with Cambridge University Press. Professor Frenkel was recently invited to give the American Mathematical Society Colloquium Lectures at the 2012 Joint Mathematics Meeting in Boston, the largest mathematics conference in the world.

In recent years, Frenkel has become a writer and filmmaker, co-writing and co-directing, with French filmmaker Reine Graves, and playing the lead in the film Rites of Love and Math. He also wrote a screenplay for a full feature film The Two-Body Problem with Berkeley novelist and El Leon Literary Arts publisher Thomas Farber. It was published as a book by the Andrea Young Arts in 2010.

(Note: This interview took place before Professor Frenkel went to Columbia University in New York, where he will be spending the Spring semester as the recipient of the Eilenberg Visiting Professorship.)

Zara Raab: I want to discuss with you your film script and play, The Two-Body Problem, but first I’d like to talk about your work in mathematics involving the Langlands Program. Can this program be explained in terms a layperson like myself can understand?

Edward Frenkel: Yes, I believe it can, and should be, at least the gist of it. The Langlands Program is a system of advanced mathematical ideas developed by Robert Langlands in the late 1960s with the goal of tying together different areas of mathematics. This theory has also been recently used to connect mathematics with quantum physics. Langlands is a mathematician who currently occupies the Einstein office at the Institute for Advanced Study in Princeton. In recent years, I had the opportunity to collaborate with him on this subject.

ZR: One of your areas of expertise is symmetry, is that right?

EF: Symmetry is one of the central concepts in science. If I had to summarize my mathematical research in one word, I would say it is about symmetry. But symmetry can mean a lot of different things in different fields. Most simply put, as one of the characters explains in my screenplay with Thomas Farber The Two-Body Problem, an object is symmetrical if it can be transformed in non-trivial ways without changing its shape and position. For example, snowflakes are symmetrical, as are butterflies or diamonds. In mathematics, symmetry becomes a more precise concept. The closest to our intuitive understanding of symmetry is the idea of symmetry in geometry. But in mathematics, we go further, in saying, for example, that a mathematical equation can also be symmetrical. Understanding the symmetry of an equation helps us understand what the formula is telling us. In quantum physics, you have elementary particles, these tiny pieces of matter, that also have symmetries, but they aren’t naïve geometric symmetries. These are the symmetries of the inner world of an elementary particle, if you will. Understanding these symmetries leads us to a much better understanding of their behavior. My work is on the interface of all these fields, math and quantum physics, finding common trends and patterns between them using the concept of symmetry.

ZR: You grew up in a town near Moscow, and came to the US as a young man right out of college. I gather that was the USSR. Is that correct? Did you come before the disintegration of the USSR or after? Was it difficult? What about the rest of your family, your parents?

EF: I came to America just as the Berlin Wall was coming down. While I was a college student in Moscow, I wrote some math papers that became known, and because of this, I was invited to Harvard University as a Visiting Professor. I remember it all so clearly: My plane touches down at Logan Airport in Boston. Wow, this was such a big change! But I felt at home. I immediately felt it was my place. My life in the Soviet Union wasn’t particularly easy. I wasn’t accepted to Moscow University because my father was Jewish. A lot of doors were closed to me. It was an uphill battle. Suddenly I found myself as a visiting professor at Harvard. It was a time of economic crisis in the Soviet Union. Here in the U.S., it was a different situation. But I was torn, because my family was still in Russia. I missed them. I wondered what to do: Should I go back to Russia? Should I stay in the United States? My parents kept calling me, saying, “Don’t come back. This is your opportunity. You should stay.” I decided to stay at Harvard. And then I arranged for my family to immigrate. My family came about five years after me. They are still living in the Boston area.

I’m going to visit my family in Boston in January. There is this big meeting of the American Mathematical Society, 7,000 people. There is one such meeting every year. It happens to be in Boston this year. And the Society invited me to give the Colloquium Lectures, which have been annually given since 1896, so it’s a great honor. My family will be able to come to see me give this address in front of a large audience. So it’s like a homecoming for me.

ZR: You showed great mathematical promise at a very young age in Russia, as I understand it. And yet you were not admitted to the top university in Moscow—for sinister reasons, I gather. Do you want to tell me more about that?

EF: In Moscow, in those days, there was special treatment at the entrance exams for students targeted as Jewish. The exams were designed specifically to keep out Jewish students. My father was Jewish; Frenkel is a Jewish name, so I had to endure a four hour oral exam during which I was asked questions significantly more difficult than those asked of other applicants, questions that ordinary high school students could not have been expected to know. At the same time, none of my answers were accepted as correct. The examiner, for example, asked me to define a circle. I replied by saying that a circle was the set of points in a plane, equidistant from a fixed point. But my answer was judged wrong, because, as the examiner explained, “It is the set of all points in a plane, equidistant from a fixed point.” It was ludicrous! The examiner, who failed me on the exam, later, perhaps out of a vague sense of guilt, told me that I showed an extraordinary grasp of mathematics. Can you believe this?

ZR: What happened then? Where did you go?

EF: The only place for me to study mathematics in Moscow was the Institute of Oil & Gas. It had a small applied math program, where a lot of bright Jewish students ended up. While I was an undergraduate there, I met some amazing mathematicians who took me under their wings and mentored me. So in the end I was able to do some cutting-edge research and I got invited to Harvard as a Visiting Professor when I was 21. I then got my Ph.D. in one year there, and after that I became a Junior Fellow and then an Associate Professor at Harvard. Then the University of California at Berkeley made me an offer I couldn’t refuse. (Frenkel smiles.)

The story of my education in Moscow––it’s a story that I think more people should know about. A lot of lives were broken at that time by the system in the Soviet Union. I was only 16 years old, but strong enough to survive. In some ways, my struggles there as a student made me stronger. I had a lot of support from my family, and I benefited from the generosity of some wonderful mathematicians. But a lot of young people suffered from this, and their careers were broken, their lives were broken. For what? Just because of anti-Semitism. There’s simply no justification for this. We need to talk more about it, to prevent this from happening in the future.

ZR: Not only are you a mathematician, you have in recent years, made the extraordinary leap into filmmaking as a way of expressing your feelings for the beauty of mathematics. Your first film was Rites of Love and Math. which you co-directed with the French filmmaker Reine Graves. Tell us how that came about?

EF: It does sound like a leap of faith. But for me it was a natural continuation of my work in mathematics. What interests me the most is bringing together different fields: algebra, geometry, physics, … There are many different branches of mathematics nowadays. The study of mathematics has become more and more fractured over time. And specialists in different areas talk to each other less and less. I like working on building bridges between different fields, and to use these to gain new insights. If you connect different areas, that can be beneficial to all. The analogy I like to use is to solving a jigsaw puzzle. You make a lot of progress if you connect different parts of the puzzle.

I wrote several review articles and books over the years to introduce the topics I was working on to mathematicians working in other areas and then also to physicists. And I saw that many of them found this useful. Then my next natural step was to move outside of math and start talking about math to non-mathematicians. Partly, this was to dispel the myths about mathematics in the popular culture. To me, that was a natural continuation of the work I was doing within mathematics. The film Rites of Love and Math was the first project that I embarked on because I was fascinated with cinema. I thought, where do you even begin when you want to reach people who are not mathematicians about mathematical ideas? Most people just shut down when you try to broach the subject of math. They might pretend they are listening, but they aren’t, really. One reason people don’t want to hear you is bad math education. The subject is abstract, so if your teacher does not find a way to explain it clearly, then this leaves you with a bad taste, and this taste stays with you. And there’s fear, too. People think they will not be able to understand. But in fact I believe that everyone is capable of understanding math, if it is explained in the right way.

So I felt that I had to find an unconventional way, a more creative way, where you aren’t talking to people directly about the subject. The language of cinema allows you to jump barriers in a very short period of time. The Russian poet Joseph Brodsky has said that poetry is an extraordinary accelerator of conscience. Likewise, with cinema you can convey a lot in one image. The idea of our film Rites of Love and Math was not to talk about the subject so much, but to let people see and feel it.  To most people this sounds very surprising, but I actually believe that Love and Math are not that far away from each other. Math requires the same kind of love and passion as poetry, art, and music, it’s a creative process of going against the unknown. I wanted to convey that in a more emotional way as opposed to cerebral way.

It was very fortunate for me that I met a wonderful French filmmaker Reine Graves who liked the idea of making a film about the beauty of mathematics. I was living in Paris, because I was invited by a French mathematical Foundation to come and do my research there, and we were introduced by a mutual friend. I wanted to make a film about math, and Reine was very receptive to this idea. She had earlier made very interesting experimental films, so she understood the potential of this project. We had a great collaboration. We decided to make a film about a tattoo of a mathematical “formula of love.” It is a homage to a film by the Japanese writer Yukio Mishima. It’s a fantasy, an allegory, and a meditation on what most people consider to be incompatible notions: mathematics, beauty, and love.

ZR: You have also written a screenplay, which was recently performed at the Aurora Theater here in Berkeley, called The Two-Body Problem.  The play uses the mathematical problem of “the two-body problem” as a metaphor for the problem of love between two human beings—a striking metaphor, I must say. As I understand it, the two-body problem is the mathematical problem of finding the trajectories of two objects which interact only with each other. Once we know the forces of attraction between the two objects, we know their behavior, or we can figure out their behavior, all the way into the future.

EF: That’s right. The Two-Body Problem started as a screenplay that I wrote with a great writer and my good friend Thomas Farber. Later we did a theatrical adaptation, and the director Barbara Oliver agreed to direct it at the Aurora Theater. Cinema allows you do more than theater — flashbacks to the past, for example — but the theater brings you live performance. Barbara Oliver did a fantastic job with directing the play. I must say I am fascinated with both film and the theater.

ZR: The phrase “two-body problem” becomes in the script a metaphor for love and male-female bonding. And the trouble in the real world as in mathematics seems to be that if there is a THIRD object (or love object), then it is impossible to predict what will happen. And this is kind of what the movie or play is saying, isn’t it? Do you wish to elaborate?

EF: That’s part of it. Our screenplay Two-Body Problem is about the connection and collision between the real world and the abstract world. In mathematics, “the two-body problem” has a unique solution. But in the real world, that’s not the case. The relationship of two people is complicated and it doesn’t always have a solution. One of the characters in the play, Phillip, is a mathematician, and he is trying to come to terms with this dichotomy between mathematical truth and human truth. He is so used to being able to solve all problems, but in real life situations, these recipes cannot be applied.

ZR: The romantic difficulties portrayed in The Two-Body Problem–could they be attributed in part to your own displacement from your country of origin, from the USSR, or Russia? To carry on the metaphor of the play/film, if a person is a planetary body in orbit, then when you left Russia, you flew out of your orbit. That’s enough to create havoc in any system, am I right?

EF: The story in our screenplay is not biographical, but for sure many of my real life experiences contributed to the writing of The Two-Body Problem. You write from your own experiences, but more importantly, you write to create compelling characters. Once we decided what we wanted to convey in the story, we had to shape the characters in a certain way.  So the character of Phillip in the play is different from me in many ways. I don’t do things the way he does.

Going back to my “displacement,” as you called it, it’s certainly true that my leaving Russia was a very important event in my life. I was 21 years old when I came to the United States. I was still growing up.  But I felt like I was at home here. In fact, I felt more at home here than in my country of birth. I haven’t been back to Russia in 20 years. I would like to go back one day, I have friends there, I feel very connected to the culture there, and I care deeply about what’s happening in Russia. But it was a good thing, my coming to this country. So in that sense, I don’t feel that I was displaced.

What I think is more interesting is how growing up in Russia influenced my writing. One could wonder whether some of the darker undertones of my writing, reflected in Rites of Love and Math and The Two Body Problem come from my Russian heritage. There’s a tragic element in both the short film and the screenplay. I was definitely inspired by the great Russian writers, like Dostoyevsky and Bulgakov. As I said, my coming to the US helped me develop my life more fully. Nonetheless, my immersion in Russian culture has led me to see the two sides of life, the dark and the light, more clearly. I mentioned the tragic element. In Rites of Love in Math the mathematician creates a “formula of love,” and he wants to tattoo this formula on the body of his beloved. And then it all ends in tragedy… So of course in many ways this is taken from the great Russian literature. It’s also taking elements from the work of the Japanese writer Mishima, whose film inspired our film. And of course, Japanese culture in closer to Russian culture than it is to Western art and literature.

ZR: The character in The Two Body Problem says he loves to travel and is glad to have the chance to do it—I mean, there he is on the French Riviera as the play opens. Do you think there’s any connection here with Liminality? Psychologists have posited a link between the liminal aspects of travel and promiscuous behavior in human, a habit or preference for new and on the surface experiences? The term is used to “refer to in-between situations and conditions that are characterized by the dislocation of established structures, the reversal of hierarchies, and uncertainty regarding the continuity of tradition and future outcomes.”

EF: The desire to travel, to be exposed to different experiences, can be connected to something in one’s personal outlook and in one’s relationships. That’s certainly true. But the point of the screenplay is that Phillip is torn between his love for his ex-girlfriend and his new experiences with other women. The way Phillip explains it in one scene, mathematics is the world of infinite possibilities. Nothing ever dies. You never have to sacrifice anything. He wants to hold on onto his former love and not sacrifice the world of possibilities in front of him. This is what we wanted to explore.

I have to say that in most films and books mathematicians are portrayed in a particular way, as people who are enclosed in themselves, and sometimes on the verge of mental illness. Like the mathematician in the film A Beautiful Mind, for example. Phillip, the mathematician in our screenplay The Two-Body Problem, is not like this at all. He is an intellectual who is very much driven by his intellectual pursuit, but he also has a fascinating and fulfilling personal life. In my view, there is no contradiction, you can have both. But then the question is: In what way does the mathematician’s fluency in the abstract world influence his perceptions of the real world? I think people haven’t asked this question, people never get to that point, because the popular perception is that a mathematician is always this closed human being, with absolutely no connection to the real world. But mathematicians are more complex beings, they are not like the character of A Beautiful Mind. They are intellectuals in love with their profession, but at the same time, nothing human is alien to them. In the case of The Two-Body Problem, the two main characters, the writer and the mathematician, are like that. To them, the real and the abstract worlds are inter-connected in many ways, and they both benefit from this connection, but they also have to sacrifice something.

ZR: One connection in The Two Body Problem that is not explored is the idea of deepening a relationship with one other human being. You know, in all those Oriental paintings, there are two geese in the sky flying together across the sky, supposedly emblematic of the companionship of two soul-mates. Isn’t that one of the parallels with mathematics? The mathematician’s deep understanding of a theorem—take Fermat’s theorem—the years or time he had to have spent to solve it. He might have felt distracted at times by other ideas or mathematical problems, but he went deeper into this one problem.

EF: Well, both characters in The Two Body Problem are looking for a deep relationship. Richard, the writer, says he is waiting for a princess who will come and kiss him and wake him up. So he wants a deep relationship, he is looking for it, but he’s also happy to settle for less. And Phillip, the mathematician, likewise, something is drawing him to his past lover, so he is drawn to that deep relationship with someone.  This is the ideal that he wants to pursue. But at the same time he has no trouble meeting other women. Life is full of contradictions like this, and we wanted to explore it in the screenplay.

ZR: You said in an interview recently with the e-zine Indoorboys, and I quote: “The language of cinema allows you to convey ideas in a highly compressed form, so that the viewer can grasp, in a very short period of time, information that may take years to process in other, more conventional, formats.”  [This is about the other film ] The image of the formal . . .What is it that The Two-Body Problem conveys specifically about math in a highly compressed form. Is it really a film about math? It seems to me to be a screenplay about love, not math.

EF:  Although there are some mathematical concepts discussed in it, such as symmetry, infinity, and catastrophe theory, The Two-Body Problem is more a study of the psychology of a creative person, and how his or her intellectual pursuit is sometimes helpful, sometimes detrimental to their understanding of the real world. The screenplay also tries to break that stereotype of the mathematician as that guy in the corner of a cafe, not noticing what’s out there, not even noticing the beautiful women out there. Our character is more multi-dimensional, there’s more spectrum and more variety––not necessarily what people are used to when they think about mathematicians.

ZR:  In The Two-Body Problem the character Phillip—he is a mathematician, like yourself—says at one point, “. . . the moment you stop thinking about the glass and focus on it symmetries and their inner structure is the moment you become a mathematician.” Isn’t this true of philosophy or any kind of intellectual discipline? The moment you start thinking about properties in an abstract way, you become an intellectual, a philosopher.

EF: Absolutely. For Richard, the writer, there’s also the collision between the real world and the abstract world–– for him, it’s the world of literature–– and he wants to draw his stories from life’s situations and experiences, he forgets about the boundary between the two, and it gives him a desire to manipulate reality. We learn that his previous novel was based on his personal experiences. It’s only a small step from there to actually trying to mold real people into characters of your story. And we also asked: What does it take to create a story? For different authors it’s different. At the end of the day, the writer in The Two-Body Problem gets his story by interfering in the lives of the other characters in a tricky way. But at what cost to him as a human being?

ZR: In The Two-Body Problem, Phillip quotes Saul Bellow: “more people die of heartbreak than radiation”. Do you yourself read Saul Bellow’s novels? I was a little surprised not to hear you quoting Tolstoy on marriage and love—something perhaps from “The Death of Ivan Ilyich” perhaps? What about the Russian novelists of the 19^th and 20^th centuries? What other writers throw light on the two-body problem?

EF: As I already said, in my early years I was deeply engaged by the classic Russian novels of the 19^th Century. And the character of Phillip in the screenplay, who is Russian, is also influenced by Russian culture. But he quotes from his new culture. The Russian culture is his sub-culture, reflecting his sub-conscious, and the American culture is his consciousness. He  quotes from E.E. Cummings, for example. My mathematical book, Langlands Correspondence for Loop Groups, by the way, has an epigraph from EE. Cummings:

Concentric geometries of transparency slightly

joggled sink through algebras of proud

inwardlyness to collide spirally with iron arithmethics…

The way I see it, he talks here, in a poetic way, about the unity of three mathematical fields: algebra, geometry, and arithmetics, and that’s exactly what my book is about.

ZR: Will the screenplay of The Two-Body Problem become a film? Tell us where that stands now.

EF: We are in talks with a well-known French producer who wants to make a film based on our screenplay. I also attended the Cannes Film Festival the last couple of years and met some amazing producers and filmmakers, who have read our screenplay. A lot of people have found it very interesting and have seen in it a lot of potential. We’ve made it much stronger and more compelling. I think we are getting closer to the point where it will get produced as a film and also as a play. (By the way, I want to play Phillip in the film.)

I have to say that the world of filmmaking, even independent filmmaking, is in many ways different from my native world of mathematics. Mathematics, as you mentioned earlier, is a lonely profession. You work by yourself or you work with one or two others, even though you depend on what other people have done. When you actually make an effort, and write up your results and your ideas, it’s a solitary effort. In this sense math is also similar to writing. In contrast, filmmaking involves many people working collaboratively throughout the whole process.

My first film Rites of Love and Math is a short film, 26 minutes, but it involved more than 30 people. I co-directed, co-wrote, co-produced it (with Reine Graves), and I played the lead. I was also very much involved in editing and post-production, in every step of making a film, from an idea to a finished product, and it was all fascinating to me. I had to get used to many things I am not accustomed to in my mathematical work. One of the surprises was the way people responded to the film.  This film evoked some strong reactions from people—some positive and some negative. But I wanted to do something that was accessible to people, and in the world of art there isn’t a single truth, different people perceive things differently. This came as a kind of “cultural shock” to me at first. But I think that as long as it makes an impression, evokes a response, a work of art is doing its job. What matters is that it touches people in some way. That experience matured me, which is good because now, working on a full-length film, I can use what I learned. It has been a long journey.

Thomas Farber and I started working on TheTwo-Body Problem three years ago. We finished the first draft very quickly. The rewrites––that’s the real work. I was very fortunate to have Thomas as my co-author, to enter the world of writing with a wonderful writer whom I admire. It’s been a great experience.

ZR: What about your published work in mathematics? That’s a whole different kettle, I would think.

EF: I continue doing my mathematical research full speed. I have several exciting projects I am working on right now, involving the Langlands Program and Quantum Physics. Mathematicians publish most their research in scientific journals. But we also write books; usually, to give a survey of a particular area, or to present the material in a novel way, to be used as a textbook by students.

Mathematical publishing is currently at a threshold. For high-end math there are three or four most prestigious publishers in mathematics. Typically, they publish a print version, and then they put the PDF File online and sell it––close to the full price. But with a very small effort you can create a much better product, one with links to all references in the text, so you jump easily within the text or from the text to the references and back. These documents should be available at a much lower price, to make them accessible to students who often don’t have much money.

When I published my latest book, I wanted an electronic version with the links to all my sources. I didn’t want just the bare PDF file. Unfortunately, the publishers are way behind on electronic publishing. This is why when I negotiated with Cambridge University Press, I kept the rights to the electronic version of my book. The print version is doing well; it’s going to libraries, people buy it in stores and on Amazon, and so on. Because I kept the rights to an electronic version, I was able to go to a small publisher here in Berkeley called Mathematical Sciences Publishers, run by one of my colleagues at the university. They produced a state of the art, fully hyper-linked electronic version of my book. I think this is the future of publishing in mathematics. This is how scientific texts will be produced in the future. Mine is one of the first.

In fact, I put the electronic version of my book on my homepage at Berkeley. Anyone can download it for free. Here is the link: http://math.berkeley.edu/~frenkel/loop.pdf

Nowadays, everything is online. All the scientific papers are online. There are special archival sites online, so they become accessible immediately. The problem with book publishers is that traditionally they expect you to give them all the rights. I was lucky I was able to keep the electronic rights to my book, and I was able to find people to set up a quality electronic version.

If I am writing a technical paper, and I need to refer to the work of a colleague, to check on something related to my own work, I want that information right away. I don’t have time to go to the library and research it, and I certainly can’t afford to own all the relevant books—they are way too expensive and clunky as hardbound objects. An electronic book is a solution to this problem. Unfortunately, it’s not common yet. My book is an example of how it should be done––especially in math, where we depend so much on the work of others.

ZR: What are you working on right now?

EF: I’m finishing a book about my education in Russia, my struggle with adversity, my journey from Russia to America, my mathematical life, my journey from math to the arts. I present some beautiful mathematical concepts in very simple terms, just to give people an idea and to show people how much bigger and more fascinating mathematics is than they think. I want this book to reach the widest possible audience. The working title is Love and Math, and I think it summarizes well what it’s about. I’m also going to Columbia University from January to May, as the recipient of their prestigious visiting position, the Eilenberg Chair. I think it’s the opportune time. While I am in New York, I hope to meet some people who will help me publish my new book.

ZR: What are you reading right now?

EF: I’m reading Joseph Campbell’s Hero with a Thousand Faces. It’s the perfect book for a writer and a filmmaker. It was a present from a friend who is a mathematician. In a curious way, even though it’s about mythology, it’s indispensable for writers. It’s everything I always wanted to know about storytelling but was afraid to ask. (Frenkel smiles.)

ZR: Professor Frenkel, thank you for speaking with me.

EF: My pleasure.

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About the Interviewer, Zara Raab

Zara lives in Berkeley and is one of the first women to graduate in architecture from UC Berkeley. She grew up along California’s North Coast, attending school in Portland when she was fourteen, and later Mills College and the University of Michigan (Ann Arbor) for college and graduate school. In her twenties, she traveled, living in Paris, Seattle, and Washington, D.C., where she made a living as a freelance editor and writer, participating for a time in the Capitol Hill Poetry Group, before returning to the West Coast to raise her children.

Early California is a subject of her book Swimming the Eel, just as the drama of family life is the subject of  The Book of Gretel. In leaving behind the rural counties, she became a part of the human potential movement of the 1960′s, and that movement perhaps more than anything, shapes her life and her work. Since she was a teenager, she kept journals, and sometimes returns to those early notebooks for ideas. Her poems appear in many literary reviews and magazines, including The Dark Horse, The Evansville Review, River Styx, Crab Orchard Review, Nimrod, Dos Passos Review, Arts & Letters, and others. She also review books and writes essays on literature for various publications, including the Redwood Coast Review, Poetry Flash, Valparaiso Poetry Review, Colorado Review, San Francisco/Sacramento Book Reviews, and The Boxcar Poetry Review.