The Daily Princetonian sat down with University mathematics professor Charles Fefferman GS ’69 to discuss his work and career. Fefferman was recently jointly awarded the 2017 Wolf Prize in Mathematics with Stanford mathematics professor Richard Schoen for his work in numerous fields such as complex variables, partial differential equations, and subelliptic problems, as well as his contributions to the Navier Stokes equation and Euler Equation, according to the Wolf Foundation’s press release. Fefferman was also awarded the Fields Medal in 1978 for his work on convergence and divergence.
The Daily Princetonian: First of all, Professor, congratulations on winning the Wolf Prize. Can you describe your reaction when you found out that you had won this award?
Charles Fefferman: My first reaction, since we live in interesting times, was one of suspicion. I wanted to make sure that it wasn’t a hoax. I was checking my email. There was an obvious spam, you know, “You’ve won a million dollars and please enter your bank account number,” something like that. I deleted that, and the next email was, “I need to speak to you urgently, please call me at this number in Israel from the Wolf Foundation.” I thought there were two possibilities: either it’s real or it’s a hoax, and so in fact I did call the number and the CEO of the Wolf Foundation very, very nicely told me congratulations and so I said, “Well, that’s great, but how do I know this is genuine?” She was very cool, I said, “How do I check?” and she said, “You don’t have to do a thing, it’ll be public in 24 hours.” And so, indeed, I didn’t do a thing and it was public in 24 hours, and lo and behold, it was genuine. I’m very, very happy and deeply honored. It’s a nice beginning to 2017.
DP: Can you tell us a little bit about the research that led to you winning this prize, and what most excites you about it?
CF: Before I describe the research, I should say how I feel about my own research: I’m an addict. I’m addicted to math, I have been since I was a little kid. I love being a math professor in large part because I get to do what I’m addicted to. Alright, so, what is the research about? Well, of course, it’s math. Within math, it’s analysis. Analysis is sort of further developments in calculus. Let’s say when a student takes a calculus course here at Princeton, then what’s taught is calculus problems about functions that people have known for several hundred years how to solve, but there were plenty of problems about functions and about derivatives and integrals and equations involving ideas that nobody has the faintest idea how to solve, and many mathematicians are trying to make progress on those and I’m one of them.
DP: How did you decide to study these specific topics in math? How do you go about researching and solving the problems around which your work revolves?
CF: I got a wonderful start by being a grad student here, and I was very lucky to have a magnificent advisor, Elias Stein, who was a great mathematician and a great teacher of math, and, by the way, who also — whatever it is, 20 years ago or so — won the Wolf Prize himself. I took his grad course, I was blown away, I thought, “This is what I’d like to work on.”
DP: What was the grad course?
CF: A reasonable title for it would have been “Fourier Analysis,” but I don’t remember the actual title of the course. We’re talking about events in the 1960s.
DP: Can you tell us about what inspired you to pursue math as a child?
CF: I was interested in science as a little kid. At some point, I was not satisfied with the standard little kiddie explanations of science, and so I took a freshman physics text out of my local public library. I couldn’t understand a single word of it, and my wonderful father told me, “Well, of course you don’t read this, it uses math.” “Oh, can I study math?” “Okay, what grade are you?” I think I was in fourth grade. “Okay, fine, I’ll go buy you a fourth grade math textbook.” So I read it, I read it quickly. Then I said, “Okay, can I have a fifth grade math textbook?” So on and so on, through calculus. My father knew math through calculus, but once I finished that, then I wanted to go further and he arranged for me to be tutored at our local university, the University of Maryland, and I later became a student there. That’s where I got my undergraduate degree. They were wonderful to me. I can’t praise them enough. I think that [of] two of the great good fortunes of my life — well, maybe three — one was that I was exposed to the subject that I loved so much at an early age and the second is that I got such wonderful undergraduate training at Maryland. The third was that I came here and worked with Elias. Without all three of those ingredients I don’t know how my life would have gone. I also have a personal life and there are other things. I’m lucky to be married and have children and so on, but in my career, in my scientific work, those were the three formative things.
DP: You entered the University of Maryland, College Park, at the age of 12 and graduated at the top of your class when you were 17. You finished your Ph.D. from Princeton in just three years, and soon thereafter became the youngest full professor in the U.S. when you joined the University of Chicago’s faculty at the age of 22. What was it like simultaneously being one of the youngest and the best throughout your post-secondary education and at the beginning of your career?
CF: At the time, it wasn’t so clear to me that I would be as successful as I turned out to be. I did a lot of wondering. “Do I have the stuff to be a mathematician?” That happened until I became an assistant professor. Then I thought to myself, “Okay, I’ve done math, I can do math,” and then I relaxed a little. But until then, there was a lot of self-doubt.
DP: What advice would you give to current students who feel that same self-doubt about whether they can be as successful as you are in the future?
CF: If you really love something and are driven to study it so that you’re addicted to it, then go for it. There’s no way to tell in advance; [there are] very, very, very few exceptions that you can tell in advance. Students who look very brilliant and very promising just peter out when they have to work at the highest level, and other students look a lot less promising but somehow develop the spark or keep with it or something clicks. You just can’t tell in advance. That’s very scary when your career is on the line. But there were some people — I was one of them — who just loved the subject so much that it wasn’t a choice. Well, actually, when I was a little kid, there was some choice. I loved painting, so I thought I might be a painter. As I look back, I’m very happy I chose mathematics.
DP: What motivated your decision to return to Princeton in 1973 and assume a full professorship here? How has your work been affected by being a professor at your old alma mater?
CF: There was a specific reason and general reason. The specific reason was my teacher, Eli Stein. The general reason was just that I was convinced — actually I’m still convinced — that this is the best math department in the world. One can think that I was brainwashed as a graduate student, but I sincerely believe it.
DP: According to college rankings such as the U.S. News and World Report, Princeton ranks #1 in terms of math institutions in the country. Why do you think that’s the case from your experience?
CF: There are different perspectives from which one can view it. You could ask which math department does the best research, then you could ask which department does the best job of educating grad students, then you could ask which department does the best job of educating undergraduate math majors, and finally you could ask which math department does a good job in service teaching, teaching calculus and linear algebra to students who need those subjects but don’t particularly care about math for its own sake. The Princeton math department tries to do all those things well. I think that we succeed in doing all those things pretty well. But the big thing that sets us apart even from the other first-ranked institutions is the strength of our graduate program. We do magnificent research. There are great mathematicians here. In the future, when people study math, the work that’s being done in this building will play a prominent role. There are wonderful, wonderful researchers. That’s true elsewhere also; there are a few other places that are really top-notch. I think maybe we have a critical mass of incredible quality and numbers of researchers that I think sets us apart. I’m a Princeton partisan; there are partisans of other universities, but it seems to me the effectiveness of the grad program in turning out the next generation of absolutely top-notch researchers seems to be unmatched. I went through it myself a long time ago; it’s changed somewhat in the million years since I was a student, but it’s very effective.
DP: In your 30-plus years of teaching at Princeton, what would you say you most enjoy about this university?
CF: Perhaps I enjoy most of all simply that I’m allowed to work on anything that interests me and to throw myself into it and there’s enough time given to me so that I can think. There’s enough patience so that if I think of something and I come up with no success for a long time, that’s okay. Obviously, the problems that I’m working on are very hard, so I’m normally stuck. If a researching mathematician isn’t stuck all the time, that means the problems are too easy. I enjoy contact with several of my colleagues. They’re very nice people, they’re very smart. It’s exciting to be in the middle of that. I enjoy contact with the students. I actually enjoy service teaching. I teach first-semester calculus. That’s often considered a dirty job, but I like it, it gives me the feeling that I’m doing good. I don’t want to have professional interactions only with other people, with Ph.D.s with distinguished research credentials who I’ve known for 30 years. Service teaching gives me an outlet for that. The campus is beautiful. I think that has a psychological effect — I think it’s affected the quality of my work.
DP: Where do you see your research in mathematics going in the future?
CF: There are some problems that I’ve been working on a for very long time that I plan to keep working on, but also simply what happens to me is that every couple decades some problem I hear about or think of or read about, some problem, just grabs me, and I can’t stop thinking about it. I hope that will continue. It feels as if I don’t have control. The problem owns me. It picks me, rather than the other way around. Maybe that’s what it’s like to be an addict. I have the good luck to be addicted to math instead of something more destructive.
DP: What’s the most fun or addicting problem you’ve ever worked on?
CF: I don’t think I could pick just one. Each one, as I’m working on it, seems to me to be the very best of them all. Afterwards, it’s on to the next. I could describe particular problems that I’ve worked on, but probably that would make everybody’s eyeballs glaze over.
DP: For any aspiring mathematicians reading this, what advice would you give them about the field?
CF: The field is so beautiful that they’ve made a wise decision to pick it. It’s infinitely deep. One nice thing about studying math as opposed to studying many other subjects that one might love is that there are fallback positions along the way. If you discover that you can succeed as an undergraduate math major but maybe not as a grad student, there a plenty of career paths. A math major gets you into law school and so on. If you’re a grad student and you find that you can get your Ph.D. but you wind up not writing the thesis you wanted to write, there are fallback positions. You can have a nice career and nice life and so on. All the way from the beginning to the very highest levels, I think there’s probably less risk and fear involved in studying math from that point of view than there is from, let’s say, studying the piano. I remember many years ago when I was a first-year grad student I went to the orientation session for first-year physics students, and the job market wasn’t so good. The director of grad[uate] studies in the physics department said at the time, “Alright, now is the time to think. If you love physics so much that you can’t do anything else, then welcome. But if you don’t love physics that much, now would be an excellent time to quit.” The job market was pretty bad, and I absolutely don’t make that recommendation to anyone now, but you may find maybe you love math so much that you can’t imagine yourself doing anything else. In that case, you’re a very privileged person because to love something so much and to have the chance to do it is a very great privilege.
DP: Before we finish the interview, is there anything else you wanted to add?
CF: Yes. This particular prize, the Wolf Prize, there are I think eight people who [either] have been grad students or professors here at Princeton who have gotten the Wolf Prize in math. So this is not the sole propriety of the Princeton math department, but we are very well represented in this and many other prestigious prizes.