## Leonhard Euler

## "Mathematics Is Not a Race"

## An Interview with Benedict Hyman Gross

Selin Deniz Akdoğan

Biography

Benedict Gross was born on June 22, 1950. He is the George Vasmer Leverett Professor of Mathematics, Emeritus at Harvard University. In 1971 he graduated Phi Beta Kappa from Harvard University. He then received an M.Sc. from Oxford University as a Marshall Scholar in 1974 before returning to Harvard and completing his Ph.D. in 1978, under John Tate. He received his A.B. and Ph.D. degrees from Harvard and taught at Princeton and Brown before joining the Harvard faculty in 1985. He joined Harvard University as a full professor in 1985 and since then has served as the Chair of the Mathematics Department and as the Dean of Harvard College. He is known for his work in number theory, particularly the Gross–Zagier theorem on L-functions of elliptic curves, which he researched with Don Zagier. He is now retired and living in the San Diego area, where he holds a part-time position in the mathematics department of UCSD.

Awards

Gross is a 1986 MacArthur Fellow.

Gross, Zagier, and Dorian M. Goldfeld won the Cole Prize of the American Mathematical Society in 1987 for their work on the Gross–Zagier theorem.

In 2012 he became a fellow of the American Mathematical Society.

He was elected as a fellow of the American Academy of Arts and Sciences in 1992.

He was elected as a member of the National Academy of Sciences in 2004.

He was elected to the American Philosophical Society in 2017.

Questions

SDA: How and when did you decide to become a mathematician? Did anyone or anything influence you?

BHG: The classes in mathematics and sciences in my public school were very good because they were trying to encourage kids to go into math and science. So I was very lucky. By 7th grade, when I was about 12, I was more advanced in math class. They pushed me ahead, and by the time I got to the high school when I was 14 years old, I had exhausted the local high school curriculum, so they suggested to my parents that I go to a private school nearby where I could learn some more math and science, and I did. I was interested in math in high school as I enjoyed the competitions. I had a wonderful teacher, Andrew Gleason, in college, and that convinced me to pursue it further. I also had several leading mathematicians, like John Tate and Barry Mazur and Jean-Pierre Serre, advise me in graduate school.

SDA: What makes a person successful in any profession is their love for their profession. How did you meet math and what made you love math? What are your favorite features of mathematics?

BHG: I liked the fact that there was a correct answer! In other subjects, it is more a question of opinion. I did not know what it was like to be a mathematician. I had no idea what a mathematician did. In the newspapers, you can read about what physicists do and what chemists do, but not so much about what mathematicians do. The first great mathematician I met was Andrew Gleason when I took his course. That was absolutely inspirational. He persuaded me to do a major in mathematics. Because I was at Harvard, I had chances to take courses from some famous mathematicians. I did not know who they were, but I took algebra from Richard Brauer and topology from Raoul Bott.

SDA: How can a person become a mathematician? What significant features does a mathematician have?

BHG: By studying mathematics with leading research mathematicians. You need a mentor to guide you to the boundary of the field. Also, mathematics requires so much dedication, focus and concentration that if you just want to do it part-time, you should do something else. It is not a spectator sport. You have to really get into it.

SDA: In what ways do you use mathematics in your daily life?

BHG: Not much, although I enjoy doing arithmetic in my head.

SDA: Could you please tell us a bit about family life?

BHG: My wife has always been super understanding, giving me a lot of quiet time when needed, and also my children, even when they were young. I believe that having kids and having a family is the most rewarding thing. Some people who are totally involved in mathematics miss out on all that.

SDA: What do you think should be done to be a successful person in life? What are the characteristics of a successful person?

BHG: The willingness to focus and work hard.

SDA: You are deeply interested in music. You want to tell us a bit about that?

BHG: I have been playing music all my life. I have studied viola and a little bit of violin from the age of 6. I have always loved music and have played in a lot of orchestras and string quartets. I took music courses in college to learn a little bit of the theory. I still play once every other week in a string quartet of other mathematicians. I am not a very high quality musician, but I love to listen to it and lose myself in it. I think there is a connection with mathematics. Nobody knows what it is, but both are formal systems. My colleague Noam

Elkies is a wonderful pianist and composer. I don’t play at that level, but I probably enjoy it just as much!

SDA: What is your current aim as a mathematician?

BHG: To continue to think about interesting problems.

SDA: What is your favourite mathematical problem?

BHG: The conjecture of Birch and Swinnerton-Dyer on rational points on elliptic curves.

SDA: What is the first mathematical result that made a huge impression on you?

BHG: It is very elementary. In Gleason’s course we proved that a continuous function on a compact set is uniformly continuous. I thought that was the greatest thing I had ever seen in my life. I was, like, Boy! Is that interesting! And I think it is always that for some people, you just see something, and it is absolutely beautiful. Tate tells me that for him it was encountering quadratic reciprocity. You know for a lot of number theorists, once they see quadratic reciprocity, they just love it. As a graduate student, I took a course with Tate on elliptic curves which expanded on the notes that Andrew and I had tried to read. That made a tremendous impression on me. Everything was just incredibly beautiful. Tate had a very original point of view on elliptic curves. You could really learn the subject from listening to him. But it was not any specific theorem. Reading A Course in Arithmetic by Serre, which gives a presentation of so many beautiful topics, also made a big impression.

SDA: What was the biggest challenge you've faced so far as a mathematician?

BHG: Getting into original research as a graduate student. It was a lot different than what I did before.

SDA: Do you think that the Internet has made things worse in some sense?

BHG: I was thinking about that because when I was working with Zagier, we weren’t together all the time. I would just wait two months, and then I would write him a letter saying here is where I am now. And now the tendency, when you are working with someone, is “Oh, I got it. I got this teeny epsilon little idea, I will just send it immediately by email.” Right! And so you get all these emails back and forth, and people spend too much time in email. It is too distracting. You know I get up in the morning, and someone wants me to write a letter for something, and you spend an hour on the computer, and you are mentally tired, and you haven’t had any time to think. And now with the Internet you have so much access to information. I can ask a question to anyone in the world and get a quick answer, and you get instant gratification. But mathematics is not about instant gratification. And without the thought that goes between the emails they are not worth much. I would like to slow that down, but I am just as addicted to emails as everybody is!

SDA: What recommendations would you give to students dreaming of becoming a mathematician in the future?

BHG: Continue to take good undergraduate courses to broaden your background. There is no rush — mathematics is not a race.