Interview with Louis Nirenberg Early Experiences Louis Nirenberg is one of the outstanding analysts of the twentieth century. He has made Notices: What were fundamental contributions to the understand- your early experiences ing of linear and nonlinear partial differential with mathematics? equations and their application to complex Nirenberg: I always analysis and geometry. liked mathematics in He was born on February 28, 1925, in Hamil- school. My father was a ton, Ontario, Canada. After receiving his bach- Hebrew teacher, and he elor’s degree from McGill University in 1945, he wanted me to learn He- went to New York University as a graduate stu- brew. But I foolishly re- dent, obtaining his M.S. in 1947 and his Ph.D. sisted. I went to He- in 1949, under the direction of James Stoker. brew school for a Nirenberg then joined the faculty of NYU and while, and that didn’t was an original member of the Courant Institute take, and he tried to of Mathematical Sciences. After spending his give me lessons, but entire academic career at Courant, he retired in that didn’t take either. 1999. Then a friend of his Nirenberg received the AMS Bôcher Prize in gave me private lessons, and that man 1959 for his work on partial differential equa- Louis Nirenberg tions. In 1982 he was the first recipient in math- liked mathematical ematics of the Crafoord Prize, established by the puzzles. So half of the Royal Swedish Academy of Sciences in areas not so-called Hebrew lessons were spent on mathe- covered by the Nobel Prizes. In 1995 he received matical puzzles. the National Medal of Science, the United States’ I went to a very good high school in Montreal highest honor for contributions to science. called Baron Byng High School. It was full of bright The following is the edited text of an inter- students. It was during the Depression, and to be view with Nirenberg, conducted on December 8, a high school teacher was considered a very good 2001, by Notices senior writer and deputy edi- job, so there were good teachers who were very de- tor Allyn Jackson. The assistance of Dieter voted. I especially liked the physics teacher, who Kotschick, Ludwig-Maximilians-Universität actually had a Ph.D. in physics. His courses made München, is gratefully acknowledged. me think that I might want to be a physicist. I —A. J. didn’t even know that there was such a career as “mathematician”. I knew you could be a math teacher, but I didn’t know you could be a mathe- matician. When I finished high school, I decided I would Allyn Jackson is senior writer and deputy editor of the do mathematics and physics. At that time one Notices. Her e-mail address is [email protected]. could do a major in both, which I did at McGill APRIL 2002 NOTICES OF THE AMS 441 University. I gradu- Nirenberg: I remember him very well. He was a ated in 1945, just complicated man; he isn’t easy to summarize. He when the war was enormously intelligent and terrific with young ended. people. He loved to be with young people and was Notices: How was very encouraging. As a teacher he was good when the mathematics at he prepared, which was seldom, but I enjoyed his McGill at that time? classes. Very often on the weekend he would invite Nirenberg: The some graduate students to his home, which was in training was pretty New Rochelle. I discovered that one of the reasons good. I guess the was to weed his garden. most prominent Courant was a great lover of music, as was his mathematician whole family. They often played chamber music at there at the time home, and sometimes I attended concerts. The was Gordon Pall, story went that when Courant hired somebody, he who was in number would ask if the person played an instrument. If theory. He was re- so, the person had a better chance of being hired. ally an inspiration But if the instrument was piano—no, because to the students Courant played the piano. Probably the story isn’t around him. But I true, but that was the story at the time. had planned to do Some of the other students were closer to L. Nirenberg at the time of receiving his theoretical physics. Courant than I was. Kurt Friedrichs was a big in- B.Sc. from McGill University, 1945. I’ll tell you the story fluence—I would say the major influence—on me of how I went into in mathematics. His view of mathematics very mathematics. When I graduated, the war had fin- much formed my view. I started with Friedrichs as ished in Europe but was still on in Japan. In Canada, an adviser, and he gave me a problem in operator the science students were not drafted, and that’s theory. I thought about it for a while, but I didn’t why I wasn’t in the armed services. In the summer get anywhere. Some months later Jim Stoker sug- of 1945, I got a job at the National Research Coun- gested a problem in geometry. Stoker was my cil of Canada in Montreal. They were working on official adviser, and he was a very kind man. But I atomic bomb research. Richard Courant’s older actually talked more with Friedrichs than I did with son was there, Ernst Courant. Ernst had recently Stoker during the time I was working on the thesis. married a girl from Montreal whom I knew, and she So I was really closer to Friedrichs. was working there too. One day she said, “We’re Notices: What was Friedrichs’s view of mathe- going down to New York for the weekend, to see matics that influenced you? Ernst’s father.” I had read part of Courant-Hilbert, Nirenberg: I’d have trouble saying. When you so I knew about Courant. I said, “Could you ask him were trying to resolve something, it didn’t matter to recommend a place where I might study theo- so much whether you would prove it was true or retical physics?” I knew nothing about where to false. The thing was to understand the problem. apply or what to do. She came back and said she’d Also, Friedrichs was a great lover of inequalities, talked to Courant about me, and he had suggested and that affected me very much. The point of view I get a master’s in mathematics at New York Uni- was that the inequalities are more interesting than versity, where he was, and then maybe go on to do the equalities, the identities. I also liked the things physics. So I went down for an interview, and I met he did in partial differential equations, which I fol- him and Friedrichs. They were very kind and offered lowed very closely. But he did other things, in quan- me an assistantship. Then I stayed in mathemat- tum theory, operator theory, shock wave theory. ics. When I was a graduate student, I felt that what Notices: Was it the Courant Institute at that time? Friedrichs was doing was where the action was. So Nirenberg: No, it was just the Graduate I went to him to do a thesis, but in the end I didn’t Mathematics Department of New York University. do the thesis with him. The department was tiny, but there were several very Notices: What was the problem you worked on good fellow students. Some of us who got Ph.D.’s in your thesis? there stayed, like Harold Grad, Joe Keller, Peter Nirenberg: It was a problem that Hermann Weyl Lax, and Cathleen Morawetz. Peter Lax’s wife, Anneli, had worked on, a problem in geometry. Weyl had was a student there when I arrived. She was the first solved it partly, and what I did was complete the person I met when I came there as a student. It was proof. Hans Lewy solved it in the analytic case. a remarkable group of people. You’re given a Riemannian metric on the 2-sphere, having positive Gauss curvature, and the question Richard Courant, A Complicated Man is, can you embed this 2-sphere isometrically into Notices: What are your impressions of Courant? 3-space as a convex surface? Weyl worked on it, 442 NOTICES OF THE AMS VOLUME 49, NUMBER 4 around 1916 I think, and had made some crucial Shou Lin. He also estimates. One needed some more estimates before worked on the one could finish the problem. What I did was to get case where the the additional estimates, essentially using ideas curvature is non- of C. B. Morrey. Morrey’s work was a very big in- negative but fluence on me, and later I got to know him. He was might have a zero. a very nice man. He didn’t have many joint papers, Other people have but we did write one paper together. Morrey un- worked on this derstood a lot of things, but he was hard to un- too. derstand. I remember a story I heard. He ran a Notices: Going seminar every year at Berkeley. One year, the back to Morrey, semester started, and the seminar met for the what did he work New York City, ca. 1953. Left to right: K. O. first time. He said, “Well, I’ll use the same notation on? Friedrichs, J. Stoker, M. Nagumo, F. John, as last year.” Nirenberg: L. Nirenberg. Notices: So if you weren’t in the seminar last One of his famous year, too bad? papers, which he Nirenberg: You’d have to catch up.