Remembering Atle Selberg, 1917–2007 Dennis Hejhal, Coordinating Editor* n August 6, 2007, Atle Selberg, one of the pre-eminent mathematicians of the twentieth century, passed away at his home in Princeton, NJ, at the age of ninety. OBorn in Langesund, Norway, on June 14, 1917, Atle Selberg was the youngest of nine children in an academic family (his father held a doctorate in mathematics, and two of his brothers, Henrik and Sigmund, also became mathematics professors). He grew up near Bergen and then studied at the University of Oslo, earning his doctorate there in October 1943, a few weeks prior to the university © C. J. Mozzochi., Ph.D., Princeton, NJ. being closed by German military authorities. Fol- Atle Selberg at Columbia University, 1998. lowing a five-year research fellowship and encour- aged by Carl L. Siegel, in 1947 (the newly married) During the course of his career—a career span- Selberg moved to the U.S. and the Institute for ning more than six decades—he was variously a Advanced Study in Princeton, where he was a masterful problem solver, a creator of powerful member for one year. After spending the 1948–49 and lasting tools, and a gifted theory builder. academic year at Syracuse as associate professor, Depth, elegance, and simplicity of method were Selberg returned to IAS as a permanent member the hallmark of Selberg’s style. and in 1951 was promoted to professor. He retired More detailed recent accounts of Selberg’s life from IAS in 1987 but remained mathematically and work can be found in [3–6]. active for at least another decade. Curiously, in a 1989 interview [2], after first Noted for his profound contributions to number reminiscing how theory, discrete groups, and automorphic forms, the things that Siegel tended to do were Selberg was honored with a Fields Medal in 1950, a usually things that seemed impossible. Wolf Prize in 1986, and a special Abel Bicentennial Also, after they were done, they seemed Anniversary Prize in 2002. still almost impossible… The impact of Selberg’s work can be seen from some of the many mathematical terms that bear and then describing the daunting effect that Sie- his name: the Selberg trace formula, the Selberg gel’s lectures sometimes had on younger people sieve, the Selberg integral, the Selberg eigenvalue at IAS, Selberg went on to say: conjecture, and the Selberg zeta function. Well, I knew of course that I could do Dennis Hejhal, coordinating editor for this article, is pro- other things. I couldn’t do the kind of fessor of mathematics at the University of Minnesota and things that he did. I think the things I Uppsala University, Sweden. His email address is hejhal@ have done, really all of them, are things math.umn.edu. that—although sometimes there were *The advice and technical assistance of Nils A. Baas and technical details, and sometimes even Peter Sarnak are gratefully acknowledged. a lot of calculation, in some of my 692 NOTICES OF THE AMS VOLUME 56, NUMBER 6 early work—the basic ideas were rather We differed in age by only six years, but to simple always, and could be explained call myself a contemporary is a bit misleading, in rather simple terms. I think in some because in 1943 he had published more than ten ways, I probably have a rather simplis- articles and was receiving tic mind, so that these are the only kind his Ph.D. at the University of ideas I can work with. I don’t think of Oslo, while I was a col- that other people have had grave dif- lege undergraduate with no ficulties understanding my work. publications. We both came to the Insti- There was a certain understated (distinctively tute for Advanced Study in Scandinavian) quality in Selberg that could be quite Princeton in mid-September inspiring, particularly for younger mathematicians. of 1947, each of us being Those who got to know him soon came to real- newly wed. I came with my ize something else. Blessed with an impressive wife, Evelyn; his wife, Hed- memory, Selberg was generally able—even during vig, was delayed for several his seventies and beyond—to reconstruct with weeks because of immigra- minimal need for “any faded old notes” the essen- tion formalities. tial details of proofs that he had worked out years, I first heard of Atle Sel- if not decades, earlier.1 There was an ongoing vital- berg from one of my col- ity not only in Selberg’s ideas but also in the man. leagues at Fine Hall, where I What follows are some recollections of Atle had an office. My officemate Selberg by mathematicians from a number of spoke of Selberg with such generations. Together with the interview in [1], it awe that I can still remem- ber his exact words, uttered is hoped that they can give the reader a glimpse of Selberg in 1935, shortly in hushed tones, to this the remarkable person that Atle Selberg truly was. before graduation from Gjøvik day: “There came out of the Gymnasium. References North a star who lit up for [1] N. Baas and C. F. Skau, The lord of the numbers, the first time a large piece Atle Selberg: On his life and mathematics, Bull. Amer. of the Riemann Conjecture.” Math. Soc. 45 (2008), 617–649. See also the extended That mythic aura persisted version in Normat 56 (2008), as well as at www.math. throughout his career. ntnu.no/Selberg-interview/. As it turned out, Atle be- B. Devine [2] , Interview with Atle Selberg, unpublished, came my neighbor. Evelyn IAS Archives, 1989, 57 pp. and I were housed in one of [3] R. Heath-Brown, Obituary: Atle Selberg, The Guard- the two apartments in the ian, 25 September 2007, p. 41. converted carriage house [4] D. Hejhal and P. Sarnak, Some commentary on Atle Selberg’s mathematics, Bull. Amer. Math. Soc. 45 of Maxwell Manor; Hedi (2008), 485–487. and Atle occupied the other [5] In Memoriam: Atle Selberg, The Institute Letter, IAS, apartment. Fall 2007, pp. 6–7, and Summer 2008, p. 10. (See As is customary in Nor- http://www.ias.edu/about/publications/) The way, Atle was reserved with IAS website also contains streaming videos from the strangers. There was a sin- Selberg Memorial (at: video.ias.edu/). gle narrow footpath leading [6] Norsk Biografisk Leksikon, vol. 8, Kunnskapsforlaget, from Fuld Hall to our build- Oslo, 2004, p. 161 ff. (See also the 1958 edition, vol. ing. Before Hedi’s arrival in 13, H. Aschehoug, Oslo, p. 195 ff.) the U.S., Atle would avert his eyes as our paths crossed. From a 1949 rotogravure section G. D. Mostow Hedi’s ebullience changed of a Norwegian newspaper, in an article on his elementary proof of Atle Selberg was a mathematician whose accom- all that, and we gradually the prime number theorem. plishments will be admired throughout the ages. became good friends. Having enjoyed his friendship for nearly sixty In one conversation Atle years, I would like to describe how he was seen by even poked fun at Norwegian reserve, telling the his contemporaries. following anecdote. He was walking along the main street of Oslo when he encountered a cousin who 1One senses that the relative paucity of detailed working stopped to talk to him. As they were conversing, notes found either at home or in his office after his death the cousin’s twin brother passed by. The twins (and linked, e.g., to specific results in lectures or published acknowledged each other with only the tip of a hat. papers) is at least partially reflective of this fact. Atle asked his cousin, “Do you see your brother G. D. Mostow is professor emeritus of mathematics at Yale frequently?” The cousin replied, “We haven’t seen University. His email address is [email protected]. each other for a year.” JUNE/JULY 2009 NOTICES OF THE AMS 693 At that time, the Fuld Hall Common Room could discussing math, I would always come hold all of the Institute members. After the daily back home feeling so inspired to work! tea the members of the School of Mathematics I was twenty-six years old then. It’s would often linger in the Common Room to talk strange…but even thirty-some years shop and gossip. Among the Institute members, later, whenever Atle and I discussed Atle had the reputation of answering questions math, he still had that same effect on on number theory immediately or, if he could not me. I’ll miss that. answer fully, he invariably got to the core of the problem at once. Atle was for me not only a wonderful mathemat- His self-confidence was enviable. That may have ical colleague and mentor, but also a dear friend. been genetic, as the following story suggests. One There was a kind of synergy in our interactions, day early in the summer of 1949, one of Atle’s a kind of eclectic give-and-take, that Atle seemed brothers was visiting him in Syracuse. They had to enjoy. In my lines here I’d like to expand on been invited by Arthur Milgram to watch a doubles this a bit. tennis match. Unfortunately, at the last minute I first met Atle early in 1974 after something of one of the four players canceled. Milgram, seeing a zig-zag. As a graduate student at Stanford, I had Atle’s brother getting out of the car, ran over to already heard the name “Atle Selberg” spoken of him and asked anxiously, “Can you play tennis?” with great respect by both George Pólya and Paul The reply, delivered deliberately with a Norwegian Cohen in connection with the zeta-function.