Remembering Raoul Bott (1923–2005) Loring W. Tu, Coordinating Editor With contributions from Rodolfo Gurdian, Stephen Smale, David Mumford, Arthur Jaffe, Shing-Tung Yau, and Loring W. Tu Raoul Bott passed away The contributions are listed in the order in on December 20, 2005. which the contributors first met Raoul Bott. As Over a five-decade career the coordinating editor, I have added a short he made many profound introductory paragraph (in italics) to the beginning and fundamental contri- of each contribution. —Loring Tu butions to geometry and topology. This is the sec- Rodolfo Gurdian ond part of a two-part article in the Notices to Rodolfo Gurdian was one of Raoul Bott’s room- commemorate his life and mates when they were undergraduates at McGill. work. The first part was The imaginary chicken-stealing incident in this arti- an authorized biography, cle is a reference to a real chicken leg incident they “The life and works of experienced together at Mont Tremblant, recounted Raoul Bott” [4], which in [4]. he read and approved What follows is an account of some of the mischief a few years before his that Raoul Bott and I carried out during our days Photo by Bachrach. at McGill. Figure 1. Raoul Bott in 2002. death. Since then there have been at least three I met Raoul in 1941, when we were in our volumes containing remembrances of Raoul Bott first year at McGill University. Both of us lived in by his erstwhile collaborators, colleagues, students, Douglas Hall, a student dormitory of the university, and friends [1], [2], [7]. I have also written elsewhere but we were in different apartments. He paid about my experiences working with him [5]. This attention to me because I got a higher grade in second part presents some personal recollections trigonometry. He also noticed that I played the that do not overlap with what has already appeared guitar, and I appreciated his piano playing. in print. More reminiscences and appreciations The following year we shared an apartment, to- of his work may be found in the upcoming final gether with Frazer Farlinger, a student in medicine. volume of the Collected Papers of Raoul Bott [6]. Raoul majored in electrical engineering and I in Bott had a passion for mathematics, which he chemical engineering. The difference among us kept to the very end, even after his retirement from was that Frazer and I had to study very hard, while Harvard. At the same time, he was firmly planted Raoul didn’t. He used to say that attending the in the real world. As many of his acquaintances lectures was sufficient for him, since electrical would agree, he exemplified the French phrase joie engineering was a very logical subject. His marks de vivre. His mathematical work speaks for itself, were satisfactory but could have been much better but it is hoped that the following reminiscences if he had only worked harder. can give some idea of his personality, his zest for I met Oskar and Celia Pfeffer, his charming life, and his humanity. stepparents. Realizing that they were not very well off, I called Raoul’s attention to the fact that, being Loring W. Tu is professor of mathematics at Tufts University. His email address is [email protected]. Rodolfo Gurdian, who has since passed away, wrote this DOI: http://dx.doi.org/10.1090/noti977 piece around the year 2000 and Raoul Bott read it. 398 Notices of the AMS Volume 60, Number 4 so talented in mathematics, he could easily obtain shout back, “Of course, I a scholarship by studying just a little more. I think recognize you,” and would I influenced him, because he improved his grades shoot him dead anyway. and became one of the best students in the class. One reason we became In his last years at McGill, I believe he did obtain a good friends might have scholarship. been that, during our Rooming together, we became close friends. We childhood, we both en- loved to make mischief. On Saturdays we used to gaged in similar mischief. go to the movies, often to a theater called The Moreover, Latin Ameri- System. Buying just one ticket, we could watch cans may have more in three movies in a row. Although the ticket price was common with Europeans low, both of us being broke, we found a “system” than with North Amer- to sneak into The System without paying by taking icans. So we enjoyed advantage of the fact that only one person was in making pranks together. charge of the theater’s two entrances. One of the entrances gave access to the upper floor through a Stephen Smale wooden staircase, and the other went to the first At a conference in 1967 floor. The trick we devised was for one of us to talk Stephen Smale orga- to the ticket clerk, while the other would distract nized a beach hike in him by running upstairs and making a lot of noise. which Raoul Bott nearly As the ticket clerk followed the noisemaker, the drowned. Afterwards, Bott Figure 2. Raoul Bott (left) in the other one took advantage of the situation to sneak sometimes joked that 1930s. into the theater’s first floor. Of course, once we Smale tried to kill him. were in, it was difficult for the ticket clerk to find us, When Bott said Smale was because we sat in the first available seats, feigning his “worst” student, it was to be regular customers. not in the mathematical During the summer months every engineering sense but in the moral student was required to work to get some practical sense. Here is Smale’s ver- experience. Since Douglas Hall was closed for sion of the event. the summer, we rented a room together near the university. Raoul was six foot two, and I just Raoul often introduced me under five foot six. So you can imagine what a with the words “Steve was strange-looking pair we made! One summer Sunday my first student” and then we decided on a prank. Raoul put on his gray and added with great empha- red bathrobe and a turban and armed himself with sis “and my worst!” He a small dagger. I put on my red short pants and described our relationship (often tumultuous) in his a green T-shirt and carried a tambourine. When 1 Raoul went out to the street, I followed, playing talk at the conference for the tambourine and dancing in circles around him. my sixtieth birthday. Raoul says there, “Steve tried to People in the street were shocked. Suddenly, Raoul Figure 3. Rodolfo Gurdian and drown me,” as he describes approached an old lady and threatened her with Raoul Bott as undergraduates at one of our excursions. the dagger. When she started screaming, we ran McGill, c. 1942. like hell, realizing that the joke and the fun were It is true that I mis- getting out of hand. calculated the timing and We used to talk about our future careers. I dangers of an incoming tide at Taylor’s Point on told him that, due to my facility with money, I the Olympic Peninsula. It was at a 1967 Battelle would dedicate myself to business, which, in fact, conference in Seattle on general relativity that I I successfully achieved in life. He joked that, since put together a group of about a dozen people I would become a wealthy man while he, as a for a three-day hike, camping along the ocean professor, would be very poor, eventually he would beach. Toward the end of the trip we came to be forced to come to Costa Rica to seek my help. (the notorious) Taylor’s Point and had to make Our first meeting would be in the backyard of my a decision. My wife, Clara; daughter, Laura; and house, where he, out of hunger, would be stealing a few others decided on a detour. I convinced my chickens. Finding a thief in my backyard, I the remainder, including Raoul; his wife, Phil; his would come out with a gun. Upon seeing me, Raoul Stephen Smale is professor emeritus of mathematics at would shout, “Please, Rodolfo, don’t shoot. It’s me, the University of California, Berkeley. His email address is Raoul, your old friend.” By that time, I would have [email protected]. become an insensitive wealthy man, so I would 1The Collected Papers of Stephen Smale, Vol. 1, p. 8. April 2013 Notices of the AMS 399 Figure 6. At the Bombay Airport on the occasion Figure 4. International Symposium on Algebraic of the Colloquium on Differential Analysis, Tata Topology, Mexico City, 1956. Front row, from left Institute, Bombay, 1964. Left to right: Mr. Jalihal to right: 1 = William Massey (?), 3 = Friedrich (Public Relations Officer, Tata), Deane Hirzebruch (?), 4 = Hans Samelson, 5 = Raoul Bott, Montgomery, Donald C. Spencer, Georges de 6 = J. H. C. Whitehead. Second row: 5 = Witold Rham, Mrs. Gårding, Lars Gårding, Komaravolu S. Hurewicz (who was killed a few days later falling Chandrasekharan, Raoul Bott, Michael Atiyah, Mr. off a pyramid), 7 = Solomon Lefschetz. Third row: Puthran (Registrar, Tata). 3 = Morris Hirsch, 7 = Leopoldo Nachbin. According to Michael Atiyah, since he was not in the photo, he might have been the lecturer. was thinking, “This is how one drowns.” In fact, we all survived (my backpack was lost to the seas). Raoul also writes that, after an excursion with me, he often got on his knees to give thanks: “Back home again and still alive!” Raoul Bott and I were close friends for over five decades.