Celebratio Mathematica

Raoul H. Bott

Arthur Jaffe

Ar­thur Jaffe, pres­id­ent of the Amer­ic­an Math­em­at­ic­al So­ci­ety from 1997 to 1998, re­min­isces about his forty-year re­la­tion­ship with Raoul Bott as col­league, friend, and con­fid­ant.1

Figure 11. Freeman Dyson, Raoul Bott, and Valentine Bargmann on the occasion of the Oppenheimer Memorial, Institute for Advanced Study, 1971.
Photographer unknown (from the Shelby White and Leon Levy Archives Center, Institute for Advanced Study, Princeton, New Jersey).

I first en­countered Raoul Bott in 1964. While a stu­dent in Prin­ceton I came across the beau­ti­ful Bott–May­berry pa­per on matrices and graphs and used their rep­res­ent­a­tion of a de­term­in­ant in ana­lyz­ing a prob­lem in quantum the­ory. But that ex­per­i­ence did little to pre­pare me for our first face-to-face meet­ing. Raoul’s per­son­al­ity and spir­it struck me with awe; it left an in­delible mark in my memory.

Later we be­came col­leagues, and it was then that Raoul evolved in­to a very spe­cial and dear friend. We shared many math­em­at­ic­al dis­cus­sions to­geth­er. We also spent hours talk­ing about the world, laugh­ing over an amus­ing story, listen­ing to mu­sic, or shar­ing a meal with a good wine.

Raoul had al­ways had an in­terest in phys­ics, but that had some un­usu­al twists. For ex­ample, when Raoul learned of nor­mal or­der­ing (a simple form of renor­mal­iz­a­tion), he used to ask me if it could have something to do with the res­ol­u­tion of sin­gu­lar­it­ies in al­geb­ra­ic geo­metry, still an in­triguing ques­tion.

Figure 12. Michael Atiyah and Raoul Bott at Stonehenge in the early 1970s.
Bott Family Collection.

Raoul de­scribed dis­cus­sions he had with his neigh­bor Chen Ning Yang dur­ing 1955–57 at the time Raoul was a vis­it­or at the In­sti­tute for Ad­vanced Study. While they dis­cussed many things, con­nec­tions were not on the agenda. Only later did one real­ize their cent­ral role in Yang–Mills the­ory. In the late 1970s we had a long dis­cus­sion while driv­ing to­geth­er from Cam­bridge to an AMS sum­mer meet­ing in Provid­ence about how im­port­ant it was to have a good dic­tion­ary to trans­late between gauge the­ory as phys­ics and dif­fer­en­tial geo­metry as math­em­at­ics in or­der for people in the two sub­jects to com­mu­nic­ate.

While I had first met Raoul in a math­em­at­ics con­fer­ence be­fore I came to Har­vard in 1967, I really got to know Raoul well dur­ing the Les Houches sum­mer school in 1970. Cécile DeWitt had es­tab­lished a fam­ous sum­mer school of the­or­et­ic­al phys­ics after World War II; it was loc­ated in a small French vil­lage in the Alps, not far from Mont Blanc. The only prob­lem about try­ing to work in Les Houches was the dis­trac­tion of a strik­ing view of the Ai­guille du Midi. In 1970 the fo­cus of the school was math­em­at­ic­al quantum field the­ory. Raoul was of­fi­cially an “ob­serv­er” at the school, sent by the Bat­telle In­sti­tute, which sponsored the event.

Cécile had an in­ter­est­ing philo­sophy about Les Houches: in or­der to max­im­ize in­ter­ac­tion, the par­ti­cipants at Les Houches should come at the be­gin­ning of the meet­ing and re­main there un­til the end. And this school las­ted two full months! Both in the lec­tures and at the meals in the large din­ing room, the par­ti­cipants in­ter­ac­ted like a large fam­ily for sixty days. Raoul brought his wife, Phyl­lis, and their three young girls, and their son, Tony, also vis­ited on oc­ca­sion. So, over the course of that sum­mer, I really got to know the Botts. In fact, George and Alice Mackey and their daugh­ter, Ann, were there too, so there was a big con­tin­gent from Har­vard.

Figure 13. Raoul Bott with Henri Cartan — Bott modeling Cartan’s birthday gift T-shirt — at the seventieth birthday fête for Cartan, I.H.E.S., Bures-sur-Yvette, France, 1974.
Photo: Carol Tate.

After re­turn­ing to Cam­bridge that fall, I began a math­em­at­ic­al phys­ics sem­in­ar at which Raoul be­came a reg­u­lar at­tendee. Sev­er­al of the stu­dents from Les Houches also came to Har­vard. Raoul en­joyed them all but be­came es­pe­cially fond of Kon­rad Os­ter­walder, who even­tu­ally spent six years in Cam­bridge and be­came one of Raoul’s reg­u­lar con­fid­ants be­fore he left for the E.T.H. Zürich.

In 1976 I helped a friend in Par­is or­gan­ize a sum­mer school in Cargèse, Cor­sica, where I had been dur­ing the sum­mer of 1964. The ex­per­i­ence left me with a last­ing im­pres­sion of the beauty and his­tory of this Greek-French vil­lage by the Medi­ter­ranean Sea. The suc­cess of the res­ult­ing gath­er­ing led to our hav­ing five more schools in Cargèse. The second school in 1979 brought to­geth­er an in­ter­est­ing group of math­em­aticians and phys­i­cists, in­clud­ing Raoul, Mi­chael Atiyah, Jürg Fröhlich, Jim Glimm, Ger­ard ’t Hooft, Harry Lehmann, Is­ad­ore Sing­er, Kurt Sy­man­zik, Ken Wilson, Ed­ward Wit­ten, and Jean Zinn-Justin. The ac­com­pa­ny­ing pho­to­graphs (Fig­ures 16 and 17) show that Raoul was in good form in the school: not only did he give beau­ti­ful lec­tures but he an­im­ated less form­al mo­ments. The com­bin­a­tion of the pro­duct­ive and in­ter­act­ive sci­entif­ic at­mo­sphere, along with an in­vit­ing beach, brought Raoul and Phyl­lis back to Cargèse in 1987 and 1991.

Ori­gin­ally I had been ap­poin­ted pro­fess­or of phys­ics at Har­vard, al­though some of my courses were cross-lis­ted in math­em­at­ics. But in the spring of 1975 the math­em­at­ics de­part­ment in­vited me to be­come a mem­ber. Raoul was chair­man at the time, and I re­call the pleas­ure with which he de­scribed to me that vote. Raoul also en­livened the en­su­ing fac­ulty meet­ings fol­low­ing Thursday lunch at the Fac­ulty Club. Un­til some­time in the 1980s, the de­part­ment de­cided on teach­ing as­sign­ments in an old-fash­ioned way: dis­cuss this at a fac­ulty meet­ing, which al­ways seemed to have full at­tend­ance! The chair wrote on the board a list of ne­ces­sary courses; the per­sons present filled in their names in or­der of seni­or­ity in the de­part­ment. This gave the more seni­or mem­bers of the de­part­ment an el­ev­ated status, in which Raoul amusedly reveled.

Figure 14. Israel M. Gelfand, Robert MacPherson, Raoul Bott, and David Kazhdan at Bott’s home in Newton, Massachusetts, 1976.
Photo: Carol Tate.

In 1978 Raoul and Phyl­lis be­came Mas­ters of Dun­ster House. I had been a happy mem­ber of Low­ell House ever since some stu­dents brought me there dur­ing my first year at Har­vard. But Raoul asked me to switch and be with him at Dun­ster, which I even­tu­ally did. I brought along a few of my own col­lab­or­at­ors, and I have many fond memor­ies of even­ings with friends at Dun­ster: with stu­dents and with sci­entif­ic col­leagues in the din­ing hall, with mem­bers of the “Seni­or Com­mon Room” at their reg­u­lar meet­ings, at the Dun­ster con­certs, at the Red Tie din­ners, and dur­ing many oth­er oc­ca­sions in the mas­ter’s res­id­ence with Raoul and Phyl­lis. Raoul some­times had his math­em­at­ic­al friends stay in Dun­ster, such as Fritz Hirzebruch or Mi­chael Atiyah, and he would en­joy let­ting us know when some math­em­atician friend of his might be mak­ing an un­an­nounced vis­it to Cam­bridge.

Figure 15. Raoul Bott as a pirate king, Phyllis Bott as a maiden, and two students impersonating Phyllis and Raoul at a Dunster House Halloween party, late 1970s.
Bott Family Collection.

With our fre­quent in­ter­sec­tion at Dun­ster House, we of­ten made plans to do things to­geth­er. We both en­joyed mu­sic and of­ten had met at un­der­gradu­ate con­certs. I re­call our dis­cuss­ing the con­cert at Sanders Theat­er when Yo-Yo Ma’s un­der­gradu­ate quar­tet played Brahms. I went with Raoul to the first per­form­ance that the Tal­lis Schol­ars sang in Bo­ston in a con­cert at the Church of the Ad­vent. Much after that, I sat with Raoul in his mu­sic room in his apart­ment on Rich­dale Av­en­ue while he played Bach on his Stein­way. Later in that room we dis­cussed the dif­fer­ences between re­cord­ings of the Gold­berg Vari­ations made by Glenn Gould and An­drás Schiff. (An­drás is an­oth­er geni­us from Hun­gary whom I ad­mire. I have also come to know him as a friend, and I wish that I could have in­tro­duced Raoul and An­drás to each oth­er, for they cer­tainly would have hit it off well.)

Raoul did not al­ways re­mem­ber the sem­in­ar sched­ule, so he en­joyed hav­ing his of­fice across from the main sem­in­ar room in the de­part­ment. One felt in the middle of things with people passing by, and with the glass win­dow along the hall cor­ridor, one could al­ways see at a glance what sem­inars were tak­ing place.

Figure 16. Michael Atiyah and Raoul Bott looking at a colony of ants in Cargèse, Corsica, July 1979.
Photo: Arthur Jaffe.

Raoul could turn up at the most un­usu­al time or place. When I mar­ried in 1992, Raoul was an ush­er in the wed­ding. I re­call how proud he was to es­cort my daugh­ter, Mar­garet. And I was not sur­prised in the sum­mer of 2002 to ar­rive at the air­port in Vi­enna and find Raoul and his grand­daugh­ter, Vanessa Scott, there too. They were on their way to make a film about Raoul’s life, a won­der­ful story I saw in 2006.

Raoul’s life turned up­side down when Phyl­lis had a stroke. He began to spend every day with his Mac com­puter at Youville Hos­pit­al in Cam­bridge, where Phyl­lis was re­cu­per­at­ing. For a while George Mackey was nearby in the same hos­pit­al. Dur­ing those days Raoul of­ten came to my home for din­ner. We sat around the kit­chen table over sword­fish or blue­fish from the broil­er. The con­ver­sa­tion some­times turned to mu­sic. Raoul ad­mired the vir­tu­os­ity of my harp­ist friend, Ur­sula. Many people re­garded Raoul as a fath­er fig­ure, but Ur­sula was drawn to him for the em­pathy he ex­pressed for oth­ers in need of as­sist­ance and for his un­der­stand­ing of the prob­lems of the world. Raoul ex­plained that life would be much easi­er for him and Phyl­lis in Cali­for­nia rather than in their multistory town­house. In Cam­bridge many friends were sad to see them go.

Figure 17. Left to right: Raoul Bott, John Imbrie (in white shirt, face partially hidden), Michael Atiyah, and Konrad Osterwalder at a summer school on mathematical physics in Cargèse, Corsica, July 1979.
Photo: Arthur Jaffe.

The math­em­at­ics de­part­ment held a din­ner in the Fac­ulty Club the night be­fore Raoul and Phyl­lis left Cam­bridge. After most oth­er per­sons went home that even­ing, I gave Raoul a bottle of ex­cel­lent Bor­deaux. Oc­ca­sion­ally I spoke with Raoul by tele­phone, a nice link between Cam­bridge and Carls­bad, Cali­for­nia. It was won­der­ful to hear his voice and to get some news. Dur­ing one of those con­ver­sa­tions late in 2005, Raoul let me know that he had left that bottle of Bor­deaux with his daugh­ter Can­dace in Cam­bridge. She was bring­ing it to Cali­for­nia the next day so he could share it dur­ing a small fam­ily re­union. At the time I did not real­ize how Raoul was telling me that his end was upon him. Shortly af­ter­ward I cried at the news.