Celebratio Mathematica

Raoul H. Bott

Remembering Raoul Bott (1923–2005)

by David Mumford

Dav­id Mum­ford de­scribes Bott’s “job talk” at Har­vard and the trans­form­a­tion in the cul­ture of the Har­vard math­em­at­ics de­part­ment upon Bott’s ar­rival in 1959.1

Figure 7. Raoul Bott and Joseph H. Sampson, Conference on Manifolds, Tokyo, mid-1960s.
Bott Family Collection.

My first en­counter with Raoul was most mem­or­able. I was still a lowly un­der­gradu­ate at Har­vard, though tak­ing some ad­vanced courses. One day in 1958, Raoul came to give the col­loqui­um talk, a weekly af­fair Thursdays at 4:30 in 2 Di­vin­ity Av­en­ue (ro­tat­ing with MIT but not, if I re­call cor­rectly, with Bran­de­is as yet). The stage at 2 Di­vin­ity was on a low plat­form, maybe three feet high with low stairs on each side. After be­ing in­tro­duced, Raoul did what no one else had ever done: he marched dir­ectly onto the stage with a small jump. His en­thu­si­asm was both phys­ic­al and men­tal. He pro­ceeded to mes­mer­ize the as­sembled crew of seni­or pro­fess­ors, first ex­plain­ing Morse the­ory, a brand new tool for the con­ser­vat­ive audi­ence, and then his peri­od­icity the­or­em. Of course I didn’t know it, but it was a job talk — he was com­ing to Har­vard!

Figure 8. Explaining topology on the TV show Science and Engineering Television Journal, c. 1965.
Bott Family Collection.

To put this in con­text, it’s im­port­ant to know what sort of a place Har­vard was at the time. Dave Wid­der and Joe Walsh were the most seni­or and, to­geth­er with Gar­rett Birk­hoff, rep­res­en­ted the tra­di­tion from the 1930s. At a din­ner party with the Walshes, al­though a tuxedo was no longer ex­pec­ted, the wo­men still left the din­ing room after dessert so the men could light their ci­gars and dis­cuss mas­cu­line top­ics. Lars Ahlfors, Richard Brauer, and Oscar Za­r­iski were the European stars who had put the de­part­ment on the map. The young­er gen­er­a­tion was rep­res­en­ted by the three Amer­ic­an func­tion­al ana­lysts: Andy Gleason, George Mackey, and Lynn Loomis. But it was still a very con­ser­vat­ive place run by con­ser­vat­ive gen­tle­men. Fac­ulty wives put on white gloves to serve tea be­fore the col­loqui­um. Saun­ders Mac Lane had left for Chica­go, so his fancy ideas in to­po­logy, co­homo­logy, sheaves, and so on were un­known areas at Har­vard. Semi-simple Lie groups were a dis­tant concept.

Figure 9. Lecturing at Universität Bonn, 1969.
Bott Family Collection.

Enter Raoul. He was not a breath of fresh air; he was a gale — not merely the new and won­der­ful math­em­at­ic­al top­ics that he brought in his tool kit, but his spark, his en­ergy, his fear­less­ness. You know how uni­ver­sal it is to re­frain from ask­ing what you fear may be a stu­pid ques­tion when a sem­in­ar speak­er be­gins to lose you? Not Raoul! He reg­u­larly raised his hand and asked that “stu­pid ques­tion”, half know­ing the an­swer but want­ing to slow down the speak­er, hear it again, and bring the rest of us in­to the circle of mu­tu­al ap­pre­ci­ation present in the best sem­inars. Be­ing ashamed not to know something ba­sic was com­pletely ali­en to his tem­pera­ment.

Figure 10. Raoul Bott and David Mumford in the early 1970s.
Photo from David Mumford.

And then there were the “col­loqui­um parties”. I think these be­came a reg­u­lar fix­ture in the 1960s: every Thursday the speak­er’s host in­vited a large part of the Bo­ston re­search com­munity and their spouses to a party. Here were these clusters, typ­ic­ally the guys talk­ing math and their wives talk­ing about their fam­il­ies (there were no wo­men on the fac­ulty then). Raoul of­ten came a bit late and would raise his voice and say something like, “What’s go­ing on here? Is this a party?” or iron­ic­ally, “Is this Har­vard?” He wanted mu­sic and of­ten got Tom Lehr­er to play and even sing by the end of the even­ing.

Raoul taught me many things about both math­em­at­ics and life. I know no one who didn’t feel a lift, a rush when he came in­to the room. He was not merely large in stature but, more than that, large in spir­it. We miss him im­mensely.