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Celebratio Mathematica

Raoul H. Bott

Stephen Smale

At a con­fer­ence in 1967 Steph­en Smale or­gan­ized a beach hike in which Raoul Bott nearly drowned. Af­ter­wards, Bott some­times joked that Smale tried to kill him. When Bott said Smale was his “worst” stu­dent, it was not in the math­em­at­ic­al sense but in the mor­al sense. Here is Smale’s ver­sion of the event.1

Figure 4. International Symposium on Algebraic Topology, Mexico City, 1956. Front row, from left to right: 1 = William Massey (?), 3 \( = \) Friedrich Hirzebruch (?), 4 \( = \) Hans Samelson, 5 \( = \) Raoul Bott, 6 \( = \) J. H. C. Whitehead. Second row: 5 \( = \) Witold Hurewicz (who was killed a few days later falling off a pyramid), 7 \( = \) Solomon Lefschetz. Third row: 3 \( = \) Morris Hirsch, 7 \( = \) Leopoldo Nachbin. According to Michael Atiyah, since he was not in the photo, he might have been the lecturer.
Bott Family Collection.

Raoul of­ten in­tro­duced me with the words “Steve was my first stu­dent” and then ad­ded with great em­phas­is “and my worst!” He de­scribed our re­la­tion­ship (of­ten tu­mul­tu­ous) in his talk2 at the con­fer­ence for my six­tieth birth­day. Raoul says there, “Steve tried to drown me,” as he de­scribes one of our ex­cur­sions.

It is true that I mis­cal­cu­lated the tim­ing and dangers of an in­com­ing tide at Taylor’s Point on the Olympic Pen­in­sula. It was at a 1967 Bat­telle con­fer­ence in Seattle on gen­er­al re­lativ­ity that I put to­geth­er a group of about a dozen people for a three-day hike, camp­ing along the ocean beach. To­ward the end of the trip we came to (the no­tori­ous) Taylor’s Point and had to make a de­cision. My wife, Clara; daugh­ter, Laura; and a few oth­ers de­cided on a de­tour. I con­vinced the re­mainder, in­clud­ing Raoul; his wife, Phil; his daugh­ter, Ren­ee; Mike Shub, his wife (at that time), Beth; and my son, Nat (ten years old), that my tide cal­cu­la­tions would jus­ti­fy an at­tempt to take the sea route. Suc­cess was at hand when I looked ahead to see Raoul be­ing battered against the cliffs by the heavy sea. He writes in [◊] that he 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!”

Figure 5. Symposium on Differential Topology in Honor of Marston Morse, Institute for Advanced Study, Princeton, April 2–5, 1963. Back row (left to right): Raoul Bott, Barry Mazur, G. A. Hedlund, T. T. Frankel, Stephen Smale, N. H. Kuiper, J. F. Adams, William Browder, J. W. Milnor, M. A. Kervaire. Front row: S.-S. Chern, R. G. Pohrer, Atle Selberg, Marston Morse, Walter Leighton, Morris Hirsch, S. S. Cairns, Hassler Whitney.
Photo: Alan Richards.

Raoul Bott and I were close friends for over five dec­ades. Already in 1953 we would meet for weekly lunches, as I was tak­ing his class in ad­vanced al­geb­ra­ic to­po­logy. I have of­ten spoken of how it was Bott who star­ted me on the road to ser­i­ous math­em­at­ics. He was a great teach­er and a great in­spir­a­tion.

There were some­times di­ver­gences in our ap­proaches to math­em­at­ics as well as di­ver­gences in which fields we worked in. Very early on, Raoul seemed a bit up­set with my work­ing in or­din­ary dif­fer­en­tial equa­tions. That sub­ject was for those who found par­tial dif­fer­en­tial equa­tions too dif­fi­cult. Moreover, at that time Raoul was not too crazy about even p.d.e. In Morse the­ory he pre­ferred us­ing fi­nite-di­men­sion­al ap­prox­im­a­tions, in con­trast to my us­ing in­fin­ite-di­men­sion­al man­i­folds (Pal­ais–Smale).

Figure 6. At the Bombay Airport on the occasion of the Colloquium on Differential Analysis, Tata Institute, Bombay, 1964. Left to right: Mr. Jalihal (Public Relations Officer, Tata), Deane Montgomery, Donald C. Spencer, Georges de Rham, Mrs. Gårding, Lars Gårding, Komaravolu S. Chandrasekharan, Raoul Bott, Michael Atiyah, Mr. Puthran (Registrar, Tata).
Bott Family Collection.

The last ex­ten­ded time we spent to­geth­er was on the oc­ca­sion of his one- to two-month vis­it to the City Uni­versity of Hong Kong at my in­vit­a­tion. He and Phil were still drink­ing mar­tinis with Clara and me after all those years. He was re­do­ing in his own frame­work my joint res­ult with Mike Shub on the num­ber of real zer­os of a sys­tem of poly­no­mi­al equa­tions. Later I saw his writeup with Cliff Taubes.

Liv­ing in the world of Raoul Bott was a won­der­ful part of my life.