Bott's lectures are legendary for their seeming ease of comprehension. His style is typically the antithesis of the Definition-Theorem-Proof approach so favored among mathematical speakers. Usually he likes to discuss a simple key example that encapsulates the essence of the problem. Often, as if by magic, a concrete formula with transparent significance appears.

At a reception for new graduate students at Harvard, he once shared his view of the process of writing a Ph.D. thesis. He said it is like doing a homework problem; it's just a harder problem. You try to understand the problem thoroughly, from every conceivable angle. Much of the thesis work is perseverance, as opposed to inspiration. Above all, ``make the problem your own.''

Many of his students testify to his warmth and humanity, but he also expects the students to meet an exacting standard. He once banned the word ``basically'' from an advisee's vocabulary, because that word to Bott signifies that some details are about to be swept under a rug.

This insistence on thoroughness and clarity applies to his own work as well. I. M. Singer remarked that in their younger days, whenever they had a mathematical discussion, the most common phrase Bott uttered was ``I don't understand,'' and that a few months later Bott would emerge with a beautiful paper on precisely the subject he had repeatedly not understood.

Seminar speakers at Harvard tend to address themselves to the experts in the audience. But like Steenrod, Bott often interrupts the speakers with the most basic questions, with the salutary effect of slowing down the speakers and making them more intelligible to lesser mortals.

At Michigan and Harvard, Bott directed over 36 Ph.D. theses. Some of his students have become luminaries in their own right: Stephen Smale and Daniel Quillen received the Fields Medal in 1966 and 1978 respectively, and Robert MacPherson the National Academy of Science Award in Mathematics in 1992. The following is, I hope, the complete list of his Ph.D. students:

YearPh.D. StudentDissertation Title

1957 Smale, Stephen

1961 Edwards, Harold

Curtis, Edward

1963 Conlon, Lawrence

Zilber, Joseph Abraham

1964 Holzsager, Richard Allan

Quillen, Daniel

1965 Landweber, Peter S.

Lazarov, Connor

1969 Brooks, Morris William

Brown, Richard Lawrence

1970 Blass, Andreas R. Orderings of Ultrafilters

MacPherson, Robert D.

1973 Miller, Edward Y.

1974 Garberson, John Dayton

1975 Mostow, Mark

Perchik, James

1976 Weiss, Richard Simon

1977 Brooks, Robert

1981 Hingston, Nancy

1982 Gunther, Nicholas

Laquer, Turner Henry

1984 Ticciati, Robin

1985 Forman, Robin

1986 Corlette, Kevin

1987 Block, Jonathan

1989 Kocherlakota, Rama

Morelli, Robert

Bressler, Paul

1991 Grossberg, Michael

1992 Weinstein, Eric

Szenes, Andras

1993 Tolman, Susan

1994 Teleman, Constantine

Costes, Constantine

2000 Bernhard, James