Initially Bott wanted to stay at McGill to do a mathematics Ph.D. Because of his sketchy background, however, the McGill Math Department recommended that he pursue a Bachelor's degree in mathematics first. It would have taken another three years. Sensing his disappointment, Professor Williams of McGill then suggested Carnegie Tech (now Carnegie-Mellon University) to Bott, where John Synge was just forming a new graduate program and would need some students.
Synge received Bott warmly at Carnegie Tech, but as they read the rules of the program together, they found that Bott would have to spend three years taking courses in the newly minted master's program. In a flash of inspiration, Synge said, ``Let's look at the Ph.D. program.'' It turned out to have hardly any requirements at all! Normally the master's program is a prerequisite to the Ph.D. program, but perhaps recognizing a special gift in Bott, Synge put him in the Ph.D. program. In just two years Bott would walk out with his degree.
Bott found the Carnegie Tech atmosphere exceedingly supportive. The small coterie of mathematics students included Hans Weinberger, now at the University of Minnesota, and John Nash, an advanced undergraduate who after a thirty-year battle with schizophrenia received the Nobel prize in 1994. In later years Bott said of Carnegie Tech, ``Being a brand new graduate program, they hadn't learned yet how to put hurdles in front of graduate students.'' Bott considers himself very fortunate to have an advisor in R. J. Duffin, for Duffin treated him as an equal from the very outset and together they published two papers on the mathematics of electrical networks.
The first of these two papers, on impedance functions , so impressed Hermann Weyl that he invited Bott to the Institute for Advanced Study in 1949. Thus began Bott's initiation into the mysteries of algebraic topology. Apart from Weyl, among his main teachers were N. Steenrod, E. Specker, K. Reidemeister, and M. Morse. Of Ernst Specker, Bott said in [B2], ``I bombarded Ernst with so many stupid questions that in desperation he finally imposed a fine of 25 cents on any conjecture he could disprove in less than five minutes. This should give you some idea of the inflation of the past thirty years and also help to explain Ernst's vast fortune at this time.''
At the time Norman Steenrod was writing his classic book on the topology of fiber bundles and teaching a course based on it. This course greatly influenced Bott's mathematical development.
Bott describes Steenrod with admiration as someone who treated high and low alike, with equal respect. At Princeton, the graduate students could be intimidating, because they knew so much, and they let you know it. Steenrod, on the other hand, was different. In spite of his stature in the mathematical community, he put everyone at ease. In seminars Steenrod did not hesitate to ask the most basic questions. This was quite often a boon to the others in the audience, too intimidated and too befuddled to ask the questions themselves.
After two years at the Institute, Bott went to the University of Michigan. In 1959 he became a professor at Harvard, where he has remained since. In 1999 Bott formally retired from teaching. He is now William Casper Graustein Research Professor at Harvard.