Raoul Bott

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Raoul Bott (Harvard University News Office)

Raoul Bott, FRS (born September 24, 1923, died December 20, 2005) was a mathematician known for numerous basic contributions to geometry in its broad sense.

He was born in Budapest, grew up in Slovakia, but spent his working life in the USA. His family emigrated to Canada in 1938; there he studied at McGill University. He was a professor at Harvard University from 1959 to 1999, and received the Wolf Prize in 2000. In 2005, he was elected an Overseas Fellow of the Royal Society of London. He died in San Diego after a battle with cancer.

Initially he worked on the theory of electrical circuits (Bott-Duffin theorem from 1949), then switched to pure mathematics.

He studied the homotopy theory of Lie groups, using methods from Morse theory, leading to the Bott periodicity theorem (1956). In the course of this work, he introduced Morse-Bott functions, an important generalization of Morse functions.

This led to his role as collaborator over many years with Michael Atiyah, initially via the part played by periodicity in K-theory. Bott made important contributions towards the index theorem, especially in formulating related fixed-point theorems, in particular the so-called 'Woods Hole fixed-point theorem', a combination of the Riemann-Roch theorem and Lefschetz fixed-point theorem (it is named after Woods Hole, Massachusetts, the site of a conference at which collective discussion formulated it [1]). The major Atiyah-Bott papers on what is now the Atiyah–Bott fixed-point theorem were written in the years up to 1968; they collaborated further in recovering in contemporary language results of Ivan Petrovsky on hyperbolic partial differential equations, prompted by Lars Gårding. In the 1980s, Atiyah and Bott investigated gauge theory, using the Yang-Mills equations on a Riemann surface to obtain topological information about the moduli spaces of stable bundles on Riemann surfaces.

Official photo

He is also known in connection with the Borel-Bott-Weil theorem on representation theory of Lie groups via holomorphic sheaves and their cohomology groups; and for work on foliations.

In 1964, he was awarded the Oswald Veblen Prize in Geometry by the American Mathematical Society.

His students included Robert MacPherson, Peter Landweber, Daniel Quillen and Stephen Smale.

His mother and aunts spoke Hungarian. His Czech stepfather did not, so the principal language at home was German. He had an English governesses from a young age, so he also spoke perfect English (and retained a very faint English accent throughout his life). The language of his high school was Slovak. Despite all this Bott claimed a distaste for learning languages.