Bott received his bachelor’s degree in engineering from McGill University in 1945, as well as his master's degree in 1946; he also worked there as a teacher of calculus from 1945.

Gallery of Raoul Bott

5000 Forbes Ave, Pittsburgh, PA 15213, United States

Bott earned his doctorate of science in applied mathematics from Carnegie Institute of Technology (now called Carnegie-Mellon University), in 1949.

Career

Gallery of Raoul Bott

Gallery of Raoul Bott

Achievements

Membership

Royal Society of London

2005

London, United Kingdom

Bott was elected an Overseas Fellow of Royal Society of London in 2005.

Bott received his bachelor’s degree in engineering from McGill University in 1945, as well as his master's degree in 1946; he also worked there as a teacher of calculus from 1945.

(Developed from a first-year graduate course in algebraic ...)

Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory.

Raoul Bott was a Hungarian-American mathematician, educator and author. He made numerous contributions to twentieth century mathematics.

Background

Ethnicity:
Bott’s father was of Austrian Catholic descent, while his mother was Jewish.

Raoul Bott was born on September 24, 1923, in Budapest, Hungary. He was a son of Rudolph Bott and Margit (Kovacs) Bott, who divorced soon after his birth. His mother remarried and Raoul lived with his mother and step father, who was a German speaking Czech, in Slovakia. His mother died in 1935 and Bott was raised by his stepfather in an upper-middle class environment. Bott and his family escaped to England in 1939 because of the tensions in Europe caused by the Nazis and their anti-Jewish policies. A year later, Bott and his family emigrated to Canada.

Education

Bott entered McGill University in Montreal and studied engineering. He received his bachelor’s degree in engineering in 1945. He entered a Master’s in Engineering program at McGill that year. After earning his master's degree in 1946 with a thesis topic on impedance matching, he earned his doctorate of science in applied mathematics from Carnegie Institute of Technology (now called Carnegie-Mellon University), in 1949.

Bott served as a volunteer in the Canadian Army for the summer of 1945. After the bombing of Hiroshima in August 1945, which effectively ended World War II, Bott left the military career. That same year he began teaching calculus at McGill University. Bott emigrated to the United States in 1947. He became a member of the Institute for Advanced Study at Princeton in two years. Bott did pure mathematics there while increasing his knowledge of topology. After serving as an instructor at the University of Michigan for one school year (1951-1952), and as an assistant professor from 1952 to 1955, Bott returned to the Institute at Princeton for two more years, from 1955 to 1957. Bott served as a full professor at the University of Michigan from 1957 to 1959. He became a naturalized American citizen in 1959.

During a decade in New Jersey and Michigan, Bott’s research proved quite fruitful. Much of his work in the 1950s concerned the topology of Lie groups and Morse theory. He combined these two concepts to develop his fundamental periodicity theorem. Bott’s periodicity theorem proved useful and applicable in many areas of mathematics, especially as a powerful tool for describing phenomena in homotopy theory.

One of Bott’s early important papers, “Homogeneous Vector Bundles”, was published in 1957 in the journal Annals of Mathematics. This influential paper touched a wide range of mathematics, including representation theory, differential geometry, algebraic geometry and algebra. Bott became an associate editor at the Annals of Mathematics in 1958, a post he retained through the 1980s and early 1990s. Bott’s work at the Annals was not his only editorial experience; he also served as an editor of Topology.

In 1959, Bott left Michigan to became a professor of mathematics at Harvard University, where he worked as a professor from 1997. He took a sabbatical from Harvard to return to the Institute at Princeton for one year, 1970-71. While at Harvard, in the 1960s, Bott’s work focused on differential operators. He proved (with Michael Atiyah) the Atiyah-Bott fixed point theorem, which combines fixed point formulas for elliptic operators with K-theory, using his periodicity theorem. K-theory was used in much of his work and the work of other mathematicians in the 1960s. Bott also explored other topics, including the relationships between analysis and topology, and studied partial differential equations in hyperbolic rather than elliptic terms.

Bott’s research in the 1970s focused on foliations. He first wrote on foliation theory in a paper published in 1966. Among the many areas of foliations he studied were the integrability of foliations and their obstructions as affected by characteristic classes; the singularities of holomorphic foliations and a formula for their residue; and he studied foliations from a quantitative angle. Bott’s work on foliations brought together the Gelfand-Fuks Cohomology of vector fields and the foliations’ algebraic topology.

Bott’s personal warmth led to his and his wife serving as the master in an undergraduate dormitory, Dunsterhouse, at Harvard University, from 1977 to 1983. His mathematics students also benefited from his personal enthusiasm for learning and life.

During the 1980s Bott moved onto a new area of research, mathematics as it relates to physics. He employed the methodology he developed during his research on topology in this area.

Quotations:
"There are two ways to do great mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else - but persistent."

Membership

Bott was a member of National Academy of Science, French Academy of Science and the American Mathematical Society. He was also a fellow of the American Academy of Arts and Sciences, as well as an honorary member of the London Mathematical Society.

Royal Society of London
,
United Kingdom

2005

Personality

Quotes from others about the person

“In fact, it seems to me that his influence as a teacher and role model may be nearly comparable in importance to the influence of his mathematical research on the history of mathematics.” - Bob MacPherson, one former student

Interests

music, nature

Connections

Bott was married to Phyllis Aikman from August 30, 1947. The couple is survived by four children - Anthony, Jocelyn, Renee and Candace.