Mathematics Professor Recounts Wartime Coming-of-Age

Graustein Professor of Mathematics Raoul Bott has a favorite story about the meandering path he took to become a mathematician. As a graduate student disillusioned by engineering, he went to the Dean of the Medical School at McGill University in Canada to see if he could become a doctor.

"But [the dean] was a very shrewd fellow and started to interview me, and he asked what I liked to do and what I didn't like to do, and I could see that I was giving the wrong answers all the time," recalls Bott, who did not favor dissecting animals or chemistry.

Needless to say, Bott did not make a very good first impression on the dean.

"Finally he said,'Is it to do good to humanity? Is that why you want to be a doctor?' I hesitated in answering this, and he said, 'Because they make the worst doctors.' I got out and said to myself, 'Thank you, you sonofabitch.'Then I said, 'OK, I'll be a mathematician, because that's what I like to do."

A few months later, Bott became a graduate student at the Carnegie Institute of Technology in Pittsburgh. He received a Ph.D in mathematics two years later in 1949, and fell in love with the field of topology after a stint at Princeton as a postdoctorate student. Bott has since become a prominent contributor in the field.

Topology is the abstract study of geometric spaces and their properties that are preserved under bending. An important algebraic tool in topology is the homotopy group, which is used to classify different types of holes in spaces and which are difficult to compute, according to Daniel K. Biss '98, a student whose topology senior thesis Bott is advising.

Bott's most famous contribution to mathematics is the Bott Periodicity Theorem, which he discovered in 1956. It was the first, and in a sense the only explanation of the homotopy groups of an important space, in this case, of all-invertiable matrices. He also found a periodic structure in these homotopy groups.

This theory provided the basis for algebraic K-theory, a field which tries to understand objects by studying the algebraic-geometric structures one can put on it, according to Biss.

In 1959, Bott accepted a position in the Harvard Mathematics Department, where he remains to this day. He has taught classes on calculus, linear algebra and group theory. His most recent teaching subjects include introductory topology and differential geometry.

Looking back at his life at Harvard, Bott decries the increasing bureaucracy of large undergraduate mathematical classes, and urges students to be lively and aggressive in class.

Much of Bott's own unorthodox youth was spent avoiding educational systems that emphasized rote learning. Born in Budapest on September 24, 1923, to a Jewish mother and a Catholic father, he lived the first 16 years of his life in the Hungarian part of Slovakia. His parents divorced soon after he was born, but Bott nonetheless led a childhood of affluence, since his new stepfather was a high-ranking manager in a sugar factory.

Until the age of eight, Bott was educated by governesses in arithmetic, German and English at his Hungarian-speaking home. When he became eight, Bott says he was unhappily sent off to elementary school. School was not his forte, as he write in his memoirs.

"All in all, I went to school for five years in Bratislava, two years to the elementary school, and then for three years to the "Real-Schule." During that period, I did not earn a single A--except in singing and in German. Of course I had an alibi. These were all Slovak schools, and I started to learn this language only at 10. Unfortunately, it is hard to invoke this excuse for mathematics, and I certainly did not distinguish myself in this subject, either...My grades were C's and an occasional B."

Until he discovered his love for mathematics, his attitude toward school continued to be indifferent. As a teenage refugee from Hitler, and then as a transient English boarding school student, Bott recalls shingling stables and pursuing his interest in electrical fuses more than attending classes.

Bott received his first rigorous education when he arrived in Canada for a year of high school after skipping two years and being elevated to his senior year for answering a trick mathematics question correctly. But only after graduating as an electrical engineer from McGill University would his talent in mathematics come to the forefront.

Samit Dasgupta '99, who as a first year took Bott's introductory topology class and is currently taking Bott's differential geometry class, says he believes Bott is preoccupied with large issues as opposed to the details.

"His reputation [among students in his class] is to be a deep thinker, [rather than] someone who would do arithmetical computations off the top of his head," Dasgupta says.

To Biss, it seems that Bott's teaching style reflects the emphasis on freedom that he loved as a student.

"His teaching style is very conceptual, he tends to give you a skeleton to flesh out," Biss says, "So, if you're motivated, it can be inspiring."

Besides mathematics, Bott, a former Dunster House Master, also loves playing the piano and has studied at the Longy School of Music. He commutes to Harvard by bicycle each day.

With information from "Autobiographical Sketches & Autobiographical Fragments" by Raoul Bott