Coxeter, Harold Scott Macdonald

Harold Scott MacDonald Coxeter, known as Donald, was born on February 9 1907 in Kensington England to parents Harold Coxeter and Lucy Gee. At an early age, he demonstrated a high level of ability in both music and math. His father, realizing his son’s gifts, sought out the advice of the famous philosopher Bertrand Russell who introduced young Donald to mathematician E.H. Neville. At the advice of Neville, Coxeter left boarding school at the age of 15 and was tutored only in Math and German. He entered Cambridge in 1926 on scholarship and received his B.A. in 1929. He continued to study for his doctorate under Britain’s leading figure in geometry H.F. Baker and was awarded a Ph.D. in 1931. As a Fellow, he continued his research at Cambridge and for two years was a research visitor at Princeton working under Oswald Veblen. In 1936, Coxeter married Rien Brouwer of Holland and they set off together to Toronto where Coxeter accepted an appointment to the mathematical department at the University of Toronto. Toronto is where their life settled. They had two children Susan and Edgar.

Coxeter was considered a leading mathematician and the greatest geometer of the 20th century. His contributions of fundamental importance have been in the Theory of Polytopes, Non-Euclidean Geometry, Discrete Group and Combinational Theory. Specifically, he is best known among mathematicians for discovering how shapes will behave in higher dimensions – now known as Coxeter groups and Coxeter diagrams. His influence has reached beyond the mathematics world. Coxeter’s work in non-euclidean geometry inspired the “Circle Limits I-IV” by the famous Dutch artist M.C. Escher with whom he shared a life-long friendship. Another strand of his thinking influenced theoretical physics in the area of relativistic quantum field theory. Coxeter numbers and diagrams are used in the study of elementary particle physics. Nobel winning chemists who discovered the Carbon 60 molecule were influenced by Coxeter’s work on iconsahedral symmetries.

Over his expansive career, Coxeter published 12 books – at least four of them classics including Introduction to Geometry which first appeared in 1961 and has since seen many editions and has been translated into six languages. He also published over 200 articles and at various times acted as reviewer and referee. He was editor of the Canadian Journal of Mathematics for nearly a decade from 1948 to 1957. He served as president of the Canadian Mathematical Congress (1962-63), Vice-President of the American Mathematical Society, (1968) and president of the International Congress of Mathematicians, (1974). Coxeter was awarded numerous honorary degrees, was a fellow of the Royal Society of London (1950) and of the Royal Society of Canada (1947). In 1997 he was made a Companion of the Order of Canada.

While Coxeter officially retired from the Department of Mathematics in 1980, as Professor Emeritus he continued his engagement with the mathematical world right up to his death. In July 2002 he gave an invited lecture at a conference in Budapest Hungary. H.S.M., “Donald”, Coxeter died in Toronto at the age of 96 on March 31 2003. He is survived by his two children Susan (Coxeter) Thomas and Edgar Coxeter and several grandchildren. A biography, entitled, The King of Infinite Space, Donald Coxeter and the Magical Omnipotence of Geometry is due to be published by Anansi in September 2006.