H. S. M. Coxeter
British-Canadian geometer and mathematician, a leading figure in 20th-century geometry.
Harold Scott MacDonald "Donald" Coxeter was a British-Canadian mathematician widely recognized as one of the foremost geometers of the twentieth century. Born in Kensington, England, his father managed a family business manufacturing surgical instruments and compressed gases before retiring to pursue sculpture and singing, while his mother was a portrait and landscape painter. A gifted pianist in his youth, Coxeter believed mathematics and music were deeply connected, an idea he later explored in a published article. He initially aimed to become a composer but shifted his focus to mathematics while recovering from illness at school, where he met John Flinders Petrie, later known for Petrie polygons. Coxeter studied at Trinity College, Cambridge, earning his BA as Senior Wrangler and his doctorate. After a year as a Rockefeller Fellow at Princeton, working with Hermann Weyl and others, he returned to Cambridge and attended Ludwig Wittgenstein's philosophy seminars, eventually being selected to take notes that became part of Wittgenstein's Blue Book. In 1936, Coxeter moved to the University of Toronto, where he remained for sixty years, becoming a full professor in 1948. He co-authored *The Fifty-Nine Icosahedra* and wrote *Regular Polytopes*, among twelve books. His honors included fellowship in the Royal Society of Canada and the Royal Society, as well as the Order of Canada. Many concepts bear his name, including Coxeter groups, Coxeter–Dynkin diagrams, and the Todd–Coxeter algorithm. He also collaborated with M. C. Escher, inspiring the Circle Limit series, and helped publish the first full list of uniform polyhedra. A lifelong vegetarian, Coxeter attributed his longevity to diet, daily exercise, and a nightly cocktail.
- field
- Geometry, group theory
- nationality
- British-Canadian
- known_for
- Coxeter groups, Coxeter–Dynkin diagrams, Todd–Coxeter algorithm, Regular Polytopes, The Fifty-Nine Icosahedra
Lore & Background
Coxeter was born in Kensington, England, to Harold Samuel Coxeter and Lucy Coxeter. His father had taken over the family business of Coxeter & Son, manufacturers of surgical instruments and compressed gases, but retired early to focus on sculpting and baritone singing; Lucy Coxeter was a portrait and landscape painter. A maternal cousin was the architect Sir Giles Gilbert Scott. He was educated at King Alfred School, London, and St George's School, Harpenden, initially aiming to become a composer but deciding he had more interest in mathematics. While recovering from chickenpox at St George's, he met John Flinders Petrie, later a mathematician for whom Petrie polygons were named. He then spent a year at Princeton University as a Rockefeller Fellow, working with Hermann Weyl, Oswald Veblen, and Solomon Lefschetz. Returning to Trinity for a year, he attended Ludwig Wittgenstein's seminars on the philosophy of mathematics and was selected to take notes that later became The Blue Book. He met M. C. He also inspired innovations of Buckminster Fuller. Coxeter, M. S. Longuet-Higgins, and J. C. P.
Reader's Guide
Coxeter's significance lies in his profound contributions to geometry and group theory, particularly through the invention and classification of Coxeter groups, which describe sets of reflections in Euclidean space. These groups, associated with diagrams now known as Coxeter–Dynkin diagrams, classify finite reflection groups and are fundamental to the study of root systems, Lie algebras, and polytopes. Many concepts bear his name, including the Coxeter graph, Coxeter's loxodromic sequence of tangent circles, and the Todd–Coxeter algorithm. His work influenced artists such as M. C. Escher and Buckminster Fuller, bridging mathematics and visual art. Coxeter's 60-year career at the University of Toronto and his 12 books established him as a central figure in 20th-century geometry.
Did You Know?
- Coxeter was an accomplished pianist at age 10 and believed mathematics and music were intimately related.
- He attended Ludwig Wittgenstein's philosophy of mathematics seminars and was selected to take notes that later became The Blue Book.
- Coxeter attributed his longevity to a vegetarian diet, daily exercise including standing on his head for 15 minutes each morning, and a nightly cocktail of Kahlúa, peach schnapps, and soy milk.
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