Harold Scott MacDonald "Donald" Coxeter CC FRS FRSC (9 February 1907 – 31 March 2003) was a British-Canadian geometer and mathematician. [2][3]
Harold Scott MacDonald Coxeter | |
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Born | London, England | 9 February 1907
Died | 31 March 2003 Toronto, Ontario, Canada | (aged 96)
Alma mater | University of Cambridge (B.A., 1929; Ph.D., 1931) |
Known for | Coxeter element Coxeter functor Coxeter graph Coxeter group Coxeter matroid Coxeter notation Coxeter's loxodromic sequence of tangent circles Coxeter–Dynkin diagram Coxeter–Todd lattice Boerdijk–Coxeter helix Goldberg–Coxeter construction Todd–Coxeter algorithm* Tutte–Coxeter graph LCF notation Regular skew apeirohedra |
Spouse(s) | Hendrina, died in 1999 |
Children | a daughter, Susan Thomas, and a son, Edgar |
Awards |
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Scientific career | |
Fields | Geometry |
Institutions | University of Toronto |
Doctoral advisor | H. F. Baker[1] |
Doctoral students |
Coxeter was born in Kensington, England, to Harold Samuel Coxeter and Lucy (née Gee). His father had taken over the family business of Coxeter & Son, manufacturers of surgical instruments and compressed gases (including a mechanism for anaesthetising surgical patients with nitrous oxide), but was able to retire early and focus on sculpting and baritone singing; Lucy Coxeter was a portrait and landscape painter who had attended the Royal Academy of Arts. A maternal cousin was the architect Sir Giles Gilbert Scott.[4][3]
In his youth, Coxeter composed music and was an accomplished pianist at the age of 10.[5] He felt that mathematics and music were intimately related, outlining his ideas in a 1962 article on "Music and Mathematics" in the Canadian Music Journal.[5]
He was educated at King Alfred School, London, and St George's School, Harpenden, where his best friend was John Flinders Petrie, later a mathematician for whom Petrie polygons were named. He was accepted at King's College, Cambridge, in 1925, but decided to spend a year studying in hopes of gaining admittance to Trinity College, where the standard of mathematics was higher.[3] Coxeter won an entrance scholarship and went to Trinity in 1926 to read mathematics. There he earned his BA (as Senior Wrangler) in 1928, and his doctorate in 1931.[5][6] In 1932 he went to Princeton University for a year as a Rockefeller Fellow, where he worked with Hermann Weyl, Oswald Veblen, and Solomon Lefschetz.[6] Returning to Trinity for a year, he attended Ludwig Wittgenstein's seminars on the philosophy of mathematics.[5] In 1934 he spent a further year at Princeton as a Procter Fellow.[6]
In 1936 Coxeter moved to the University of Toronto. In 1938 he and P. Du Val, H. T. Flather, and John Flinders Petrie published The Fifty-Nine Icosahedra with University of Toronto Press. In 1940 Coxeter edited the eleventh edition of Mathematical Recreations and Essays,[7] originally published by W. W. Rouse Ball in 1892. He was elevated to professor in 1948. He was elected a Fellow of the Royal Society of Canada in 1948 and a Fellow of the Royal Society in 1950. He met M. C. Escher in 1954 and the two became lifelong friends; his work on geometric figures helped inspire some of Escher's works, particularly the Circle Limit series based on hyperbolic tessellations. He also inspired some of the innovations of Buckminster Fuller.[6] Coxeter, M. S. Longuet-Higgins and J. C. P. Miller were the first to publish the full list of uniform polyhedra (1954).[8]
He worked for 60 years at the University of Toronto and published twelve books.
Coxeter was a vegetarian. He attributed his longevity to his vegetarian diet, daily exercise such as fifty press-ups and standing on his head for fifteen minutes each morning, and consuming a nightly cocktail made from Kahlúa, peach schnapps, and soy milk.[4]
Since 1978, the Canadian Mathematical Society have awarded the Coxeter–James Prize in his honor.
He was made a Fellow of the Royal Society in 1950 and in 1997 he was awarded their Sylvester Medal.[6] In 1990, he became a Foreign Member of the American Academy of Arts and Sciences[9] and in 1997 was made a Companion of the Order of Canada.[10]
In 1973 he received the Jeffery–Williams Prize.[6]
A festschrift in his honour, The Geometric Vein, was published in 1982. It contained 41 essays on geometry, based on a symposium for Coxeter held at Toronto in 1979.[11] A second such volume, The Coxeter Legacy, was published in 2006 based on a Toronto Coxeter symposium held in 2004.[12]