Harold Scott MacDonald Coxeter

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Harold Coxeter, 1970

Harold Scott MacDonald Coxeter , CC (born February 9, 1907 in London , † March 31, 2003 in Toronto ) was a British- Canadian mathematician . His field of work was geometry , including regular polytopes .

Live and act

Coxeter attended King Alfred School in Hampstead and St George's School in Harpenden . He studied at Trinity College of Cambridge University , where he the academic degree of Ph. D. acquired.

From 1931 to 1936 he was a Research Fellow at Trinity College. During this time he was also a Rockefeller Foundation Fellow for two years and then a JE Procter Fellow at Princeton University . There he attended Hermann Weyl's lectures on Lie groups and partly took over his seminars and contributed appendices to Weyl's elaborated lecture ( Representations of Continuous Groups 1935), later known as the Dynkin diagram (or Coxeter-Dynkin diagram) has been. At Cambridge he was one of the selected students who were allowed to prepare Ludwig Wittgenstein's lectures (Blue Books). In 1936 he moved to the Canadian University of Toronto . There he was Assistant Professor of Mathematics from 1936 to 1943 , then Associate Professor until 1948 and finally Professor from 1948 to 1980.

Coxeter was considered a leading authority on classical geometry in English-speaking countries and beyond, about which he wrote well-known textbooks. He conducted geometric research at a time when geometry was generally viewed as being outside of the mathematical "mainstream". His book and his work on regular polytopes of various kinds were particularly well known. He was also interested in entertainment mathematics , got the remake of the WW Rouse Ball classic Mathematical Recreations and Essays and wrote on the mathematical background of the graphics by MC Escher . Coxeter also dealt with combinatorial group theory and the theory of Lie algebras .

From 1948 to 1957, Coxeter was editor of the Canadian Journal of Mathematics . He has also been visiting professor at universities in the UK , the Netherlands , Italy , Austria and the USA .

Coxeter corresponded not only with Escher, but also with all sorts of people who shared his geometric interests, such as B. with sculptors John Robinson, Magnus Wenninger , Alicia Boole Stott and George Odom, inmate of a mental hospital in New York, who made discoveries in the field of polytopes.

In 1936 he married Hendrina (Rina) Brouwer (a Dutch woman who was not related to the mathematician Brouwer), who died in 1999 and with whom he had a son and a daughter.


The Todd-Coxeter algorithm and the Coxeter groups were named after Coxeter . Coxeter was in 1941 as a member (" Fellow ") in the Royal Society of Canada and in 1950 in the Royal Society , which in 1997 awarded him the Sylvester Medal . From 1962 to 1963 he was President of the Canadian Mathematical Society , which awarded him the Graham Wright Award in 1995 . In 1968 he was Vice President of the American Mathematical Society . In 1995 he received the CRM / Fields Institute Prize . Also in 1997 he became Companion of the Order of Canada (CC). Coxeter had been a Foreign Member of the American Academy of Arts and Sciences since 1990 .

He received honorary doctorates from universities in Canada and Germany. In 2001 he was made an Honorary Fellow of Trinity College, Cambridge.

The Canadian Mathematical Society's Coxeter James Prize is awarded in his honor .

The asteroid (18560) Coxeter was named after him.


  • Immortal Geometry , Birkhäuser 1963, 2nd edition 1981 (English original: Introduction to Geometry , Wiley, 1961, 2nd edition 1969)
  • With SL Greitzer: Timeless Geometry , Klett 1983 (English original: Geometry revisited , Random House 1967)
  • The Beauty of Geometry: Twelve Essays , Dover 1968, 1999
  • Kaleidoscopes - Selected writings of HMSCoxeter , Wiley 1995 (editor F. Arthur Sherk)
  • Regular Polytopes , New York, Pitman 1948, 2nd edition MacMillan 1963, 3rd edition, Dover 1983
  • Regular Complex Polytopes , 1963, Cambridge University Press 1974, 2nd edition 1991
  • Non-Euclidean Geometry , University of Toronto Press 1942, 1965, Reprint Mathematical Association of America (MAA) 1998
  • Projective Geometry , Blaisdell 1964, 2nd edition, University of Toronto Press 1974, Springer 1987
  • The Real Projective Plane , McGraw Hill 1949, 3rd edition, Springer 1993 (German: Reelle projective geometry of the plane, Oldenbourg 1955)
  • The Fifty-Nine Icosahedra (with Patrick du Val , HT Flather, John Flinders Petrie ), Toronto 1938, Springer 1982
  • Mathematical Recreations and Essays , University of Toronto Press 1974 (New edition of the book by WW Rouse Ball )
  • With WOJ Moser : Generators and relations for discrete groups , Springer, 1957, 4th edition 1980
  • Published by: MC Escher - Proc.Int. Congress on MCEscher, Rome 1985 , North Holland 1986


  • Siobhan Roberts: King of infinite space: Donald Coxeter - the man who saved geometry . Toronto 2006 (the book received the Euler Book Prize )
  • Chandler Davis et al. a. (Editor): The Geometric Vein - Coxeter Festschrift . Springer 1981 (Coxeter Symposium Toronto)
  • Harold Scott Macdonald Coxeter (Ed.), Chandler Davis (Ed.), Erich W. Ellers (Ed.): The Coxeter Legacy: Reflections and Projections . AMS 2006, ISBN 0-8218-3722-2
  • Donald J. Albers, GL Alexanderson Mathematical People - Profiles and Interviews , Birkhäuser 1985

Individual evidence

  1. ^ AJ Coleman The greatest mathematical paper of all time , Math. Intelligencer, 1989, No. 3, p. 34
  2. ^ Graham Wright Award (Canadian Mathematical Society)

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