Harold Scott MacDonald Coxeter

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Harold Scott MacDonald Coxeter
Born (1907-02-09)February 9, 1907
London, England
Died March 31, 2003(2003-03-31) (aged 96)
Toronto, Ontario, Canada
Residence Toronto, Ontario, Canada
Spouse(s) Hendrina, died in 1999
Children Susan Thomas, and a son, Edgar
Awards Smith's Prize (1931)
Henry Marshall Tory Medal (1949)
CRM-Fields-PIMS prize (1995)
Sylvester Medal (1997)
Scientific career
Fields Geometry
Institutions University of Toronto
Doctoral advisor H. F. Baker[1]
Doctoral students Norman Johnson

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, CC (February 9, 1907 – March 31, 2003)[2] was a British-born Canadian geometer. Coxeter is regarded as one of the greatest geometers of the 20th century. He was born in London but spent most of his adult life in Canada. He was always called Donald, from his third name MacDonald.[3]


In his youth, Coxeter composed music and was an accomplished pianist at the age of 10.[4] He felt that mathematics and music were intimately related, outlining his ideas in a 1962 article on "Mathematics and Music" in the Canadian Music Journal.[4]

Coxeter went up to Trinity College, Cambridge in 1926 to read mathematics. There he earned his BA (as Senior Wrangler) in 1928, and his doctorate in 1931.[4][3] 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.[3] Returning to Trinity for a year, he attended Ludwig Wittgenstein's seminars on the philosophy of mathematics.[4] In 1934 he spent a further year at Princeton as a Procter Fellow.[3]

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,[5] originally published by W. W. Rouse Ball in 1892. He was elevated to professor in 1948. Coxeter was elected a Fellow of the Royal Society of Canada in 1948 and a Fellow of the Royal Society in 1950. He met Maurits 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.[3] Coxeter, M. S. Longuet-Higgins and J. C. P. Miller were the first to publish the full list of uniform polyhedra (1954).[6]

He worked for 60 years at the University of Toronto and published twelve books. He was most noted for his work on regular polytopes and higher-dimensional geometries. He was a champion of the classical approach to geometry, in a period when the tendency was to approach geometry more and more via algebra.[7]


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.[3] In 1990, he became a Foreign Member of the American Academy of Arts and Sciences[8] and in 1997 was made a Companion of the Order of Canada.[9]

In 1973 he received the Jeffery–Williams Prize.[3]


See also


  1. ^ Harold Scott MacDonald Coxeter at the Mathematics Genealogy Project
  2. ^ Roberts, S.; Ivic Weiss, A. (2006). "Harold Scott MacDonald Coxeter. 9 February 1907 -- 31 March 2003: Elected FRS 1950". Biographical Memoirs of Fellows of the Royal Society. 52: 45–66. doi:10.1098/rsbm.2006.0004. 
  3. ^ a b c d e f g O'Connor, John J.; Robertson, Edmund F., "Harold Scott MacDonald Coxeter", MacTutor History of Mathematics archive, University of St Andrews .
  4. ^ a b c d Roberts, Siobhan, King of Infinite Space: Donald Coxeter, The Man Who Saved Geometry, Walker & Company, 2006, ISBN 0-8027-1499-4
  5. ^ Frame, J. S. (1940). "Review: Mathematical Recreations and Essays, 11th edition, by W. W. Rouse Ball; revised by H. S. M. Coxeter" (PDF). Bull. Amer. Math. Soc. 45 (3): 211–213. doi:10.1090/S0002-9904-1940-07170-8. 
  6. ^ Coxeter 1954
  7. ^ The Boston Globe (September 10, 2006) "Review: The Man Who Saved Geometry by Siobhan Roberts. "Crying `Death to Triangles!' a generation of mathematicians tried to eliminate geometry in favor of algebra. Were it not for Donald Coxeter, they might have succeeded"
  8. ^ Foreign Honorary Member elected 1990 2016 American Academy of Arts & Sciences
  9. ^ Office of the Governor General of Canada. Order of Canada citation. Queen's Printer for Canada. Retrieved 26 May 2010
  10. ^ Blumenthal, L. M. (1943). "Review: Non-euclidean geometry by H. S. M. Coxeter" (PDF). Bull. Amer. Math. Soc. 49 (9): 679–680. doi:10.1090/s0002-9904-1943-07977-3. 
  11. ^ DuVal, Patrick (1950). "Review: The real projective plane by H. S. M. Coxeter" (PDF). Bull. Amer. Math. Soc. 56 (4): 376–378. doi:10.1090/s0002-9904-1950-09414-2. 
  12. ^ Hall Jr., Marshall (1958). "Review: Generators and relations for discrete groups by H. S. M. Coxeter and W. O. J. Moser" (PDF). Bulletin of the American Mathematical Society. 64, Part 1 (3): 106–108. doi:10.1090/S0002-9904-1958-10178-0. 
  13. ^ Freudenthal, H. (1962). "Review: Introduction to geometry by H. S. M. Coxeter" (PDF). Bull. Amer. Math. Soc. 68 (2): 55–59. doi:10.1090/s0002-9904-1962-10714-9. 
  14. ^ Levi, H. (1963). "Review: Introduction to Geometry by H. S. M. Coxeter". The Journal of Philosophy. 60 (1): 19–21. JSTOR 2023059. doi:10.2307/2023059. 

Further reading

External links

  • Archival papers held at University of Toronto Archives and Records Management Services
  • Harold Scott MacDonald Coxeter at the Mathematics Genealogy Project
  • H. S. M. Coxeter (1907–2003), Erich W. Ellers, Branko Grünbaum, Peter McMullen, Asia Ivic Weiss Notices of the AMS: Volume 50, Number 10.
  • www.donaldcoxeter.com www.math.yorku.ca/dcoxeter webpages dedicated to him (in development)
  • Jaron's World: Shapes in Other Dimensions, Discover mag., Apr 2007
  • The Mathematics in the Art of M.C. Escher video of a lecture by H.S.M. Coxeter, April 28, 2000.
  • H.S.MACDONALD COXETER- Pakistan Mathematical Society
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