Harold Scott MacDonald Coxeter

From Wikipedia, the free encyclopedia
Jump to: navigation, search
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
Fields Geometry
Institutions University of Toronto
Doctoral advisor H. F. Baker[1]
Doctoral students Norman Johnson
Notable awards Smith's Prize (1931)
Henry Marshall Tory Medal (1949)
CRM-Fields-PIMS prize (1995)
Sylvester Medal (1997)
Spouse Hendrina, died in 1999
Children Susan Thomas, and a son, Edgar

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.


In his youth, Coxeter composed music and was an accomplished pianist at the age of 10.[3] 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.[3]

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.[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.[3][5] 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.[5] Returning to Trinity for a year, he attended Ludwig Wittgenstein's seminars on the philosophy of mathematics.[3] In 1934 he spent a further year at Princeton as a Procter Fellow.[5]

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,[6] 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 and 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.

Coxeter, M. S. Longuet-Higgins and J. C. P. Miller were the first to publish the full list of uniform polyhedra (1954).[7]

Since 1978, the Canadian Mathematical Society have awarded the Coxeter–James Prize in his honor.

In 1990, he became a Foreign Member of the American Academy of Arts and Sciences.[citation needed] In 1997 he received a Sylvester Medal from the Royal Society and was made a Companion of the Order of Canada.[8]



See also[edit]


  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 Roberts, Siobhan, King of Infinite Space: Donald Coxeter, The Man Who Saved Geometry, Walker & Company, 2006, ISBN 0-8027-1499-4
  4. ^ 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"
  5. ^ a b c O'Connor, John J.; Robertson, Edmund F., "Harold Scott MacDonald Coxeter", MacTutor History of Mathematics archive, University of St Andrews .
  6. ^ 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. 
  7. ^ Coxeter 1954
  8. ^ Office of the Governor General of Canada. Order of Canada citation. Queen's Printer for Canada. Retrieved 26 May 2010
  9. ^ 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. 
  10. ^ 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. 
  11. ^ 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. 
  12. ^ 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. 
  13. ^ Levi, H. (1963). "Review: Introduction to Geometry by H. S. M. Coxeter". The Journal of Philosophy. 60 (1): 19–21. doi:10.2307/2023059. JSTOR 2023059. 

External links[edit]