Harold Scott MacDonald Coxeter

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Harold Scott MacDonald Coxeter
Born(1907-02-09)February 9, 1907
London, England
DiedMarch 31, 2003(2003-03-31) (aged 96)
Toronto, Ontario, Canada
ResidenceToronto, Ontario, Canada
Known forstudy of geometry and mathematics
Spouse(s)Hendrina, died in 1999
ChildrenSusan Thomas, and a son, Edgar
AwardsSmith's Prize (1931)
Henry Marshall Tory Medal (1949)
CRM-Fields-PIMS prize (1995)
Sylvester Medal (1997)
Scientific career
InstitutionsUniversity of Toronto
Doctoral advisorH. F. Baker[1]
Doctoral studentsNorman 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.[citation needed] He was born in London, received his BA (1929) and PhD (1931) from Cambridge, but lived in Canada from age 29. He was always called Donald, from his third name MacDonald.[3] 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]


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 "Mathematics and Music" in the Canadian Music Journal.[5]

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.[5][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.[5] 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,[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 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).[7]

He worked for 60 years at the University of Toronto and published twelve books.


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]


  • 1940: Regular and Semi-Regular Polytopes I, Mathematische Zeitschrift 46: 380-407, MR 2,10 doi:10.1007/BF01181449
  • 1942: Non-Euclidean Geometry (1st edition),[10] (2nd ed, 1947), (3rd ed, 1957), (4th ed, 1961), (5th ed, 1965), University of Toronto Press (6th ed, 1998), MAA.
  • 1954: (with Michael S. Longuet-Higgins and J. C. P. Miller) "Uniform Polyhedra", Philosophical Transactions of the Royal Society A 246: 401–50 doi:10.1098/rsta.1954.0003
  • 1949: The Real Projective Plane[11]
  • 1957: (with W.O.J. Moser) Generators and Relations for Discrete Groups[12] 1980: Second edition, Springer-Verlag ISBN 0-387-09212-9
  • 1961: Introduction to Geometry[13][14]
  • 1963: Regular Polytopes (2nd edition), Macmillan Company
  • 1967: (with S. L. Greitzer) Geometry Revisited
  • 1970: Twisted honeycombs (American Mathematical Society, 1970, Regional conference series in mathematics Number 4, ISBN 0-8218-1653-5)
  • 1973: Regular Polytopes, (3rd edition), Dover edition, ISBN 0-486-61480-8
  • 1974: Projective Geometry (2nd edition)
  • 1974: Regular Complex Polytopes, Cambridge University Press
  • 1981: (with R. Frucht and D. L. Powers), Zero-Symmetric Graphs, Academic Press.
  • 1985: Regular and Semi-Regular Polytopes II, Mathematische Zeitschrift 188: 559–591
  • 1987 Projective Geometry (1987) ISBN 978-0-387-40623-7
  • 1988: Regular and Semi-Regular Polytopes III, Mathematische Zeitschrift 200: 3–45
  • 1995: F. Arthur Sherk, Peter McMullen, Anthony C. Thompson and Asia Ivić Weiss, editors: Kaleidoscopes — Selected Writings of H.S.M. Coxeter. John Wiley and Sons ISBN 0-471-01003-0
  • 1999: The Beauty of Geometry: Twelve Essays, Dover Publications, LCCN 99-35678, ISBN 0-486-40919-8

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 e f g O'Connor, John J.; Robertson, Edmund F., "Harold Scott MacDonald Coxeter", MacTutor History of Mathematics archive, University of St Andrews.
  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 d Roberts, Siobhan, King of Infinite Space: Donald Coxeter, The Man Who Saved Geometry, Walker & Company, 2006, ISBN 0-8027-1499-4
  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. ^ 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. doi:10.2307/2023059. JSTOR 2023059.

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