Harold Scott MacDonald Coxeter
Harold Scott MacDonald Coxeter  

Born 
London, England

February 9, 1907
Died  March 31, 2003
Toronto, Ontario, Canada

(aged 96)
Residence  Toronto, Ontario, Canada 
Known for  study of geometry and mathematics 
Spouse(s)  Hendrina, died in 1999 
Children  Susan Thomas, and a son, Edgar 
Awards 
Smith's Prize (1931) Henry Marshall Tory Medal (1949) CRMFieldsPIMS 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 Britishborn 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 higherdimensional 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]}
Biography
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 FiftyNine 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. LonguetHiggins 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.
Awards
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]}
Works
 1940: Regular and SemiRegular Polytopes I, Mathematische Zeitschrift 46: 380407, MR 2,10 doi:10.1007/BF01181449
 1942: NonEuclidean 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. LonguetHiggins 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, SpringerVerlag ISBN 0387092129
 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 0821816535)
 1973: Regular Polytopes, (3rd edition), Dover edition, ISBN 0486614808
 1974: Projective Geometry (2nd edition)
 1974: Regular Complex Polytopes, Cambridge University Press
 1981: (with R. Frucht and D. L. Powers), ZeroSymmetric Graphs, Academic Press.
 1985: Regular and SemiRegular Polytopes II, Mathematische Zeitschrift 188: 559–591
 1987 Projective Geometry (1987) ISBN 9780387406237
 1988: Regular and SemiRegular 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 0471010030
 1999: The Beauty of Geometry: Twelve Essays, Dover Publications, LCCN 9935678, ISBN 0486409198
See also
References
 ^ Harold Scott MacDonald Coxeter at the Mathematics Genealogy Project
 ^ 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.
 ^ ^{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.
 ^ 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"
 ^ ^{a} ^{b} ^{c} ^{d} Roberts, Siobhan, King of Infinite Space: Donald Coxeter, The Man Who Saved Geometry, Walker & Company, 2006, ISBN 0802714994
 ^ 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/S000299041940071708.
 ^ Coxeter 1954
 ^ Foreign Honorary Member elected 1990 2016 American Academy of Arts & Sciences
 ^ Office of the Governor General of Canada. Order of Canada citation. Queen's Printer for Canada. Retrieved 26 May 2010
 ^ Blumenthal, L. M. (1943). "Review: Noneuclidean geometry by H. S. M. Coxeter" (PDF). Bull. Amer. Math. Soc. 49 (9): 679–680. doi:10.1090/s000299041943079773.
 ^ 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/s000299041950094142.
 ^ 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/S000299041958101780.
 ^ Freudenthal, H. (1962). "Review: Introduction to geometry by H. S. M. Coxeter" (PDF). Bull. Amer. Math. Soc. 68 (2): 55–59. doi:10.1090/s000299041962107149.
 ^ 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.
Further reading
 Davis, Chandler; Ellers, Erich W, eds. (2006). The Coxeter Legacy: Reflections and Projections. Providence, R.I.: American Mathematical Society. ISBN 9780821837221. OCLC 62282754.
 Roberts, Siobhan (2006). King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry. New York: Walker & Company. ISBN 9780802714992. OCLC 71436884.
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.
 1907 births
 2003 deaths
 Companions of the Order of Canada
 Fellows of the Royal Society
 Fellows of the Royal Society of Canada
 Geometers
 20thcentury English mathematicians
 Alumni of Trinity College, Cambridge
 University of Toronto faculty
 Canadian mathematicians
 People from Harpenden
 Academics of the University of East Anglia
 Senior Wranglers