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Person: Coxeter, Harold Scott MacDonald

Donald Coxeter's work was mainly in geometry. In particular he made contributions of major importance in the theory of polytopes, non-euclidean geometry, group theory and combinatorics.

Mathematical Profile (Excerpt):

• Another relative noted that H M S Coxeter made him sound like a ship.
• A permutation of the names resulted in Harold Scott MacDonald Coxeter.
• The 1901 Census has Harold Samuel Coxeter living with his parents Samuel and Ada Coxeter in Highgate, Hornsey, London.
• Lucy painted Donald playing the piano when he was about 2 or 3 years old and the painting is now in Trinity College, Cambridge.
• Sadly, Donald was not brought up in a happy home since his parents experienced a difficult marriage.
• Donald's parents began to talk about a divorce which the young boy found almost unbearable.
• This was a happier time for Donald who was tutored by May.
• When Harold told Donald that after he was divorced he would marry Katie Gabler, the young boy was even more unhappy.
• Donald was also becoming fascinated by geometry.
• Dimensional Analogy won a school essay prize for Donald and he filled five notebooks with further ideas, diagrams and calculations.
• Russell suggested that Donald write to Eric Harold Neville which he did on 11 September 1923.
• When Neville asked Donald what mathematics he was being taught at school he saw that the mathematics teaching he was receiving was very poor.
• He advised that Donald leave school and receive private tutoring in mathematics before beginning studies at Cambridge.
• A suitable tutor was found in Alan Robson, head of mathematics at Marlborough College, so Coxeter left St George's School, Harpenden, rented a room in Marlborough and cycled to the College for tutoring.
• Coxeter was assigned J E Littlewood as his director of studies at Trinity College who advised him to take pure mathematics courses on analytic geometry, projective geometry, differential geometry, topology, group theory, and number theory.
• At this stage Coxeter was shy having little social interaction.
• Now we noted above that Harold Coxeter had met Rosalie Gabler at meetings of the Royal Psychological Society.
• Coxeter spent the three summer months of 1928 in Vienna where he was questioned by Stekel and asked to keep a diary of his dreams.
• It is doubtful if the psychoanalysis did Coxeter any good (or harm) but while in Vienna he spent time in the reading room of the University of Vienna's mathematics library and there discovered the works of Ludwig Schläfli.
• These made a big impression on Coxeter who carried some of Schläfli's ideas into the research he was about to undertake.
• Coxeter then became a Fellow continuing his researches at Cambridge.
• This came about because Solomon Lefschetz visited Cambridge in 1931 and encouraged Coxeter to apply for a Rockefeller research fellowship.
• Interestingly, he gave his name as Macdonald Coxeter but most often he gave Harold Coxeter.
• Returning to Cambridge, Coxeter realised that despite the opportunities that Cambridge offered, he had just spent the best year of his life at Princeton.
• They quickly realised that there were surprising connections between Coxeter's finite groups and Weyl's infinite groups.
• Weyl had Coxeter take notes of the seminars as well as delivering five on his own work as part of the series.
• Coxeter was delighted to have his work appear as an Appendix to Weyl's published notes.
• This was not an easy time to be looking for a permanent post, so when he was offered a teaching post in a boarding school in Vermont, Coxeter was very tempted to accept.
• The decision went in favour of William Hodge and Coxeter began to worry about his future.
• Coxeter took up an appointment at the University of Toronto where he remained on the faculty until his death.
• Coxeter's work was mainly in geometry.
• Coxeter polytopes are the fundamental domains of discrete reflection groups, now called Coxeter groups, and they give rise to tesselations.
• In 1934 Coxeter classified all spherical and euclidean Coxeter groups.
• York was not the only university to honour Coxeter.
• Coxeter met Escher in 1954 and the two became lifelong friends.
• Another friend, R Buckminister Fuller, used Coxeter's ideas in his architecture.
• In 1938 Coxeter revised and updated Rouse Ball's Mathematical recreations and essays, a book which Rouse Ball first published in 1892.
• Coxeter had many artistic gifts, particularly in music.
• When Donald visited me and a colleague in St Andrews we took him a walk down the pier at the harbour.
• Donald never missed a seminar and never missed an opportunity to deliver a talk on his ongoing research.
• Coxeter was a vegetarian, he was active in saving the environment, and he promoted peace.
• The press is full of anecdotes on Donald.

Born 9 February 1907, London, England. Died 31 March 2003, Toronto, Canada.

View full biography at MacTutor

Tags relevant for this person:

Algebra, Group Theory, Origin England

Thank you to the contributors under CC BY-SA 4.0!

Github:

non-Github:

@J-J-O'Connor

@E-F-Robertson

References

Adapted from other CC BY-SA 4.0 Sources:

1. O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive