**Peter Hilton** was an English mathematician who made important contributions to homotopy theory. He is best known for his text-books and for his work as a code-breaker in World War II.

- Peter was born and brought up in London, England.
- Hilton was offered a position in the Foreign Office and told he had to start in January 1942.
- The main tool used in this work is a "suspension" theorem of Henry Whitehead which Hilton also generalised and applied in his major 31-page paper Suspension theorems and the generalized Hopf invariant (1951).
- During this period Hilton was employed as a Lecturer at the University of Manchester (1948-1952).
- Peter and Margaret (Meg) shared a love of the theatre and of acting; Peter enjoyed amateur acting, Meg was a professional.
- This part of Hilton's career was, like his doctoral studies, highly influenced by the friends he had made among the mathematicians at Bletchley.
- When Hilton first arrived at Bletchley Park he had worked in Hut 8 where Hugh Alexander and Shaun Wylie introduced him to the cryptanalysis methods used in decoding Naval Enigma messages.
- Later both Hilton and Wylie moved to the Newmanry run by Max Newman, where early computers (the Colossus machines) were used in decoding, and Hilton and Wylie remained close friends.
- When Hilton was appointed to the University of Manchester in 1948 it was to work in Max Newman's Department.
- However, this was not the first book that Hilton had published.
- Hilton had also published Differential calculus, a 56-page text in the Library of Mathematics series.
- By the time that Homology theory: An introduction to algebraic topology was published, Hilton was Mason Professor of Pure Mathematics at Birmingham University.
- During the 1950s Hilton had been an invited speaker at the British Mathematical Colloquium on three occasions (he is the only person to have had three invitations in a 10 year period).
- Hilton was appointed Professor at Cornell University, Ithaca, New York, in 1962, remaining there for nine years.
- After holding this position for nine years, Hilton became Distinguished Professor at the State University of New York (SUNY), Binghamton.
- Hilton has made a remarkable contribution both as a research mathematician and as an author of textbooks.
- Hilton has written many outstanding books - from first year undergraduate level, to graduate text level, to research monograph.
- Then there are three texts Homotopy theory and duality (1965); Suites spectrales et théories de cohomologie générales (1970); and Tópicos de álgebra homológica (1970) each based on courses given by Hilton.
- Continuing in our run through of some of Hilton's books, there is: General cohomology theory and K-theory (1971); Lectures in homological algebra (1971); (with Urs Stammbach) A course in homological algebra (1971); (with Yel Chiang Wu) A course in modern algebra (1974); (with Joe Roitberg and Guido Mislin) Localization of nilpotent groups and spaces (1975); Nilpotente Gruppen und nilpotente Räum (1984); (with Dereck Holton and Jean Pedersen) Mathematical reflections : In a room with many mirrors (1997); and (with Dereck Holton and Jean Pedersen) Mathematical vistas : In a room with many mirrors (2002).

Born 7 April 1923, London, England. Died 6 November 2010, Binghampton, New York, USA.

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Origin England, Topology

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