Peter John Hilton (7 April 19236 November 2010) was a British mathematician, noted for his contributions to homotopy theory and for code-breaking during World War II.
Early life
He was born in Brondesbury, London, the son Mortimer Jacob Hilton, a Jewish physician who was in general practice in Peckham, and his wife Elizabeth Amelia Freedman, and was brought up in Kilburn. The physiologist Sidney Montague Hilton (1921–2011) of the University of Birmingham Medical School was his elder brother.
Hilton was educated at St Paul's School, London. He went to The Queen's College, Oxford in 1940 to read mathematics, on an open scholarship, where the mathematics tutor was Ughtred Haslam-Jones.
Bletchley Park
A wartime undergraduate in wartime Oxford, on a shortened course, Hilton was obliged to train with the Royal Artillery, and faced scheduled conscription in summer 1942. After four terms, he took the advice of his tutor, and followed up a civil service recruitment contact. He had an interview for mathematicians with knowledge of German, and was offered a position in the Foreign Office without being told the nature of the work. The team was, in fact, recruiting on behalf of the Government Code and Cypher School. Aged 18, he arrived at the codebreaking station Bletchley Park on 12 January 1942.
Hilton worked with several of the Bletchley Park deciphering groups. He was initially assigned to Naval Enigma in Hut 8. Hilton commented on his experience working with Alan Turing, whom he knew well for the last 12 years of his life, in his "Reminiscences of Bletchley Park" from A Century of Mathematics in America: Hilton echoed similar thoughts in the Nova PBS documentary Decoding Nazi Secrets (UK Station X, Channel 4, 1999).
In late 1942, Hilton transferred to work on German teleprinter ciphers. A special section known as the "Testery" had been formed in July 1942 to work on one such cipher, codenamed "Tunny", and Hilton was one of the early members of the group. His role was to devise ways to deal with changes in Tunny, and to liaise with another section working on Tunny, the "Newmanry", which complemented the hand-methods of the Testery with specialised codebreaking machinery. Hilton has been counted as a member of the Newmanry, possibly on a part-time basis.
Recreational
A convivial pub drinker at Bletchley Park, Hilton also spent time with Turing working on chess problems and palindromes. He there constructed a 51-letter palindrome: "Doc note, I dissent. A fast never prevents a fatness. I diet on cod." He did not use paper or pencil while composing it, but lay on his bed, eyes closed, and assembled it mentally over one night. It took him five hours.
Mathematics
Hilton obtained his DPhil in 1949 from Oxford University under the supervision of John Henry Whitehead. His dissertation was "Calculation of the homotopy groups of -polyhedra". His principal research interests were in algebraic topology, homological algebra, categorical algebra and mathematics education. He published 15 books and over 600 articles in these areas, some jointly with colleagues. Hilton's theorem (1955) is on the homotopy groups of a wedge of spheres. It addresses an issue that comes up in the theory of "homotopy operations".
Turing, at the Victoria University of Manchester, in 1948 invited Hilton to see the Manchester Mark 1 machine. Around 1950, Hilton took a position at the university maths department. He was there in 1949, when Turing engaged in a discussion that introduced him to the word problem for groups. Hilton worked with Walter Lederman. Another colleague there was Hugh Dowker, who in 1951 drew his attention to the Serre spectral sequence.
In 1952, Hilton moved to DPMMS in Cambridge, England, where he ran a topology seminar attended by John Frank Adams, Michael Atiyah, David B. A. Epstein, Terry Wall and Christopher Zeeman. Via Hilton, Atiyah became aware of Jean-Pierre Serre's coherent sheaf proof of the Riemann–Roch theorem for curves, and found his first research direction in sheaf methods for ruled surfaces.
In 1955, Hilton started work with Beno Eckmann on what became known as Eckmann-Hilton duality for the homotopy category. Through Eckmann, he became editor of the Ergebnisse der Mathematik und ihrer Grenzgebiete, a position he held from 1964 to 1983.