Peter Hilton

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.

Peter John Hilton (7 April 1923 – 6 November 2010 ) was a British mathematician, noted for his contributions to homotopy theory and for code-breaking during World War II.

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.

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.

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: "It is a rare experience to meet an authentic genius. Those of us privileged to inhabit the world of scholarship are familiar with the intellectual stimulation furnished by talented colleagues. We can admire the ideas they share with us and are usually able to understand their source; we may even often believe that we ourselves could have created such concepts and originated such thoughts. However, the experience of sharing the intellectual life of a genius is entirely different; one realizes that one is in the presence of an intelligence, a sensibility of such profundity and originality that one is filled with wonder and excitement."

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.

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.'"

Turing, at the Victoria University of Manchester, in 1948 invited Hilton to see the Manchester Mark 1 machine.

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 A_n^2-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.

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.

Around 1950, Hilton took a position at the university maths department.

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.

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".

In 1955, Hilton started work with Beno Eckmann on what became known as Eckmann-Hilton duality for the homotopy category.

Hilton returned to Manchester as Professor, in 1956.

In 1958, he became the Mason Professor of Pure Mathematics at the University of Birmingham.

He moved to the United States in 1962 to be Professor of Mathematics at Cornell University, a post he held until 1971.

Through Eckmann, he became editor of the Ergebnisse der Mathematik und ihrer Grenzgebiete, a position he held from 1964 to 1983.

From 1971 to 1973, he held a joint appointment as Fellow of the Battelle Seattle Research Center and Professor of Mathematics at the University of Washington.

On 1 September 1972, he was appointed Louis D. Beaumont University Professor at Case Western Reserve University; on 1 September 1973, he took up the appointment.

Hilton echoed similar thoughts in the Nova PBS documentary Decoding Nazi Secrets (UK Station X, Channel 4, 1999).