He was initially put to work on Naval Enigma in Hut 8. In late 1942, he 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. Occasionally the same message was sent repeated, a major security blunder that Bletchley park called a "depth." Hilton derived great satisfaction from being able to look at the encoded texts coming from two separate teleprinter messages, combine them and extract two messages in clear German.
Hilton obtained his DPhil in 1949 from Oxford University under the supervision of John Henry Whitehead. His dissertation was titled, "Calculation of the Homotopy Groups of An2-polyhedra".
Hilton recounted his experience working with Alan Turing in Hut 8 in his "Reminiscences of Bletchley Park" from A Century of Mathematics in America:
I had the good fortune to work closely with Alan Turing and to know him well for the last 12 years of his short life. 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. Alan Turing was such a genius, and those, like myself, who had the astonishing and unexpected opportunity, created by the strange exigencies of the Second World War, to be able to count Turing as colleague and friend will never forget that experience, nor can we ever lose its immense benefit to us.
Hilton echoed similar thoughts in the Nova PBS documentary Decoding Nazi Secrets.
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. 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. In 1982, he was appointed Distinguished Professor of Mathematics at Binghamton University, becoming Emeritus in 2003. Latterly he spent each spring semester as Distinguished Professor of Mathematics at the University of Central Florida.
Hilton constructed the 51-letter palindrome "Doc note, I dissent. A fast never prevents a fatness. I diet on cod."
Hilton's 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.
In August 1983, an international conference on algebraic topology was held, under the auspices of the Canadian Mathematical Society, to mark Professor Hilton's 60th Birthday. Professor Hilton was presented with a Festschrift of papers dedicated to him (London Mathematical Society Lecture Notes, Volume 86, 1983). The American Mathematical Society has published the proceedings under the title 'Conference on Algebraic Topology in Honor of Peter Hilton'
Hilton was selected in October 1992, to deliver the invited lecture at the 'Georges de Rham' day at the University of Lausanne.
An International Conference was held in Montreal in May 1993, to mark the 70th birthday of Hilton. The proceedings were published as The Hilton Symposium, CRM Proceedings and Lecture Notes, Volume 6, American Mathematical Society (1994), edited by Guido Mislin.
In 1994, Professor Hilton was the Mahler Lecturer of the Australian Mathematical Society.
In the summers of 2001 and 2001, Professor Hilton was Visiting Erskine Fellow at the University of Canterbury, Christchurch, New Zealand.
In winter term of 2005 Professor Hilton received an appointment as Courtesy Faculty in the College of Arts and Sciences at University of South Florida.
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