During World War II, Turing had been recruited to work at Bletchley Park, Britain's codebreaking centre. Turing wrote to Wylie around December 1940, who was by then teaching at Wellington College, inviting him to work at Bletchley Park. He accepted, and arrived in February 1941. He joined Turing's section, Hut 8, which was working on solving the Enigma machine as used by the Kriegsmarine. He became head of the crib subsection, and allocated time on the bombe codebreaking machines. Hugh Alexander, successor to Turing as head of Hut 8, commented that "except for Turing, no-one made a bigger contribution to the success of Hut 8 than Shaun Wylie; he was astonishingly quick and resourceful and contributed to theory and practice in a number of different directions". Wylie transferred in Autumn 1943 to work on "Tunny", a German teleprinter cipher. He married Odette Murray, a WREN in the section. In 1945, soon after the victory in Europe, Wylie demonstrated how Colossus — electronic machines used to help solve Tunny — could have been used unmodified to break the Tunny "motor wheels", a task which had been previously done by hand. While at Bletchley Park, he became president of the dramatic club. He had also played international hockey for Scotland, but according to fellow codebreaker I. J. Good, he "never mentioned any of his successes".
Post-war
After the war, he was a fellow at Trinity Hall until 1958 and lectured in mathematics. He was the Ph.D. advisor for Frank Adams, Max Kelly, Crispin Nash-Williams, William Tutte and Christopher Zeeman. With Peter Hilton, he authored Homology Theory: An Introduction to Algebraic Topology, published in 1960. In 1958, he became Chief Mathematician at GCHQ, the UK signals intelligence organisation. In July 1969, he was sent a draft paper by James H. Ellis, another GCHQ mathematician, about the possibility of what was termed "non-secret encryption", or what is now more commonly known as public-key cryptography, on which Wylie commented "unfortunately, I can't see anything wrong with this". He retired in 1973, and taught at Cambridgeshire High School for Boys in Cambridge for seven years. He was elected an honorary fellow at Trinity Hall in 1980. Wylie supervised five PhD students at Cambridge, through whom he has 1037 "descendants" according to the American Mathematical SocietyMathematical Genealogy Project. In addition he influenced the intellectual development of generations of pupils at the Cambridgeshire High School for Boys / Hills Road Sixth Form College where he taught maths and classical Greek and where he also produced plays, such as Chekhov's The Cherry Orchard and coached the school Chess Team which rather than playing other schools, played and usually won against college and university teams. He also came out of retirement temporarily to teach Mathematics at Long Road Sixth Form College. After retirement from teaching, Wylie was instrumental in the founding of the Liberal Democrats and in the Cambridge-based University of the Third Age and at the time of his death was preparing to read in the next Cambridge Greek Play, Aeschylus' Agamemnon. Shaun "Doc" Wylie, as he was known to his pupils and students, possessed an incisive insightful intellect and was a man who brought good humour to those around. He was reticent and modest about his many significant accomplishments. He would patiently encourage and coach those who he felt were promising but under-performing. He was an inspiration to those who came in contact with him. His eldest son, the late Keith Wylie, a barrister, was a croquet international and open champion of Great Britain. He died on 2 October 2009.
