He joined Turing's section, Hut 8, which was working on solving intercepts of German Navy messages encoded on the Enigma machine, which relied on a series of rotors to scramble "clear" text into a cipher with billions of variables. Wylie became head of the "crib" subsection, which was on the lookout for repeated words or phrases in German messages (such as the names of senior officers, or the phrase "nothing to report") which became useful aides, or "cribs", to start breaking the code.
As head of the "crib", Wylie spent much time and effort with the Bletchley "bombe", a giant electro-mechanical machine that slowly chuntered through possible solutions to the code, and which depended largely on the educated guesses about the "cribs" that Wiley and his team proposed.
According to Hugh Alexander, Turing's successor as head of Hut 8, only Turing made a "bigger contribution to the success of Hut 8 than Wylie", whom he described as "easily the best all-rounder in the section, astonishingly quick and resourceful". Historians working at Bletchley today consider Wylie "highly significant in Allied codebreaking efforts".
In the autumn of 1943 Wylie transferred to work on "Tunny", a German teleprinter cipher, which was heavier than the Enigma machines and generally used for high level communications between two fixed points, rather than between army or naval units which were, by necessity, mobile. While codebreakers at Bletchley had seen and been able to analyse early versions of the Enigma machine, however, they had never seen Tunny. Only a breach of security, in which a German message was retransmitted with the same encryption settings, had allowed them a chance of cracking the code. A series of machines were then built to decipher Tunny, including Colossus, now considered the world's first electronic computer.
Shaun Wylie was born on January 17 1913 in Oxford. His father, Sir Francis Wylie, was the first warden of the Rhodes Trust. Educated at the Dragon School and Winchester, he won a scholarship to New College, Oxford, where he read Mathematics and Classics. In 1934 he went to study Topology at Princeton University, obtaining a PhD in 1937 and meeting Turing.
After the war Wylie was a fellow until 1958 at Trinity Hall, Cambridge, where he was regarded as an outstanding lecturer and worked alongside the astronomer Fred Hoyle. One of his students, the computer pioneer Norman Sanders, recalled his lectures on linear algebra as miracles of clarity: "I still remember his little diagrams of the undiagrammable with vast amusement. Mathematics is not perhaps the most hilarious of subjects, but in Shaun's hands it was pretty close. Every sentence was a quiet joke, and at the end of each proof he would turn to his audience with a diabolical leer exacting much laughter from an appreciative public."
During his time at Trinity Hall, Wylie was known as a leading expert in topology (the manner in which shapes stretch and deform), and when James Watson and Francis Crick were coming up with the design of DNA as a double helix they sought his opinion about whether the two helices could move apart or would need to unravel. They were pleased to hear that they needed to unravel.
In 1958 Wylie became chief mathematician at GCHQ in Cheltenham, the British signals intelligence headquarters. Eleven years later he reviewed a draft paper on the possibility of "non-secret encryption", now more commonly known as public-key cryptography. Being a codebreaker rather than an code-maker, Wylie commented: "Unfortunately, I can't see anything wrong with this."
Retiring in 1973, he taught Mathematics and Greek at Cambridgeshire High School for Boys (later Hills Road Sixth Form College) for seven years. He was elected an honorary fellow of Trinity Hall in 1980.
A modest man, Wylie never sought the limelight despite his many achievements. When the secrecy surrounding the work at Bletchley Park was finally relaxed, he became only a rather reluctant celebrity. With his wife Odette, a former Wren whom he had met on the Tunny project in 1943, he contributed to the burgeoning library of Enigma literature.
Aside from his mathematical and cryptanalytic career, Wylie was an international hockey player (representing Scotland in 1938), and compiled crosswords. His nom-de-plume for The Listener was Petti, "wyliecoat" being an old Scottish term for a petticoat. He was also an accomplished chess and bridge player, and a keen long distance walker.
A governor of both Cheltenham College and Pates Grammar School, he was also a founder member of the Social Democratic Party and an active supporter of the Liberal Democrats. He took part in activities organised by the University of the Third Age in Cambridge, including play-reading in the original Greek, impressing his fellow readers of plays until the end of his life.
Shaun Wylie died on October 2. His wife Odette (née Murray) and their eldest son predeceased him. He is survived by a daughter and two sons.
20 Oct 2009 © Telegraph Group Limited 2009.