"He was one of the finest people I have ever met"

Last Updated: 17 Jan 2017
Shaun Wylie, international hockey player and Bletchley Park codebreaker, who became GCHQ Chief Mathematician

Cryptanalysis has always attracted more than its fair share of polymaths, but even within that area Shaun Wylie stands out.

Having persuaded his school to let him study the unusual combination of classics and mathematics in the sixth form, Wylie went to Oxford University to study mathematics. However, finding that he had already learnt much of the pure mathematics at school and not liking the applied mathematics, he switched to studying classics after one year.

After graduating, he still wanted to study mathematics; he was advised to apply for a scholarship at Princeton to take a PhD in topology. His three years at Princeton included a year at the Institute for Advanced Study. In addition to renewing his relationship with mathematics, Wylie engaged in a social life that included him popularising the sport of hockey  (he played to international standard, representing Scotland in 1938), play readings, treasure hunts, and various recreational games. In the last year of Wylie's time at Princeton, the social group included Alan Turing; it was a friendship that would lead to an important opportunity.

Wylie returned to the UK in 1937 and in 1940 received a letter from Turing inviting him to work at the Government Code & Cypher School (GC&CS) at Bletchley Park. Wylie accepted the offer and was put to work in the now famous Hut 8, where Turing led work on attacking the German Naval Enigma traffic. Wylie's facility with both languages and mathematics was vitally important for his role as head of the "cribs" section. Cribs were common fragments of written German, typically of 20 letters or more, such that if they could be successfully "guessed" to be a known part of a message, one could then create a "menu". The menus formed the input to the bombe electro-mechanical devices that exhausted possible wheel settings for Enigma. Identifying a good crib is not just a matter of spotting long, recurrent phrases, but also taking advantage of phrases where several letters appear repeatedly which lead to mathematically better menus.


A very old photo of a Bombe


Wylie excelled at both the technical and management side of the section and found the work highly absorbing. Hut 8 colleague Hugh Alexander stated that "except for Turing, no one made a bigger contribution to the success of Hut 8 than Wylie; he was easily the best all-rounder in the section, astonishingly quick and resourceful." One tale has it that when Winston Churchill called a snap visit to Hut 8 to commend them on their work, his entry was blocked by a cross-legged Wylie completely consumed by a textbook and oblivious to the Prime Minister's presence.

In 1943, as the Enigma challenges shifted from research and towards development and implementation, Wylie was moved to the even more challenging and important work attacking the German High Command cipher known as TUNNY. By 1943 the structure of TUNNY was well-understood thanks to an amazing diagnosis by Bill Tutte. It was known that TUNNY key was made up from regularly-stepping "chi" wheels and irregularly-stepping "psi" wheels; the motion of the psi wheels was in turn determined by two motor or "mu" wheels. Using ideas of Tutte and Turing, the recovery TUNNY settings could be broken down into three stages: 1) recovering the key contribution of the chi wheels, 2) recovering the key contribution of the psi wheels, and 3) recovering the stepping induced by the mu wheels. These ideas were already being used to good effect by cryptanalysts in the Testery1 section at Bletchley who attacked the problem with traditional pencil and paper approaches. Max Newman however felt that some, if not all, parts of the attack could be improved by automation. In this he laid out a vision not just for the future of cryptanalysis, but also the development of the modern computer.

Wylie was recruited into the new section known as the Newmanry, where mathematical and statistical methods were implemented at speed, at first on devices known as ROBINSONs2 and after on the prototypical computer COLOSSUS. He was one of five researchers privileged to spend one day every five weeks with no duties other than to sit in the research room and think without constraint on ways to improve the TUNNY attacks. Wylie's contribution was mainly in stage 2, the recovery of the psi contribution. He came up with a method known as the algebra of proportional bulges that exploited the statistical properties of both the TUNNY machine and the German language. It was implemented by using COLOSSUS to keep track of scores known as Shaun counts, after Wylie. Shortly after VE Day, Wylie was finally able to show that the third stage of the TUNNY attack could also be implemented on an unmodified COLOSSUS, confirming that Newman's dream of a full end-to-end process could be realised.

As well as his cryptanalytic contributions, Wylie was key to the social life of Bletchley. He continued his interests in games and puzzles as well as running the Bletchley Park dramatic society. While in the Newmanry he met and married one of his co-workers, Odette Murray. The couple received a dispensation that allowed them both to continue working in the Newmanry while married provided that they worked in separate shifts.

After the war, Wylie took up a fellowship at Trinity Hall, Cambridge. He was not a prolific researcher, but instead threw his energies into teaching. There are many reports of the clarity, enthusiasm, and wit of his mathematics lectures. He supervised five PhD students, starting with Bill Tutte. Although his students were relatively few, they each turned into highly influential and successful mathematicians, three of them becoming Fellows of the Royal Society. Tracing out the PhD students of his PhD students and so on, over 1,200 mathematicians can track their mathematical genealogy to Wylie, marking him out as one of the founding fathers of the highly successful British school of algebraic topology. To further cement this claim, his textbook written with Peter Hilton "Homology Theory: An Introduction to Algebraic Topology" is regarded as the classic text on the subject. His reputation for topological insight and clarity led two Cambridge biologists, Watson and Crick, to quiz him as to whether a double helix can be separated without unravelling. Wylie's negative answer confirmed some of their theory of the structure of DNA.

Throughout this time, Wylie remained in contact with his former Bletchley Park colleagues. Together with Donald Michie he designed one of the earliest computer chess programs MACHIAVELLI3 in competition with David Champernowne's and Turing's TUROCHAMP. He corresponded with Jack Good on mathematical topics. In 1958 the continued connection led to him replacing Good as GCHQ's Chief Mathematician. This also allowed him to resume working with Hugh Alexander, who was now Head of Cryptanalysis. Wylie's tenure included the beginnings of a revolution in cryptography as James Ellis produced proposals for researching "non-secret encryption"4 in 1969. Ellis's heterodox papers were passed to Wylie to determine whether the ideas were worth investigating. "Unfortunately, I can't see anything wrong with this." was Wylie's response.

Wylie retired from GCHQ in 1973. He then worked as a high school teacher for seven years; in this he maintained a broad portfolio of mathematics, Greek, theatre, and chess. He was then elected an Honorary Fellow of Trinity Hall. Never one to idle he continued to interest himself in a wide range of topics: he taught both schools and for the University of the Third Age (U3A), he was a founder member of the Social Democratic Party (SDP), he compiled crosswords for the Listener5 (considered the hardest of all mainstream crossword puzzles), was a long distance walker, and wrote an unclassified historical account of the work of the Newmanry in 20016.

For all his undoubted intellectual skills, those who knew Wylie consistently comment first and foremost on his human qualities. Jonathan Steinberg, Vice-Master of Trinity Hall, wrote: "Shaun Wylie was one of the most refined and delightful human beings I have ever known, modest, amusing and utterly without the usual vanity." Wylie's student, Sir Christopher Zeeman, wrote in Wylie's obituary: "He was one of the finest people I have ever met, and I was honoured to model myself on him." It was, perhaps, Wylie's ability to bring out the best in people that was the greatest of his manifold talents.

A GCHQ Senior Mathematician



1 Named after Major Ralph Tester, head of the section.

2 Named after cartoonist William Heath Robinson, famous for his imaginary complex devices.

3 A pun on the names Michie and Wylie.

4 Non-secret encryption is now better known as public key cryptography.

5 Wylie composed under the name of "Petti" (wyliecoat is a Scottish term for a petticoat), one of his puzzles came third in the 1997 Ascot Gold Cup for setters.

6 See "Breaking TUNNY and the Birth of COLOSSUS" in "Action This Day" ed. Erskine and Smith.