Last Sunday, I visited Bletchley Park for a symposium and the unveiling of an exhibition on mathematician Bill Tutte on what would have been his 100th birthday. You may not have heard of Bill Tutte but (in what was later called “the greatest intellectual achievement of the war") Tutte helped to crack the Lorenz code that the German forces used to encrypt and communicate messages during World War II  without ever actually seeing a working model. His work extends far beyond his days at Bletchley. Bill was educated at Cheveley Village School in Cambridgeshire, before going to Trinity College, Cambridge, in 1935. He studied Natural Science and specialised in Chemistry  but his childhood love of mathematics grew during his time at Cambridge. Bill became close friends with three mathematics students: Leonard Brooks, Cedric Smith and Arthur Stone, and the foursome spent their time solving mathematical problems. They were particularly attracted to a problem known as "Squaring the Square"  a simple puzzle where you are tasked with dividing a square into smaller squares of different sizes. Simple as it may sound, it was assumed at the time that this puzzle could not be solved. But the foursome cracked it by discovering an unexpected link between electrical circuits and mathematics. They were pipped to the post by Roland Sprague, a German mathematician, who published the solution  but not the theory behind it. Speaking at the symposium, Claire Butterfield from the Bill Tutte Memorial Fund, said: "Mathematics was where his true passion lay and his reputation as a problem solver meant he was interviewed at Bletchley." Bletchley ParkIn May 1941, Bill arrived at Bletchley Park and was put to work in the research section. He initially worked on the Italian Naval Cipher, before he was introduced to the Lorenz Cipher. The Lorenz system was more advanced than the Enigma machine  and the British knew very little about how it worked. So, Bill and the team were faced with a harder problem with less information to solve it. But he did solve it  in about six months. Bill's approach was to try to work out how the cipher wheels on the Lorenz machine (known to the Allies as Tunny) worked by writing down on squared paper the first dot or cross of every character of the cipher text. Just like the countless mathematical problems he'd worked on during his life, he was searching for a pattern. Bill once said: "I do not think I had much faith in this procedure, but I thought it best to seem busy." Using this approach (and a security blunder by a German operator where two versions of the same message were sent with sloppy changes), Bill and the other members of the Research Station worked out the structure and movement of the wheels on Tunny. Dr David Kenyon, a research historian at Bletchley Park, said: "Tutte's contribution was a turning point in what Bletchley Park was able to achieve during World War Two. The Allies' understanding of the German plans in France prior to DDay is very significantly based on Fish [Lorenz] intercepts rather than Enigma. Had they not had this intelligence, their understanding would have been much weaker." To find out more about Bill's life in codebreaking, click here. Cambridge to CanadaAfter the war, Bill moved back to Cambridge to finish his PhD. His love of mathematics continued and he had a real interest in a phenomenon known as "Graph Theory". His PhD advisor (and a fellow codebreaker) Shaun Wylie wasn't keen for Bill to conduct research in this area. Claire said: "He was recommended not to do Graph Theory as it was seen as trivial in the field of mathematics  but Bill just enjoyed solving problems." There was no possibility for Bill to continue this work in Graph Theory at Cambridge after his PhD  so he moved to Canada where he first taught at the University of Toronto, before moving to the Univerity of Waterloo, where he held the position of Professor of Combinatorics and Optimisation. "He had the luxury of teaching subjects that were close to his heart," Claire added. "His lectures had an element of storytelling about them and he would also teach local children to play chess over milk and cookies." As idyllic as Bill's life in Canada sounds, his professional career had just as many highs. He received the Order of Canada and was elected a Fellow of the Royal Society of Canada, and a Fellow of the Royal Society of London. His work on Graph Theory transformed this field into one of the most important areas of mathematics. Bill's work in Graph Theory led to some of the key mathematical developments that have shaped the internet today, including the science behind search engines. A simple messageThe thread that pulls Bill's extraordinary life together is that he did all of this because he followed his heart. He had no agenda, no lofty ambitions  he had a love of mathematics and puzzles, and an aptitude to communicate these ideas effectively. That's what really struck a chord with me as I listened to the series of lectures on the life and work of Bill Tutte. Against all the advice from his peers, he worked in an area that was of little to no interest to the wider mathematical world. And against his own better judgement, he tinkered with a statistical method that meant Lorenz could be broken. His work had a huge impact on the outcome of World War Two and the technology we rely on today. And that's really the beauty of Bill Tutte's mind. He had no ego  he just understood that from the simplest questions and concepts, the most complex machines like Lorenz can be cracked. I'd like to think Bill may agree with my mantra that "Science is Simple" and that any work in science and technology is important and interlinked. Whether it's the musings of a child who questions why we don't hurtle off the Earth as it whizzes round the Sun, or a scientist sitting in CERN trying to find the most elusive matter in the universe with every bit of scientific kit as their disposal  there is no room for arrogance and assumptions in science. Thank goodness there was room for Bill Tutte. I'm going to end with a quote, beautifully written by the man himself as he introduces the seminal book on Graph Theory, Theory of Finite and Infinite Graphs by Denes Konig: Low was the prestige of Graph Theory in the Dirty Thirties. It is still remembered, with resentment now shading into amusement, how one mathematician scorned it as 'The slums of Topology'. It was the socalled science of trivial and amusing problems for children, problems about drawing a geometrical figure in a single sweep of a pencil, problems about threading mazes, and problems about colouring maps and cubes in cute and crazy ways. It was too hastily assumed that the mathematics of amusing problems must be trivial, and that if noticed at all it need not be rigorously established. Students tempted by Graph Theory would be advised by their supervisors to turn to something respectable or even useful, like differential equations. I am reminded that my own most recent research in Graph Theory has involved differential equations. Mathematics is One, after all.
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March 2018
