Bill Tutte

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Mathematician who, as a Bletchley Park codebreaker, gained access to the ciphers of the German Army High Command

Although his name is not widely known, Bill Tutte accomplished one of the great feats of the Second World War. While working at the codebreaking centre Bletchley Park -- where he had gone without formal training in mathematics — he managed to deduce the structure of the German machines that generated the cipher known as Fish. This was a most significant breakthrough, for while the standard Enigma codes broken at Bletchley could give information on everyday German troop movements, Fish was used for top-level communications by the German Army High Command.

It was in January 1941 that, as a shy young graduate student in chemistry at Cambridge, Tutte was asked by his tutor to go to Bletchley Park. He went there in May, having trained at the Code and Cipher School in London. At Bletchley he was one of 8,000 people, including mathematicians, linguists, clerks and secretaries, helping to process 10,000 German ciphers each day. They made an incalculable contribution to winning the war.

The deciphering of the codes produced by the Enigma machines is now well documented. The version used by the German army proved, however, more resistant to analysis than its naval and airforce counterparts. Denied regular access to army Enigma, the codebreakers tried instead to read the higher-level machine-cipher named Fish, which used an alphabet of 32 letters called the Baudot Teleprinter code.

Fish, the name of which is thought to derive from a German referring to one of their codes as "Sägefisch" (sawfish), was produced by a Lorenz machine, or "Tunny" as the British called it -- a 12-wheel contraption with hundreds of metal lugs. A teleprinter was attached and made each character into a string of electrical pulses, which before transmission were converted into code.

The first Fish traffic to be intercepted was on a German Army radio link in 1941 between Athens and Vienna. On August 30 of that year, a German radio operator made a serious mistake, and two long cipher messages arrived, of around 4,000 letters, with the same "indicator" -- a 12-letter sequence at the start of each message. The same message had been sent twice, but with more word-spacing and punctuation on one occasion than on the other, and with the same stream of obscuring characters. Using these two messages, after four months' toil, in which he worked from the messages alone and wrote out vast sequences by hand, Tutte deduced the structure of the machines.

In a sequence of brilliant observations, he deduced that there was in the Lorenz machine a wheel of 41 sprockets, and another with 31. He went on, with others at Bletchley, to calculate that there were 12 wheels, and also determined the structure of their interconnection. He had worked out the entire machine without ever having seen one.

Tutte was then involved in creating algorithms to break the codes and to decipher the messages that the Fish machines produced. The deciphering continued into 1943, but then the enemy took precautions to make decoding difficult. The algorithms developed by Tutte and his colleagues, Max Newman and Ralph Tester, could be carried out only by machine. As a result, in 1943, Post Office engineers, led by Tommy Flowers, built Colossus — arguably the world's first electronic computer. With the aid of Colossus, and using Tutte's algorithms to break the Lorenz codes, vital intelligence was obtained about Hitler's intentions in the run up to D-Day in 1944.

Tutte did have one regret from his time at Bletchley Park. While he was working there, the authorities had decided to focus on Tunny rather than looking at it along with the Air Force version known as "Sturgeon". This was because it was thought better, with limited resources, to attack one cipher system whole-heartedly, and Sturgeon was producing a less satisfactory flow of information. Tutte later described Sturgeon as "the one that got away".

William Thomas Tutte was born in Newmarket in Suffolk, the son of a gardener. His family moved around the country in his early years, but returned to the area when he was five years old. William was educated locally and in 1935 went up to Cambridge to study chemistry.

It was there that he formed a particularly close bond with three fellow members of the Trinity Mathematical Society. The group collaborated on the problem of "squaring the square" -- dividing a square into unequal smaller squares -- and in 1940 published a paper that described their solution; Tutte believed that it was as a result of this work that he was asked to go to Bletchley.

At the end of the war he returned to Cambridge to study mathematics. Having received his doctorate he moved to the University of Toronto, where he became prominent in the field of combinatorics, the science of counting.

In 1962 he joined the University of Waterloo in Ontario. It had been founded five years previously and Tutte helped it to establish its reputation, attracting combinatorialists from around the world. He had said after the war that he dreamt of a future university department which was "devoted to the study of how Fish was broken and, more importantly, of how it ought to have been broken". In his later years he served as the University of Waterloo's Honorary Director of the Centre for Cryptographic Research.

Tutte was elected to the Royal Society, and to the Royal Society of Canada. Last year he was appointed an Officer of the Order of Canada.

His wife Dorothea died in 1994. They had no children.

Professor Bill Tutte, OC, FRS, mathematician and codebreaker, was born on May 14, 1917. He died on May 2, 2002, aged 84.

© The Times, 2002