He was one of the brilliant mathematical geniuses who helped crack the Nazi codes, but few have ever heard of his name. So who was Bill Tutte?
One of the greatest mathematicians and codebreakers of the 20th century, William (Bill) Tutte, was born a century ago as of Sunday, May 14, 2017.
His wartime work enabled the British to break into the communications of the highest levels of the Nazi regime, motivated the development of a special-purpose electronic codebreaking computer, shortened World War II and saved countless lives.
Tutte, who died aged 84 in Canada in 2002, went on to do far-reaching work in mathematics but few people have heard of him and his contributions.
First breakthrough
Tutte’s origins were humble. He was born in Newmarket, a market town in England north of London, the son of a gardener and a housekeeper.
He excelled at school and entered Trinity College, Cambridge, in 1935, where he majored in chemistry.
While still an undergraduate he became close friends with three mathematics students: Leonard Brooks, Cedric Smith and Arthur Stone. Together, these four threw themselves into mathematical problem-solving and research.
They were attracted to a simple recreational puzzle, on whether it is possible to divide a square up into smaller squares, all of different sizes, known as Squaring the Square.
The prevailing belief was that it could not be done. But they managed to do it, partly by discovering an unexpected link with the mathematics of electrical circuits.
The theoretical framework they developed has had a lasting influence. A German mathematician, Roland Sprague, working independently, just pipped them to a solution to the puzzle, but not the theory behind it.
The work of Tutte and his friends was published in an academic journal in 1940. It got Tutte noticed at Cambridge, and from there he joined Britain’s wartime codebreaking operation at Bletchley Park in 1941.
The codebreakers
Other Cambridge mathematicians were there before Tutte. Among them was Alan Turing, who had worked out how to break the version of the Enigma code used by the German navy.
The Enigma code was already so difficult that even there, at Bletchley Park – the best codebreaking operation of the war – it had sat in the too-hard basket until Turing’s arrival. It was a very tough problem, even for him.
Tutte worked on different cypher machine, known as the Lorenz cypher. This was the one used by the Nazi high command, including Hitler himself.
It was much more complex than Enigma, and on top of that, the British knew very little about how it worked, whereas with Enigma they knew everything.
So it was a harder problem with less information, and yet Tutte solved it. It was a staggering achievement.
Tutte’s breakthrough was based on careful analysis of intercepted encrypted traffic to identify some periodic behaviour that indicated the size of a “wheel” component in the machine.