In its purest form, mathematics is the search for truth. It's the solution to the problem. This year is a special year for me and other mathematicians like me as it marks 100 years since the birth of Alan Turing who possessed perhaps one of the greatest mathematical minds of the 20th century. Turing was a mathematician, cryptographer and pioneer of computer science, whose life was one of secret triumphs shadowed by public tragedy. Perhaps known today for his part in breaking the German Enigma Code during World War II, Turing was by that time already established as a mathematician of extraordinary capability.
Born on the 23rd of June 1912, Turing spent his childhood split between Hastings in Kent and Sherborne in Dorset. displaying a precocious talent at school for maths and science, including condensing Einstein's theory of relativity for his mum at the age of 15. Turing's abilities led him to receiving a scholarship at King's College, Cambridge. He arrived here to study as an undergraduate in 1931. Like many great minds, Turing was never happier than when he had a problem to solve.
And in keeping with the exceptional skill that I'm he had already displayed, he turned his attentions to the decision problem, or Entscheidungsproblem in German. Laid out by the legendary German mathematician David Hilbert at the turn of the century, the problem was one of the most important unsolved mathematical challenges for the 20th century. It was here in the spring of 1935, by the flow of the River Cam at Grantchester Meadows in Cambridge, that Turing, decided to take on the giants of mathematics at the time.
Turing conceived of a hypothetical machine that reads symbols on a strip of tape, rewriting or deleting them based on a finite set of rules. In fact, originally, Turing described a person slavishly performing these operations. He called this person the computer.
Given a problem to compute, this machine would either stop, and give you the answer, or run forever if the answer doesn't exist. Turing mathematically proved that you can never know if and when the machine will stop. He did this by creating the definitive example of the undecidable problem, an astounding feat that disproved Hilbert's question of decidability, showing that dark areas in mathematics will always remain a barrier to complete truth. The imagined Turing machine model went on to become one of the cornerstones of computer science and is arguably one of the most influential mathematical abstractions of the 20th century.
And Turing was only 22. Returning to Cambridge following time at Princeton, Turing began working for the Government Code and Cipher School, the UK's codebreakers. For many years before the Second World War, the German military had been using a cipher machine called Enigma to encrypt their secret messages. About the size of a typewriter, an Enigma machine has a second set of letters that light up, called the lamp board.
If you press a letter on the keyboard, the machine generates a different letter to represent it on the lamp board, creating the code. The standard Enigma machine had over 150 million, million, million possible daily settings. Inside an Enigma are three rotors which turn after pressing a key, making the wires of the circuit rotate, thus changing the circuit completely.
So pressing the same letter will generate a different result. Double letters for example may not become double letters in the code. Enigma posed a formidable challenge for that.
the Allied codebreakers. Codebreaking is a battle of mathematical wits and cunning, and during wartime the stakes are high. Turing relished such challenges.
A day after the UK declared war with Germany, he reported to Bletchley Park for work on breaking the German Enigma cipher. Turing's contribution to the codebreakers was quite simply vital to the war effort. Not only did he make the first breakthroughs with the naval Enigma code, allowing Britain's food and supplies to be shipped across the Atlantic, but along with Gordon Welchman, he designed a machine to smash the German Enigma code, called the Bomb, named for an earlier Polish code-breaking machine.
By using the fact that the German codes often contained a common phrase, such as those found in weather reports, the code breakers would try and guess a short phrase or crib that might appear in an enigma message. They would input this guess into the bomb, designed to perform a sweep of the myriad ways in which an enigma machine could have been set up. By using the principle of contradiction combined with extraordinary mathematical insight, the codes were eroded and eventually cracked. On a good day the bomb machine could find an enigma setting in 15 minutes. In 1945, Turing received an OBE for services to the Foreign Office, though the real reason for this honour remained top secret for another 30 years, long past Turing's death.
Today, historians believe that the work of the codebreakers shortened the war by two years, and in doing so, saved countless lives. Following the war, Turing went on to work at the University of Manchester. and continued to make hugely significant contributions to computing and later biology until his death in 1954. He is credited with laying the foundations for computer technology and artificial intelligence and worked on the first recognisable modern computers. In September 2009, 55 years after his death, the British government made a public apology to Alan Turing.
Turing was gay, at a time when it was illegal to be gay. On discovering the truth about his sexuality, the authorities forced Turing to endure horrific hormone treatment. He was labelled as a security risk, and he lost his job as a codebreaker.
In the end, Turing committed suicide by biting from an apple laced with cyanide. A desperately sad end to the life of a genius. Today we live in a world...
dominated by computer technology. From cars to smartphones, desktops to rockets, life in the 21st century is almost unimaginable without computers. They facilitate our existence. For Alan Turing, hero of Bletchley Park and father of computer science, this was never the aim or even the point.
He cared about filling the gaps in our knowledge, about finding the light, the truth. The solution to the problems.