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 Sherbourne in Dorset. Displaying a precocious talent at school for math
and science including condensing Einstein'sTheory 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 and ambition 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 Camb 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 cypher school the UK's code breakers. 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
present 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 this 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 the Allied
code breakers. Code-breaking 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
the 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 bombe 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 bombe machine could find an enigma
setting in fifteen 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 path Touring's death. Today historians
believe that the work of the code breakers 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 continue 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 toing was gay at a time when it was illegal to be
gay. On discovering the truth about his sexuality the authorities forced toeing
to endure horrific hormone treatment he was labeled as a security risk and he
lost his job as a codebreaker. In the end towing 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.