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Historical Profile - Alan Turing
By Hayden Tronnolone
Figure 1: Alan Mathison Turing. Photo by Elliott
and Fry. c National Portrait Gallery, London.
Reproduced under an academic licence.
Alan Mathison Turing is one of the most important
figures in 20th century mathematics. He was instrumental in developing techniques to break German codes during the Second World War and is often credited with bringing the conflict to an early
finish. He made significant contributions to the
study of computation and computer science, such
as developing some of the first electronic computers, and also introduced fundamental new ideas to
mathematical biology. Despite his wartime e↵orts,
his exceptional life ended with him labelled a crim-
inal by his own government due to an unjust and
antiquated law.
Turing was born in London on the 23rd of
June, 1912. From an early age he showed signs
of great potential, often ignoring the instructions
of his teachers in order to pursue his own more advanced studies. His headmaster reported that Turing’s mathematical abilities were “not very good.
He spends a great deal of time in investigations
in advanced mathematics to the neglect of his elementary work.” Similar sentiments were expressed
regarding Turing’s work in science; in particular his
studies of chemistry.
While at school Turing also displayed his great
athletic skill. On the day he was due to leave for
his first day at boarding school a strike resulted
in the closure of all public transport. Turing took
the opportunity to ride his bike instead, a trip of
around 95 kilometres. Later in life he would continue to cycle long distances and would participate
in the marathon, a footrace 42 kilometres long.
Despite his talents, Turing’s individual thinking almost resulted in expulsion from boarding
school. His lack of interest in French was described
by one teacher as “. . . very depressing except when
something amuses him”. Turing, however, would
often ignore his teachers all term and still manage
to top his class his exams. His headmaster was
critical of Turing’s interest in science and mathematics, suggesting that “If he is to be solely a Scientific Specialist, he is wasting his time at a public
school.”
Unperturbed by his teachers, Turing maintained an interest in science and by the age of 16
was reading Einstein’s work on relativity. He sat
a university scholarship exam in 1929 and received
an award worth less financially than a full scholarship. Unsatisfied with the result and at the suggestion of his father, he rejected the o↵er and sat the
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exam again in 1931. This time he earnt a full scholarship and commenced an undergraduate degree in
mathematics at King’s College, Cambridge. Turing graduated in 1934 and the following year was
elected a fellow of the same college for his work in
statistics.
During his time at Cambridge Turing began to
study computation and mathematical logic. In order to formalise the theory of computation he developed the idea of a Turing machine, which is a
hypothetic computer able to perform computations
that could be described by an algorithm. Turing’s
ideas, although abstract at the time, would lead to
the development of modern computers.
In 1938 Turing began to work part-time as a
cryptanalyst (a code breaker) at the Government
Code and Cypher School (GC & CS). One year after commencing his employment Britain declared
war on Germany, following which Turing immediately took up a full-time position at the GC & CS
wartime workshop at Bletchley Park. He focused
on trying to decipher messages encoded by German Enigma machines, which employed a system
of mechanical rotors and leads to encode messages.
These could be set in over 1020 di↵erent combinations that were usually changed daily, making
the Enigma codes almost impossible to break by
hand. Studying ideas from Polish cryptanalysts
he developed an electromechanical device known
as a bombe that could take fragments of a coded
message, along with guesses for some of the words,
and use this to determine the likely Enigma encryption settings. Turing also developed the statistical procedures that could guide the operation
of the bombe. Such were Turing’s contributions
that Jerry Roberts, a college of Turing at Bletchley Park, has stated that that “without him, I, and
many people are convinced that we would have lost
the war.” Winston Churchill, British Prime Minister during World War II, has even suggested that
Turing made the single biggest contribution to the
war against Germany. Despite receiving an OBE
in 1945 in recognition of his services much of his
work was classified by the British Government and
his accomplishments were hidden from the public.
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Two articles he wrote while at Bletchley Park remained unpublished until as late as 2012.
Following the war, Turing made many other
important contributions to mathematics and computer science. He was instrumental in designing
the first computers to use electronic memory and
the software they ran on. He introduced the Turing
test for artificial intelligence, which specifies that
a machine should be considered intelligent if a human in conversation with the machine could not
tell it apart from another human. This test is still
in use today. Turing’s interest in mathematical biology led him to study morphogenesis (the process
by which an organism develops its shape) and pattern formation. He proposed a reaction-di↵usion
model for these processes, referred to as the Turing
mechanism, that would become one of the leading
theories for the cause of these phenomena. He is
also notable for devising the LU (lower upper) factorisation method for matrices, still taught today
in undergraduate courses on numerical methods.
The triumph of Turing’s achievements would be
equalled in magnitude by the atrocious events that
would befall him during his final years. In 1952,
a time in which homosexual acts were illegal in
Britain, Turing began a relationship with Arnold
Murray. Soon afterwards Turing’s house was burgled by an acquaintance of Murray’s. When Turing reported this incident to the police he revealed
the relationship, claiming that the homosexuality
laws would soon be repealed. No such change to
the laws occurred and both men were charged with
gross indecency. Turing was found guilty and allowed to choose between imprisonment or chemical castration, which involved injections of synthetic oestrogen. Turing chose the latter, which
took a significant toll upon his health. He conviction meant he was no longer allowed to work in
his government cryptanalysis job and he was also
denied entry to the USA where he had been working on a secure speech device for sending encrypted
messages.
On the 8th of June, 1954, two years after his
conviction, Turing died of cyanide poisoning alone
in his house. A half-eaten apple was found next to
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him and it was suspected that he had committed
suicide by lacing the apple with poison, despite the
apple never being tested for cyanide. It has been
suggested that his death was not suicide but rather
accidental as Turing often used cyanide in his home
laboratory. Whatever the true cause, Turing died
a convicted criminal, the victim of heinous laws
and disgraceful prejudices, and shunned by his own
government: an ignoble and shameful end to the
life of any person, let alone one who had contributed so much.
Following a 2009 petition, British Prime Minister Gordon Brown issued an apology to Turing, with the concise acknowledgement that “we’re
sorry, you deserved so much better.” Further
petitions called for Turing to receive a full pardon; however, these were met with legal arguments
that delayed the process. The British Government
eventually appealed directly to the Queen who, in
December, 2013, issued Turing a full pardon.
Through his mathematical insight, Alan Turing helped to end the War in Europe and save
uncountable lives. He introduced several fundamental ideas in computer science and also made
significant contributions to mathematical biology.
Turing’s contributions to mathematics were so profound that they are still taught in undergraduate
courses. It is of the greatest shame that he was
judged not for his work but rather his personal relationships and, worse still, was punished severely
for them. Turing was betrayed by the country
he had saved and soon after su↵ered an untimely
death that robbed the world of his talents and fu-
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ture contributions. While he will never hear the
apologies made and we can never undo his su↵ering, we can continue to marvel at his contributions
and remember his plight in the hope that it will
serve to eradicate the homophobia that still prevails and prevent us from repeating the mistakes
of the past. Let us never forget Turing.
Hayden has stopped counting the years of his PhD.
References
Elliott, J. J. and Fry, C. E. (1951), ‘Alan
Mathison Turing’, http://www.npg.org.uk/
collections/search/portrait/mw63680/
Alan-Mathison-Turing, accessed February
2014.
Hodges, A. (1992), Alan Turing: The Enigma,
Vintage.
Legh, H. (2009), “‘without him — we would
have lost the war”’, http://www.bbc.co.uk/
threecounties/content/articles/2009/09/
07/captain_jerry_roberts_feature.shtml,
accessed February 2014.
Spencer, C. (2009), ‘Profile: Alan turing’, http://
news.bbc.co.uk/2/hi/uk_news/8250592.stm,
accessed February 2014.
Turing, S. S. (1959), Alan M. Turing, Cambridge
Eng. W. He↵er.