**Alan Turing**'s work was fundamental in the theoretical foundations of computer science.

- Alan was sent to school but did not seem to be obtaining any benefit so he was removed from the school after a few months.
- Now 1926 was the year of the general strike and when the strike was in progress Turing cycled 60 miles to the school from his home, not too demanding a task for Turing who later was to become a fine athlete of almost Olympic standard.
- Many of the most original thinkers have found conventional schooling an almost incomprehensible process and this seems to have been the case for Turing.
- Despite producing unconventional answers, Turing did win almost every possible mathematics prize while at Sherborne.
- This says far more about the school system that Turing was being subjected to than it does about Turing himself.
- However, Turing learnt deep mathematics while at school, although his teachers were probably not aware of the studies he was making on his own.
- An event which was to greatly affect Turing throughout his life took place in 1928.
- Perhaps for the first time Turing was able to find someone with whom he could share his thoughts and ideas.
- However Morcom died in February 1930 and the experience was a shattering one to Turing.
- Turing sat the scholarship examinations in 1929 and won an exhibition, but not a scholarship.
- In many ways Cambridge was a much easier place for unconventional people like Turing than school had been.
- The year 1933 saw the beginnings of Turing's interest in mathematical logic.
- Turing joined the anti-war movement but he did not drift towards Marxism, nor pacifism, as happened to many.
- Turing graduated in 1934 then, in the spring of 1935, he attended Max Newman's advanced course on the foundations of mathematics.
- Turing began to work on these ideas.
- Turing was elected a fellow of King's College, Cambridge, in 1935 for a dissertation On the Gaussian error function which proved fundamental results on probability theory, namely the central limit theorem.
- Although the central limit theorem had recently been discovered, Turing was not aware of this and discovered it independently.
- In 1936 Turing was a Smith's Prizeman.
- Turing's achievements at Cambridge had been on account of his work in probability theory.
- It is in this paper that Turing introduced an abstract machine, now called a "Turing machine", which moved from one state to another using a precise finite set of rules (given by a finite table) and depending on a single symbol it read from a tape.
- The Turing machine could write a symbol on the tape, or delete a symbol from the tape.
- He defined a computable number as real number whose decimal expansion could be produced by a Turing machine starting with a blank tape.
- However, Turing understood the source of the apparent paradox.
- It is impossible to decide (using another Turing machine) whether a Turing machine with a given table of instructions will output an infinite sequence of numbers.
- Turing's approach is very different from that of Church but Newman had to argue the case for publication of Turing's paper before the London Mathematical Society would publish it.
- Turing's revised paper contains a reference to Church's results and the paper, first completed in April 1936, was revised in this way in August 1936 and it appeared in print in 1937.
- A good feature of the resulting discussions with Church was that Turing became a graduate student at Princeton University in 1936.
- At Princeton, Turing undertook research under Church's supervision and he returned to England in 1938, having been back in England for the summer vacation in 1937 when he first met Wittgenstein.
- Before this paper appeared, Turing published two other papers on rather more conventional mathematical topics.
- Perhaps the most remarkable feature of Turing's work on Turing machines was that he was describing a modern computer before technology had reached the point where construction was a realistic proposition.
- Although to Turing a "computer" was a person who carried out a computation, we must see in his description of a universal Turing machine what we today think of as a computer with the tape as the program.
- While at Princeton Turing had played with the idea of constructing a computer.
- When war was declared in 1939 Turing immediately moved to work full-time at the Government Code and Cypher School at Bletchley Park.
- Turing's brilliant ideas in solving codes, and developing computers to assist break them, may have saved more lives of military personnel in the course of the war than any other.
- Together with another mathematician W G Welchman, Turing developed the Bombe, a machine based on earlier work by Polish mathematicians, which from late 1940 was decoding all messages sent by the Enigma machines of the Luftwaffe.
- The Enigma machines of the German navy were much harder to break but this was the type of challenge which Turing enjoyed.
- By the middle of 1941 Turing's statistical approach, together with captured information, had led to the German navy signals being decoded at Bletchley.
- From November 1942 until March 1943 Turing was in the United States liaising over decoding issues and also on a speech secrecy system.
- Turing was not directly involved with the successful breaking of these more complex codes, but his ideas proved of the greatest importance in this work.
- Turing was awarded the O.B.E. in 1945 for his vital contribution to the war effort.
- At the end of the war Turing was invited by the National Physical Laboratory in London to design a computer.
- Turing's design was at that point an original detailed design and prospectus for a computer in the modern sense.
- Turing returned to Cambridge for the academic year 1947-48 where his interests ranged over many topics far removed from computers or mathematics; in particular he studied neurology and physiology.
- By 1948 Newman was the professor of mathematics at the University of Manchester and he offered Turing a readership there.
- Turing resigned from the National Physical Laboratory to take up the post in Manchester.
- The expectation was that Turing would lead the mathematical side of the work, and for a few years he continued to work, first on the design of the subroutines out of which the larger programs for such a machine are built, and then, as this kind of work became standardised, on more general problems of numerical analysis.
- In 1950 Turing published Computing machinery and intelligence in Mind.
- Turing's view, expressed with great force and wit, was that it was for those who saw an unbridgeable gap between the two to say just where the difference lay.
- Turing did not forget about questions of decidability which had been the starting point for his brilliant mathematical publications.
- Turing thought at first that he had proved the same result for groups but, just before giving a seminar on his proof, he discovered an error.
- Boone used the ideas from this paper by Turing to prove the existence of a group with insoluble word problem in 1957.
- Turing was elected a Fellow of the Royal Society of London in 1951, mainly for his work on Turing machines in 1936.
- Turing was arrested for violation of British homosexuality statutes in 1952 when he reported to the police details of a homosexual affair.
- With the cold war this became an important operation and Turing continued to work for GCHQ, although his Manchester colleagues were totally unaware of this.
- A holiday which Turing took in Greece in 1953 caused consternation among the security officers.
- Turing died of potassium cyanide poisoning while conducting electrolysis experiments.

Born 23 June 1912, London, England. Died 7 June 1954, Wilmslow, Cheshire, England.

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Algebra, Analysis, Group Theory, Origin England

**Oâ€™Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive