What was alan turing contribution to mathematics

Despite producing unconventional answers, Turing did win almost every possible mathematics prize while at Sherborne. In chemistry, a subject which had interested him from a very early age, he carried out experiments following his own agenda which did not please his teacher. Turing's headmaster wrote see for example [ 6 ] :- If he is to stay at Public School, he must aim at becoming educated. If he is to be solely a Scientific Specialist, he is wasting his time at a Public School. 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. He read Einstein 's papers on relativity and he also read about quantum mechanics in Eddington 's The nature of the physical world. An event which was to greatly affect Turing throughout his life took place in He formed a close friendship with Christopher Morcom, a pupil in the year above him at school, and the two worked together on scientific ideas.

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 and the experience was a shattering one to Turing. He had a premonition of Morcom's death at the very instant that he was taken ill and felt that this was something beyond what science could explain. He wrote later see for example [ 6 ] :- It is not difficult to explain these things away - but, I wonder! Despite the difficult school years, Turing entered King's College, Cambridge, in to study mathematics.

This was not achieved without difficulty. Turing sat the scholarship examinations in and won an exhibition, but not a scholarship. Not satisfied with this performance, he took the examinations again in the following year, this time winning a scholarship. In many ways Cambridge was a much easier place for unconventional people like Turing than school had been.

He was now much more able to explore his own ideas and he read Russell 's Introduction to mathematical philosophy in At about the same time he read von Neumann 's text on quantum mechanics, a subject he returned to a number of times throughout his life.

The year saw the beginnings of Turing's interest in mathematical logic. He read a paper to the Moral Science Club at Cambridge in December of that year of which the following minute was recorded see for example [ 6 ] :- A M Turing read a paper on "Mathematics and logic". He suggested that a purely logistic view of mathematics was inadequate; and that mathematical propositions possessed a variety of interpretations of which the logistic was merely one.

Of course was also the year of Hitler's rise in Germany and of an anti-war movement in Britain. Turing joined the anti-war movement but he did not drift towards Marxism, nor pacifism, as happened to many.

Turing graduated in then, in the spring of , he attended Max Newman 's advanced course on the foundations of mathematics. In one sense 'decidability' was a simple question, namely given a mathematical proposition could one find an algorithm which would decide if the proposition was true of false.

For many propositions it was easy to find such an algorithm. The real difficulty arose in proving that for certain propositions no such algorithm existed. When given an algorithm to solve a problem it was clear that it was indeed an algorithm, yet there was no definition of an algorithm which was rigorous enough to allow one to prove that none existed. Turing began to work on these ideas. Turing was elected a fellow of King's College, Cambridge, in 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 Turing was a Smith's Prizeman. Turing's achievements at Cambridge had been on account of his work in probability theory.

However, he had been working on the decidability questions since attending Newman 's course. In he published On Computable Numbers, with an application to the Entscheidungsproblem. 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.

Turing wrote [ 13 ] :- Some of the symbols written down will form the sequences of figures which is the decimal of the real number which is being computed. The others are just rough notes to "assist the memory".

It will only be these rough notes which will be liable to erasure. He defined a computable number as real number whose decimal expansion could be produced by a Turing machine starting with a blank tape. He then described a number which is not computable and remarks that this seems to be a paradox since he appears to have described in finite terms, a number which cannot be described in finite terms. Yet Turing's halting problem is regarded as the more intuitive and easier to understand.

For many years, even before the Second World War, the German military had been using a cipher machine to encrypt their secret message, a machine called Enigma. The Enigma machine was about the size of a typewriter, except instead of having a carriage and paper like a normal typewriter it had a second set of letters that lit up; this was called the lampboard. Typing a message on the keyboard resulted in letters lighting up on the lampboard, so if you pressed 'A' on the keyboard, the letter 'H' might then light up on the lampboard - this was your code!

The Enigma Machine was essentially a simple circuit, connecting a battery to a bulb. Pressing a key on the keyboard would complete a circuit, and illuminate a letter on the lampboard. The standard Enigma Machine had over million million million daily settings, but this is not why Enigma was so hard to break.

Inside, Enigma contained three moving parts, called rotors. These rotors would turn after pressing a key, making the wires of the circuit rotate, thus changing the circuit completely.

So if you now pressed 'A' for a second time it may not be the same letter as before. Double letters, for example, may not become double letters in the code. It was these rotors that made Enigma so difficult to break. Turing's contribution to the effort at Bletchley Park was indispensible. 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, designed a machine to break Enigma.

This code breaking machine was called the Bombe, a name chosen to honour the earlier Polish code breaking machine called Bomba. The Bombe worked using the mathematical principle of contradiction. Given an Enigma code, the code breakers would try and guess a short phrase, or 'crib', that might appear in the message. They would input this guess into the Bombe and, if this input did not result in a valid Enigma code, it would be rejected. However, if left to continue, all other deductions made by the Bombe Machine were then equally invalid, and so could all be rejected at once as fruit of the poison tree.

On a good day, the Bombe machine could find the Enigma setting in 15 minutes. In Turing received an OBE for his work at Bletchley Park, even though the work remained top secret for another 30 years. Now working at Manchester University, Turing continued to make significant contributions in computing until his death in Alan Turing was gay at a time when it was illegal to be gay.

Turing was made to choose between going to jail or undergoing hormonal treatment intended to reduce his libido. He chose the latter. Turing was found dead on 8 June , as a result of cyanide poisoning. His death was ruled a suicide. Often considered the father of modern computer science, Alan Turing was famous for his work developing the first modern computers, decoding the encryption of German Enigma machines during the second world war, and detailing a procedure known as the Turing Test, forming the basis for artificial intelligence.

Key facts Full name : Alan Mathison Turing Birth : 23 June , Maida Vale, London Death : 7 June , Wilmslow, Cheshire Often considered the father of modern computer science, Alan Turing was famous for his work developing the first modern computers, decoding the encryption of German Enigma machines during the second world war, and detailing a procedure known as the Turing Test, forming the basis for artificial intelligence.

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