Alan Matheson Turing (1912 - 1954)
R. Ramanujam, The Institute of Mathematical Sciences, Chennai

The twentieth century saw some amazing inventions, many new products of science and technology. But among them all, if there is one single invention that entirely changed the modern world, reshaped it, and reached a major part of humanity, it would be the digital computer. The telecommunication revolution would not have taken place without computers either. For all that, the person who gave us the digital computer never got to see computers as we know them. But he was convinced nonetheless of its tremendous capability: so much so, he also founded the area of artificial intelligence that tries to build computers which show human-like intelligence.
This year is the birth centenary of that very interesting man, Alan Matheson Turing, a British mathematician, who not only founded computer science, but also played a very important role for Britain in the second world war. Yet he died a tragic death at the age of 42.
Alan Turing was in fact conceived in our city, Madras as it was called then. His father Julius Turing worked in the Indian Civil Service. However, Alan's mother moved to England before he was born in July 1912, and Alan Turing never visited India. But with his parents living in India, Alan was brought up in a series of foster homes, which contributed to making him a loner later in life.
At school, Alan Turing showed great interest in science, especially in Chemistry, an interest to which he was to return towards the end of his life. In his teen years, he was fascinated by Eddington's book "The nature of the physical world" and Einstein's relativity theory.
At the age of 21, Turing proved the Central Limit Theorem on his own, not having realised that it was a cornerstone of modern mathematics. This earned him a prestigious Fellowship in King's College in 1935. At this time he started reading von Neumann's book on the foundations of quantum mechanics and the Principia Mathematica of Bertrand Russell and A N Whitehead.
One passion that Turing developed in Cambridge was for long distance running, something he relished till the end of his life. Indeed, only a minor injury prevented him from being part of the British runners' team in the 1948 London Olympics.
At King's, Turing attended a lecture course by the topologist Newman, in which Newman discussed Goedel's incompleteness theorem: this was a statement that Goedel had proved only in 1931, showing that in any inference system for arithmetic, there would always be true sentences that would not be provable in the system. Newman also mentioned that the so-called Entscheidungsproblem, posed by Hilbert, lay open. This question asked: is there a method by which it could be decided whether every mathematical question stated in logic was provable? 
Turing was greatly intrigued by this question. Like many others, he too thought the answer must be negative, but what he found intriguing was this: what does method mean? How can one mathematically define a vague notion like method? And that is precisely what Turing did, and in the process came up with a notion of an algorithm that can be executed by a machine. That machine is what we call the digital computer.
Once Turing had the definition on hand, he could show that no method existed that could decide whether every mathematical question stated in logic was provable. He just needed to show that no machine of his kind could do this.
When Turing was ready with the result in April 1936, he went and showed it to Newman with great enthusiasm. He was in for a shock: Newman had just then received an article from a famous American logician, Alonzo Church, proving just that same negative result. It took a few months to check that Turing's approach was original and different, and his paper was published in August 1936.
Alan Turing's paper was a masterstroke of creativity. In one single article, he achieved much:
-- He defined a mathematical model of computation.
-- He showed its limitations.
-- He demonstrated how it captured any intuitive notion of method or procedure.
-- He showed its universality, by building a machine that could simulate every machine of its kind.
-- He gave an application, answering Hilbert's question.
This model, which we call the Turing machine, offers a physically realizable device that acts on logical instructions and embodies the action of the mind. Goedel, who had offered his own notion of effective procedure but was not satisfied with it, said Turing's idea was immediately convincing.
Turing went to Princeton in the USA to work with Alonzo Church for his Ph. D. thesis, getting the degree in 1938. Back at King's in Cambridge, he joined the war effort and moved to Bletchley Park to work on codes used by the military for communications.
In 1940, Turing and a Polish mathematician Welchmann came up with a way to break the codes used by the German Air Force. The German Navy used the Enigma machine which was much harder to break: Turing managed to do so in 1943, which played a critical role for the Allied invasion of Normandy in 1944.
By the time the war was over, Turing was convinced of three key ideas: 
(1) He realised that his 1936 concept of universal machine was not only correct, but was the best way to build one.
(2) The potential speed and reliability of electronics would make the machine very capable.
(3) Designing different machines for different logical processes was wasteful and inefficient; `programming' a general purpose machine would be much better. He conceived of a single machine capable of handling *any* programmed task. 
Unfortunately Turing could not get money to build the computer he wanted to, and the Americans built the first machine. Turing moved to Manchester (from Cambridge) in May 1948.
In Manchester he started working on networks of neurons. He wrote an
article titled "Computing machinery and intelligence" that begins with
the sentence: "Can a machine think?" This is the paper that initiated the study of machine intelligence.
In 1950 Turing started his work on mathematics of morphogenesis. His paper on this had a great influence on developmental biology. Turing was fascinated by the question of why a leopard has spots all over, but not on its tail. He came up with a theory of diffusion reaction that allows for processes which proceed uniformly but are self-limiting, by purely mathematical means. It is sad that Turing could write only one paper on the subject, though it was path-breaking in itself.
In 1951, Alan Turing was elected Fellow of the Royal Society, a great honour for a British academician.
For all his accomplishments, Turing was lonely and depressed in his private life. On June 8, 1954, he was found dead at home by his cleaner. The death was declared to be accidental, due to cyanide poisoning, referring to Turing's amateur work in Chemistry.
Thus ended a short life, but one which had immeasurable impact on code breaking, computer science and biology.