Turing was conceived in 1911 in Chatrapur, India. His father Julius Mathison Turing was a member of the Indian Civil Service. Julius and wife Ethel (née Stoney) wanted Alan to be born in Britain, so they returned to Paddington where Alan was eventually born. His father's Indian Civil Service commission was still active, and during Turing's childhood years his father travelled between England and India, leaving his family to stay with friends in England due to concerns over the dangers of the British colony. Very early in life, Turing early showed signs of the genius he was to display more prominently later. He is said to have taught himself to read in three weeks, and to have shown an early affinity for numbers and puzzles.
His parents enrolled him at St. Michael's, a day school, at six years of age. The headmistress recognised his genius early on, as did many of his subsequent educators at Marlborough College (a public school). At Marlborough, he first reported having problems with bullies. In 1926, and at the age of 14, he went on to the Sherborneboarding school in Dorset. His first day of term coincided with a general strike in England, and so determined was he to attend his first day that he rode his bike unaccompanied over sixty miles from Southampton to school, stopping overnight at an inn — a feat reported in the local press.
Turing's natural inclination toward the sciences did not earn him respect with the teachers and administrators at Sherborne, whose definition of education placed more emphasis on the classics rather than the area of science. But despite this, Turing continued to show remarkable ability in the studies he loved, solving advanced (for his age) problems in 1927 without having even studied elementary calculus.
In 1928, aged sixteen, Turing encountered Albert Einstein's work, and not only did he grasp it, but he extrapolated Einstein's Law of Motion from a text in which it was never made explicit.
In his momentous paper "On Computable Numbers, with an Application to the Entscheidungsproblem" (submitted on May 28, 1936), Turing reformulated Kurt Gödel's 1931 results on the limits of proof and computation, substituting Gödel's universal arithmetics-based formal language by what are now called Turing machines, formal and simple devices. He proved that such a machine would be capable of performing any conceivable mathematical problem if it were representable as an algorithm, even if no actual Turing machine would be likely to have practical applications, being much slower than alternatives. Turing machines are to this day the central object of study in computational theory. He went on to prove that there was no solution to the Entscheidungsproblem by first showing that the halting problem for Turing machines is unsolvable: it is not possible to algorithmically decide whether a given Turing machine will ever halt. While his proof was published subsequent to Alonzo Church's equivalent proof in respect to his lambda calculus, Turing's work is considerably more accessible and intuitive. It was also novel in its notion of a "Universal (Turing) Machine", the idea that such a machine could perform the tasks of any other machine. The paper also introduces the notion of definable numbers.
Most of 1937 and 1938 he spent at Princeton University, studying under Alonzo Church. In 1938 he obtained his Ph.D from Princeton; his dissertation introduced the notion of hypercomputation where Turing machines are augmented with so-called oracles, allowing a study of problems that cannot be solved algorithmically.
Back in Cambridge in 1939, he attended lectures by Ludwig Wittgenstein about the foundations of mathematics. The two argued and disagreed vehemently, with Turing defending formalism and Wittgenstein arguing that mathematics is overvalued and does not discover any absolute truths.
During the World War II he was a major participant in the efforts at Bletchley Park on cracking Nazi cyphers. He contributed several mathematical insights, both to breaking the Enigma cypher machine and the Fish teletype cyphers (teletype cypher machines made by both Lorenz Electric and Siemens & Halske). The Fish insights were useful in the development of the first digital programmable electronic computerColossus, which was designed by Max Newman and team, and built at the Post Office Research Station at Dollis Hill by a team led by Thomas Flowers in 1943. It was used to crack Fish cyphers (in particular the Lorenz machine traffic). Turing also helped design the "Bombes", advanced versions of Polish Rejewski's "Bomba" machine used to assist in finding keyss for Enigma messages. These were electromechanical devices coupling several "Enigma machine clones" which were able to eliminate at high speed large numbers of possible key settings for Enigma messages.
Turing's work on breaking the Enigma cypher was kept secret until the 1970s; not even his close friends knew about it.
In 1952 Turing wrote a chess program. Lacking a computer powerful enough to execute it, he himself simulated the computer, taking about half an hour per move. One game was recorded; the program lost to a colleague of Turing.
Prosecution of Turing for his homosexuality crippled his career. In 1952, his male lover helped an accomplice to break into Turing's house and commit larceny. Turing went to the police to report the crime. As a result of the police investigation, Turing was said to have had a sexual relationship with a 19 year old man, and Turing was charged with "gross indecency and sexual perversion". He unapologetically offered no defence, and was convicted. Following the well-publicised trial, he was given a choice between incarceration and libido-reducing hormonaltreatment. He chose the estrogen hormone injections, which lasted for a year, with side effects including the development of breasts during that period. In 1954, he died of cyanidepoisoning, apparently from a laced apple he left half eaten. Most believe that his death was intentional, and the death was ruled a suicide. His mother, however, strenuously argued that the ingestion was accidental due to his careless storage of laboratory chemicals.