Alan Mathison Turing, OBE, FRS ( /ˈtjʊərɪŋ/ TEWR-ing; 23 June 1912 – 7 June 1954), was an English mathematician, logician, cryptanalyst, and computer scientist. He was highly influential in the development of computer science, providing a formalisation of the concepts of "algorithm" and "computation" with the Turing machine, which played a significant role in the creation of the modern computer.^[1][2] Turing is widely considered to be the father of computer science and artificial intelligence.^[3]

During the Second World War, Turing worked for the Government Code and Cypher School (GCCS) at Bletchley Park, Britain's codebreaking centre. For a time he was head of Hut 8, the section responsible for German naval cryptanalysis. He devised a number of techniques for breaking German ciphers, including the method of the bombe, an electromechanical machine that could find settings for the Enigma machine.

After the war he worked at the National Physical Laboratory, where he created one of the first designs for a stored-program computer, the ACE. In 1948 Turing joined Max Newman's Computing Laboratory at Manchester University, where he assisted in the development of the Manchester computers^[4] and became interested in mathematical biology. He wrote a paper on the chemical basis of morphogenesis,^[5] and he predicted oscillating chemical reactions such as the Belousov–Zhabotinsky reaction, which were first observed in the 1960s.

Turing's homosexuality resulted in a criminal prosecution in 1952, when homosexual acts were still illegal in the United Kingdom. He accepted treatment with female hormones (chemical castration) as an alternative to prison. He died in 1954, just over two weeks before his 42nd birthday, from cyanide poisoning. An inquest determined it was suicide; his mother and some others believed his death was accidental. On 10 September 2009, following an Internet campaign, British Prime Minister Gordon Brown made an official public apology on behalf of the British government for the way in which Turing was treated after the war.^[6]

Childhood and youth[link]

Turing was conceived at Chhatrapur, Orissa, then part of British India.^[7][8] His father, Julius Mathison Turing, was a member of the Indian Civil Service. He and his wife Ethel Sara Stoney (1881–1976), daughter of Edward Waller Stoney, chief engineer of the Madras Railways, wanted their children to be brought up in England, so they returned to Maida Vale,^[9] London, where Turing was born on 23 June 1912, as recorded by a blue plaque on the outside of the house of his birth,^[10] later the Colonnade Hotel.^[7][11] He had an elder brother, John. His father's civil service commission was still active, and during Turing's childhood years his parents travelled between Hastings, England^[12] and India, leaving their two sons to stay with a retired Army couple. Very early in life, Turing showed signs of the genius he was later to display prominently.^[13]

His parents enrolled him at St Michael's, a day school at 20 Charles Road, St Leonards-on-Sea, at the age of six. The headmistress recognised his talent early on, as did many of his subsequent educators. In 1926, at the age of 14, he went on to Sherborne School, a famous independent school in the market town of Sherborne in Dorset. His first day of term coincided with the 1926 General Strike in Britain, but so determined was he to attend his first day that he rode his bicycle unaccompanied more than 60 miles (97 km) from Southampton to school, stopping overnight at an inn.^[14]

King's College, Cambridge, where the computer room is named after Turing, who became a student there in 1931 and a Fellow in 1935

Turing's natural inclination toward mathematics and science did not earn him respect with some of the teachers at Sherborne, whose definition of education placed more emphasis on the classics. His headmaster wrote to his parents: "I hope he will not fall between two stools. 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".^[15] Despite this, Turing continued to show remarkable ability in the studies he loved, solving advanced problems in 1927 without having even studied elementary calculus. In 1928, aged 16, Turing encountered Albert Einstein's work; not only did he grasp it, but he extrapolated Einstein's questioning of Newton's laws of motion from a text in which this was never made explicit.^[16]

At Sherborne Turing formed a friendship with fellow pupil Christopher Morcom. This friendship, cut short by Morcom's death in February 1930 from complications of bovine tuberculosis (contracted after drinking infected cow's milk some years previously), would provide inspiration for Turing's future achievements.^{[17] [18]} Turing's religious faith was shattered by Morcom's death and he became an atheist. He adopted the conviction that all phenomena, including the workings of the human brain, must be materialistic,^[19] but he still believed in the survival of the spirit after death.^[20]

University and work on computability[link]

Alan Turing memorial statue in Sackville Park, Manchester

After Sherborne, Turing went to study at King's College, Cambridge. He was an undergraduate there from 1931 to 1934, graduating with first-class honours in Mathematics. In 1935, at the young age of 22, he was elected a fellow at King's on the strength of a dissertation in which he proved the central limit theorem,^[21] despite the fact that he had failed to find out that it had already been proved in 1922 by Jarl Waldemar Lindeberg.^[22]

In 1928, German mathematician David Hilbert had called attention to the Entscheidungsproblem (decision problem). In his momentous paper "On Computable Numbers, with an Application to the Entscheidungsproblem" (submitted on 28 May 1936 and delivered 12 November),^[23] Turing reformulated Kurt Gödel's 1931 results on the limits of proof and computation, replacing Gödel's universal arithmetic-based formal language with what became known as Turing machines, formal and simple hypothetical devices. He proved that some such machine would be capable of performing any conceivable mathematical computation if it were representable as an algorithm. He went on to prove that there was no solution to the Entscheidungsproblem by first showing that the halting problem for Turing machines is undecidable: in general, it is not possible to decide algorithmically, whether a given Turing machine will ever halt.

While his proof was published shortly after Alonzo Church's equivalent proof in respect of his lambda calculus, Turing was unaware of Church's work at the time that he developed it.^[24] Turing's approach is considerably more accessible and intuitive than Church's. It was also novel in its notion of a 'Universal Machine' (now known as a Universal Turing machine), with the idea that such a machine could perform the tasks of any other machine, or in other words, is provably capable of computing anything that is computable. Turing machines are to this day a central object of study in theory of computation. In his memoirs Turing wrote that he was disappointed about the reception of this 1936 paper, which also introduced the notion of definable numbers, and that only two people had reacted – these being Heinrich Scholz and Richard Bevan Braithwaite.^{[citation needed]}

From September 1936 to July 1938 he spent most of his time at the Institute for Advanced Study, Princeton, New Jersey, studying under Alonzo Church. In addition to his purely mathematical work, he studied cryptology and also built three of four stages of an electro-mechanical binary multiplier.^[25] In June 1938 he obtained his PhD from Princeton University; his dissertation (Systems of Logic Based on Ordinals^[26]) introduced the concept of ordinal logic and the notion of relative computing, where Turing machines are augmented with so-called oracles, allowing a study of problems that cannot be solved by a Turing machine.

Back in Cambridge, he attended lectures by Ludwig Wittgenstein about the foundations of mathematics.^[27] The two argued and disagreed, with Turing defending formalism and Wittgenstein arguing that mathematics does not discover any absolute truths but rather invents them.^[28] He also started to work part-time with the Government Code and Cypher School (GCCS).

Cryptanalysis[link]

Two cottages in the stable yard at Bletchley Park. Turing worked here in 1939 and 1940, before moving to Hut 8.

During the Second World War, Turing was a leading participant in the breaking of German ciphers at Bletchley Park. The historian and wartime codebreaker Asa Briggs has said:

You needed exceptional talent, you needed genius at Bletchley and Turing's was that genius.^[29]

From September 1938, Turing had been working part-time with the Government Code and Cypher School (GCCS), the British code breaking organisation. He concentrated on Cryptanalysis of the Enigma, with Dilly Knox, a senior GCCS codebreaker.^[30] Soon after the July 1939 Warsaw meeting at which the Polish Cipher Bureau had provided the British and French with the details of the wiring of Enigma rotors and their method of decrypting Enigma messages, Turing and Knox started to work on a less fragile approach to the problem.^[31] The Polish method relied on an insecure indicator procedure that the Germans were likely to change, which they did in May 1940. Turing's approach was more general, using crib-based decryption for which he produced the initial functional specification of the bombe.

On 4 September 1939, the day after the UK declared war on Germany, Turing reported to Bletchley Park, the wartime station of GCCS.^[32] Specifying the bombe was the first of five major cryptanalytical advances that Turing made during the war. The others were: deducing the indicator procedure used by the German navy; developing a statistical procedure for making much more efficient use of the bombes dubbed Banburismus; developing a procedure for working out the cam settings of the wheels of the Lorenz SZ 40/42 (Tunny) dubbed Turingery and, towards the end of the war, the development of a portable secure voice scrambler at Hanslope Park that was codenamed Delilah.

By using statistical techniques to optimise the trial of different possibilities in the code breaking process, Turing made an innovative contribution to the subject. He wrote two papers discussing mathematical approaches which were entitled Report on the applications of probability to cryptography^[33] and Paper on statistics of repetitions^[34] which were of such value to GCCS and its successor GCHQ, that they were not released to the UK National Archives until April 2012, shortly before the centenary of his birth. A GCHQ mathematician said at the time that the fact that the contents had been restricted for some 70 years demonstrated their importance.^[35]

Turing had something of a reputation for eccentricity at Bletchley Park. He was known to his colleagues as 'Prof' and his Treatise on Enigma was known as 'The Prof's Book'.^[36] Jack Good, a cryptanalyst who worked with him, is quoted by Ronald Lewin as having said of Turing:

in the first week of June each year he would get a bad attack of hay fever, and he would cycle to the office wearing a service gas mask to keep the pollen off. His bicycle had a fault: the chain would come off at regular intervals. Instead of having it mended he would count the number of times the pedals went round and would get off the bicycle in time to adjust the chain by hand. Another of his eccentricities is that he chained his mug to the radiator pipes to prevent it being stolen.^[37]

While working at Bletchley, Turing, a talented long-distance runner, occasionally ran the 40 miles (64 km) to London when he was needed for high-level meetings,^[38] and he was capable of world-class marathon standards.^[39]

In 1945, Turing was awarded the OBE for his wartime services, but his work remained secret for many years.

Turing–Welchman bombe[link]

A complete and working replica of a bombe at the National Codes Centre at Bletchley Park

Within weeks of arriving at Bletchley Park,^[32] Turing had specified an electromechanical machine that could help break Enigma more effectively than the Polish bomba kryptologiczna, from which its name was derived. The bombe, with an enhancement suggested by mathematician Gordon Welchman, became one of the primary tools, and the major automated one, used to attack Enigma-enciphered messages.

Jack Good opined:

Turing's most important contribution, I think, was of part of the design of the bombe, the cryptanalytic machine. He had the idea that you could use, in effect, a theorem in logic which sounds to the untrained ear rather absurd; namely that from a contradiction, you can deduce everything.^[40]

The bombe searched for possible correct settings used for an Enigma message (i.e. rotor order, rotor settings and plugboard settings), using a suitable crib: a fragment of probable plaintext. For each possible setting of the rotors (which had of the order of 10¹⁹ states, or 10²² for the four-rotor U-boat variant),^[41] the bombe performed a chain of logical deductions based on the crib, implemented electrically. The bombe detected when a contradiction had occurred, and ruled out that setting, moving on to the next. Most of the possible settings would cause contradictions and be discarded, leaving only a few to be investigated in detail. The first bombe was installed on 18 March 1940.^[42] More than two hundred bombes were in operation by the end of the war.^[43]

Hut 8 and Naval Enigma[link]

Statue of Turing by Stephen Kettle at Bletchley Park, commissioned by the American philanthropist Sidney E Frank.^[44]

Turing decided to tackle the particularly difficult problem of German naval Enigma "because no one else was doing anything about it and I could have it to myself".^[45] In December 1939, Turing solved the essential part of the naval indicator system, which was more complex than the indicator systems used by the other services.^[45][46] That same night he also conceived of the idea of Banburismus, a sequential statistical technique (what Abraham Wald later called sequential analysis) to assist in breaking naval Enigma, "though I was not sure that it would work in practice, and was not in fact sure until some days had actually broken".^[45] For this he invented a measure of weight of evidence that he called the Ban. Banburismus could rule out certain sequences of the Enigma rotors, substantially reducing the time needed to test settings on the bombes.

In 1941, Turing proposed marriage to Hut 8 co-worker Joan Clarke, a fellow mathematician and cryptanalyst, but their engagement was short-lived. After admitting his homosexuality to his fiancée, who was reportedly "unfazed" by the revelation, Turing decided that he could not go through with the marriage.^[47]

Turing travelled to the United States in November 1942^[48] and worked with U.S. Navy cryptanalysts on Naval Enigma and bombe construction in Washington, visiting their Computing Machine Laboratory at Dayton, Ohio. His reaction to the American Bombe design was far from enthusiastic:

It seems a pity for them to go out of their way to build a machine to do all this stopping if it is not necessary. I am now converted to the extent of thinking that starting from scratch on the design of a Bombe, this method is about as good as our own. The American Bombe program was to produce 336 Bombes, one for each wheel order. I used to smile inwardly at the conception of test (of commutators) can hardly be considered conclusive as they were not testing for the bounce with electronic stop finding devices.^[49]

During this trip, he also assisted at Bell Labs with the development of secure speech devices.^[50]

He returned to Bletchley Park in March 1943. During his absence, Hugh Alexander had officially assumed the position of head of Hut 8, although Alexander had been de facto head for some time—Turing having little interest in the day-to-day running of the section. Turing became a general consultant for cryptanalysis at Bletchley Park.

Alexander wrote as follows about his contribution:

There should be no question in anyone's mind that Turing's work was the biggest factor in Hut 8's success. In the early days he was the only cryptographer who thought the problem worth tackling and not only was he primarily responsible for the main theoretical work within the Hut but he also shared with Welchman and Keen the chief credit for the invention of the Bombe. It is always difficult to say that anyone is absolutely indispensable but if anyone was indispensable to Hut 8 it was Turing. The pioneer's work always tends to be forgotten when experience and routine later make everything seem easy and many of us in Hut 8 felt that the magnitude of Turing's contribution was never fully realized by the outside world.^[51]

Turingery[link]

In July 1942, Turing devised a technique termed Turingery (or jokingly Turingismus)^[52] for use against the Lorenz cipher messages produced by the Germans' new Geheimschreiber (secret writer) machine. This was a teleprinter rotor cipher attachment codenamed Tunny at Bletchley Park. Turingery was a method of wheel-breaking, i.e. a procedure for working out the cam settings of Tunny's wheels.^[53] He also introduced the Tunny team to Tommy Flowers who, under the guidance of Max Newman, went on to build the Colossus computer, the world's first programmable digital electronic computer, which replaced a simpler prior machine (the Heath Robinson), and whose superior speed allowed the statistical decryption techniques to be applied usefully to the messages.^[54] Some have mistakenly said that Turing was a key figure in the design of the Colossus computer. Turingery and the statistical approach of Banburismus undoubtedly fed into the thinking about cryptanalysis of the Lorenz cipher,^[55][56] but he was not directly involved in the Colossus development.^[57]

Secure speech device (Delilah)[link]

Following his work at Bell Labs in the US,^[58] Turing pursued the idea of electronic enciphering of speech in the telephone system, and in the latter part of the war, he moved to work for the Secret Service's Radio Security Service (later HMGCC) at Hanslope Park. There he further developed his knowledge of electronics with the assistance of engineer Donald Bayley. Together they undertook the design and construction of a portable secure voice communications machine codenamed Delilah.^[59] It was intended for different applications, lacking capability for use with long-distance radio transmissions, and in any case, Delilah was completed too late to be used during the war. Though Turing demonstrated it to officials by encrypting and decrypting a recording of a Winston Churchill speech, Delilah was not adopted for use.^[60] Turing also consulted with Bell Labs on the development of SIGSALY, a secure voice system that was used in the later years of the war.

Early computers and the Turing test[link]

From 1945 to 1947 Turing lived in Richmond, London^[61] while he worked on the design of the ACE (Automatic Computing Engine) at the National Physical Laboratory (NPL). He presented a paper on 19 February 1946, which was the first detailed design of a stored-program computer.^[62] Von Neumann's incomplete First Draft of a Report on the EDVAC had predated Turing's paper, but it was much less detailed and, according to John R. Womersley, Superintendent of the NPL Mathematics Division, it "contains a number of ideas which are Dr. Turing’s own".^[63] Although ACE was a feasible design, the secrecy surrounding the wartime work at Bletchley Park led to delays in starting the project and he became disillusioned. In late 1947 he returned to Cambridge for a sabbatical year. While he was at Cambridge, the Pilot ACE was built in his absence. It executed its first program on 10 May 1950. Although Turing's ACE was never built, a number of computers around the world owe a lot to it, for example, the English Electric DEUCE and the American Bendix G-15.

According to the memoirs of the German computer pioneer Heinz Billing from the Max Planck Institute for Physics, published by Genscher, Düsseldorf (1997), there was a meeting between Alan Turing and Konrad Zuse. It took place in Göttingen in 1947. The interrogation had the form of a colloquium. Participants were Womersley, Turing, Porter from England and a few German researchers like Zuse, Walther, and Billing. (For more details see Herbert Bruderer, Konrad Zuse und die Schweiz).

In 1948, he was appointed Reader in the Mathematics Department at the University of Manchester. In 1949, he became Deputy Director of the Computing Laboratory there, working on software for one of the earliest stored-program computers—the Manchester Mark 1. During this time he continued to do more abstract work, and in "Computing machinery and intelligence" (Mind, October 1950), Turing addressed the problem of artificial intelligence, and proposed an experiment which became known as the Turing test, an attempt to define a standard for a machine to be called "intelligent". The idea was that a computer could be said to "think" if a human interrogator could not tell it apart, through conversation, from a human being.^[64] In the paper, Turing suggested that rather than building a program to simulate the adult mind, it would be better rather to produce a simpler one to simulate a child's mind and then to subject it to a course of education. A reversed form of the Turing test is widely used on the Internet; the CAPTCHA test is intended to determine whether the user is a human or a computer.

In 1948, Turing, working with his former undergraduate colleague, D. G. Champernowne, began writing a chess program for a computer that did not yet exist. In 1952, lacking a computer powerful enough to execute the program, Turing played a game in which he simulated the computer, taking about half an hour per move. The game was recorded.^[65] The program lost to Turing's colleague Alick Glennie, although it is said that it won a game against Champernowne's wife.

His Turing test was a significant and characteristically provocative and lasting contribution to the debate regarding artificial intelligence, which continues after more than half a century.^[66]

He also invented the LU decomposition method in 1948, used today for solving matrix equations.^[67]

Pattern formation and mathematical biology[link]

Turing worked from 1952 until his death in 1954 on mathematical biology, specifically morphogenesis. He published one paper on the subject called The Chemical Basis of Morphogenesis in 1952, putting forth the Turing hypothesis of pattern formation.^[68] His central interest in the field was understanding Fibonacci phyllotaxis, the existence of Fibonacci numbers in plant structures. He used reaction–diffusion equations which are central to the field of pattern formation. Later papers went unpublished until 1992 when Collected Works of A.M. Turing was published. His contribution is considered a seminal piece of work in this field.^[69]

Conviction for indecency[link]

Anthony Cave Brown's book, "C": The Secret Life of Sir Stewart Menzies, Spymaster to Winston Churchill, states:

Menzies had known that Turing was a practicing and aggressive homosexual; this had emerged soon after his employment at Bletchley. But since he caused no offence to his colleagues at Bletchley, and since he was perhaps the only man in Menzies's service who might have been called ‘indispensable,’ his services were retained... Early in 1944 a suspicion arose that he might have been the man responsible for molesting schoolboys at the main public library in Luton, a large industrial town not far from Bletchley. While no proceedings arose, it was decided that the need for good order and discipline required his removal — but not before he had done his finest work.^[70]

In January 1952, Turing met Arnold Murray outside a cinema in Manchester. After a lunch date, Turing invited Murray to spend the weekend with him at his house, an invitation which Murray accepted although he did not show up. The pair met again in Manchester the following Monday, when Murray agreed to accompany Turing to the latter's house. A few weeks later Murray visited Turing's house again, and apparently spent the night there.^[71]

After Murray helped an accomplice to break into his house, Turing reported the crime to the police. During the investigation, Turing acknowledged a sexual relationship with Murray. Homosexual acts were illegal in the United Kingdom at that time,^[72] and so both were charged with gross indecency under Section 11 of the Criminal Law Amendment Act 1885.^[73]

Turing was given a choice between imprisonment or probation conditional on his agreement to undergo hormonal treatment designed to reduce libido. He accepted chemical castration via oestrogen hormone injections.^[74]

Turing's conviction led to the removal of his security clearance, and barred him from continuing with his cryptographic consultancy for the Government Communications Headquarters (GCHQ), the UK signals intelligence agency that had evolved from GCCS in 1946. At the time, there was acute public anxiety about spies and homosexual entrapment by Soviet agents,^[75] because of the recent exposure of the first two members of the Cambridge Five, Guy Burgess and Donald Maclean, as KGB double agents. Turing was never accused of espionage but, as with all who had worked at Bletchley Park, was prevented from discussing his war work.^[76]

Death[link]

On 8 June 1954, Turing's cleaner found him dead; he had died the previous day. A post-mortem examination established that the cause of death was cyanide poisoning. When his body was discovered an apple lay half-eaten beside his bed, and although the apple was not tested for cyanide,^[77] it is speculated that this was the means by which a fatal dose was delivered. An inquest determined that he had committed suicide, and he was cremated at Woking Crematorium on 12 June 1954.^[78] Turing's mother argued strenuously that the ingestion was accidental, caused by her son's careless storage of laboratory chemicals. Biographer Andrew Hodges suggests that Turing may have killed himself in an ambiguous way quite deliberately, to give his mother some plausible deniability.^[79] David Leavitt has suggested that Turing was re-enacting a scene from the 1937 film Snow White, his favourite fairy tale, pointing out that he took "an especially keen pleasure in the scene where the Wicked Witch immerses her apple in the poisonous brew."^[80]

Epitaph[link]

Hyperboloids of wondrous Light
Rolling for aye through Space and Time
Harbour those Waves which somehow Might

Play out God's holy pantomime^[81]

Recognition and tributes[link]

A Blue Plaque marking Turing's home at Wilmslow, Cheshire

A biography published by the Royal Society shortly after Turing's death (and while his wartime work was still subject to the Official Secrets Act) recorded:^[1]

Three remarkable papers written just before the war, on three diverse mathematical subjects, show the quality of the work that might have been produced if he had settled down to work on some big problem at that critical time. For his work at the Foreign Office he was awarded the OBE.

Since 1966, the Turing Award has been given annually by the Association for Computing Machinery to a person for technical contributions to the computing community. It is widely considered to be the computing world's highest honour, equivalent to the Nobel Prize.^[82]

Breaking the Code is a 1986 play by Hugh Whitemore about Alan Turing. The play ran in London's West End beginning in November 1986 and on Broadway from 15 November 1987 to 10 April 1988. There was also a 1996 BBC television production. In all cases, Derek Jacobi played Turing. The Broadway production was nominated for three Tony Awards including Best Actor in a Play, Best Featured Actor in a Play, and Best Direction of a Play, and for two Drama Desk Awards, for Best Actor and Best Featured Actor.

On 23 June 1998, on what would have been Turing's 86th birthday, Andrew Hodges, his biographer, unveiled an official English Heritage Blue Plaque at his birthplace and childhood home in Warrington Crescent, London, later the Colonnade Hotel.^[83][84] To mark the 50th anniversary of his death, a memorial plaque was unveiled on 7 June 2004 at his former residence, Hollymeade, in Wilmslow, Cheshire.^[85]

On 13 March 2000, Saint Vincent and the Grenadines issued a set of stamps to celebrate the greatest achievements of the 20th century, one of which carries a recognisable portrait of Turing against a background of repeated 0s and 1s, and is captioned: "1937: Alan Turing's theory of digital computing". On 1 April 2003, Turing's work at Bletchley Park was named an IEEE Milestone.^[86] On 28 October 2004, a bronze statue of Alan Turing sculpted by John W. Mills was unveiled at the University of Surrey in Guildford, marking the 50th anniversary of Turing's death; it portrays him carrying his books across the campus.^[87] In 2006, Boston Pride named Turing their Honorary Grand Marshal.^[88]

Turing was one of four mathematicians examined in the 2008 BBC documentary entitled "Dangerous Knowledge".^[89] The Princeton Alumni Weekly named Turing the second most significant alumnus in the history of Princeton University, second only to President James Madison. A 1.5-ton, life-size statue of Turing was unveiled on 19 June 2007 at Bletchley Park. Built from approximately half a million pieces of Welsh slate, it was sculpted by Stephen Kettle, having been commissioned by the late American billionaire Sidney Frank.^[90]

Turing has been honoured in various ways in Manchester, the city where he worked towards the end of his life. In 1994, a stretch of the A6010 road (the Manchester city intermediate ring road) was named "Alan Turing Way". Part of this road runs alongside the City of Manchester Stadium, where Manchester City play their games. A bridge carrying this road was widened, and carries the name Alan Turing Bridge. A statue of Turing was unveiled in Manchester on 23 June 2001. It is in Sackville Park, between the University of Manchester building on Whitworth Street and the Canal Street gay village. The memorial statue, depicts the "father of Computer Science" sitting on a bench at a central position in the park. The statue was unveiled on Turing's birthday.

Turing memorial statue plaque in Sackville Park, Manchester

Turing is shown holding an apple—a symbol classically used to represent forbidden love, the object that inspired Isaac Newton's theory of gravitation, and the means of Turing's own death. The cast bronze bench carries in relief the text 'Alan Mathison Turing 1912–1954', and the motto 'Founder of Computer Science' as it would appear if encoded by an Enigma machine: 'IEKYF ROMSI ADXUO KVKZC GUBJ'.

A plinth at the statue's feet says 'Father of computer science, mathematician, logician, wartime codebreaker, victim of prejudice'. There is also a Bertrand Russell quotation saying 'Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture.' The sculptor buried his old Amstrad computer, which was an early popular home computer, under the plinth, as a tribute to "the godfather of all modern computers".^[91]

In 1999, Time Magazine named Turing as one of the 100 Most Important People of the 20th century for his role in the creation of the modern computer, and stated: "The fact remains that everyone who taps at a keyboard, opening a spreadsheet or a word-processing program, is working on an incarnation of a Turing machine."^[2] Turing is featured in the 1999 Neal Stephenson novel "Cryptonomicon."

In 2002, Turing was ranked twenty-first on the BBC nationwide poll of the 100 Greatest Britons.^[92] In 2010, actor/playwright Jade Esteban Estrada portrayed Turing in the solo musical, "ICONS: The Lesbian and Gay History of the World, Vol. 4.". In 2011, in the Guardian's "My hero" series, writer Alan Garner chose Turing as his hero and described how they had met whilst out jogging in the early 1950s. Garner remembered Turing as "funny and witty" and said that he "talked endlessly". ^[93]

In February 2011, Turing's papers from the Second World War were bought for the nation with an 11th-hour bid by the National Heritage Memorial Fund, allowing them to stay at Bletchley Park.^[94]

The logo of Apple computer is often erroneously referred to as a tribute to Alan Turing, with the bite mark a reference to his method of suicide.^[95] Both the designer of the logo^[96] and the company deny that there is any homage to Turing in the design of the logo.^[97] In Series I, Episode 13 of the British television quiz show QI presenter Stephen Fry recounted a conversation had with Steve Jobs, saying that Jobs' response was, "It isn't true, but God, we wish it were."

Government apology[link]

In August 2009, John Graham-Cumming started a petition urging the British Government to posthumously apologise to Alan Turing for prosecuting him as a homosexual.^[98][99] The petition received thousands of signatures.^[100][101] Prime Minister Gordon Brown acknowledged the petition, releasing a statement on 10 September 2009 apologising and describing Turing's treatment as "appalling":^[6][100]

Thousands of people have come together to demand justice for Alan Turing and recognition of the appalling way he was treated. While Turing was dealt with under the law of the time and we can't put the clock back, his treatment was of course utterly unfair and I am pleased to have the chance to say how deeply sorry I and we all are for what happened to him ... So on behalf of the British government, and all those who live freely thanks to Alan's work I am very proud to say: we're sorry, you deserved so much better.^[100][102]

In December 2011, William Jones created an e-petition^[103] requesting the British Government pardon Alan Turing for his conviction of "gross-indecency":^[104]

We ask the HM Government to grant a pardon to Alan Turing for the conviction of "gross indecency". In 1952, he was convicted of "gross indecency" with another man and was forced to undergo so-called "organo-therapy" - chemical castration. Two years later, he killed himself with cyanide, aged just 41. Alan Turing was driven to a terrible despair and early death by the nation he'd done so much to save. This remains a shame on the UK government and UK history. A pardon can go to some way to healing this damage. It may act as an apology to many of the other gay men, not as well known as Alan Turing, who were subjected to these laws.

The petition gained over 21,000 signatures, but the request was declined by Lord MacNally:^[105]

A posthumous pardon was not considered appropriate as Alan Turing was properly convicted of what at the time was a criminal offence. He would have known that his offence was against the law and that he would be prosecuted. It is tragic that Alan Turing was convicted of an offence which now seems both cruel and absurd—particularly poignant given his outstanding contribution to the war effort. However, the law at the time required a prosecution and, as such, long-standing policy has been to accept that such convictions took place and, rather than trying to alter the historical context and to put right what cannot be put right, ensure instead that we never again return to those times.

Tributes by universities[link]

The Alan Turing Building at the University of Manchester

A celebration of Turing's life and achievements arranged by the British Logic Colloquium and the British Society for the History of Mathematics was held on 5 June 2004.

• The Turing Room at the University of Edinburgh's School of Informatics houses a bust of Turing by Eduardo Paolozzi, and a set (#42/50) of his Turing prints (2000).
• The University of Surrey has a statue of Turing on their main piazza.
• Istanbul Bilgi University organises an annual conference on the theory of computation called "Turing Days".^[106]
• The University of Texas at Austin has an honours computer science programme named the Turing Scholars.^[107]
• The University of Puerto Rico in Humacao has a computer lab named after Turing.
• Keele University's School of Computing and Mathematics has a computing laboratory named after Turing.
• In the early 1960s Stanford University named the sole lecture room of the Polya Hall Mathematics building "Alan Turing Auditorium".^[108]
• One of the amphitheatres of the Computer Science department (LIFL^[109]) at the University of Lille in Northern France is named in honour of Alan M. Turing (the other amphitheatre is named after Kurt Gödel).
• The Department of Computer Science at Pontifical Catholic University of Chile, the Polytechnic University of Puerto Rico, Los Andes University in Bogotá, Colombia, King's College, Cambridge, Bangor University in Wales and Universities of Ghent and Mons in Belgium have computer laboratories named after Turing.
• The University of Manchester, the Open University, Oxford Brookes University and Aarhus University (in Århus, Denmark) all have buildings named after Turing.
• Alan Turing Road in the Surrey Research Park is named for Alan Turing.
• Carnegie Mellon University has a granite bench, situated in the Hornbostel Mall, with the name "A. M. Turing" carved across the top, "Read" down the left leg, and "Write" down the other.
• The École Internationale des Sciences du Traitement de l'Information has named its recently acquired third building "Turing".
• The University of Oregon has a bust of Turing on the side of the Deschutes Hall, the computer science building.^[110]
• The École Polytechnique Fédérale de Lausanne has a road and a square named after Alan Turing (Chemin de Alan Turing and Place de Alan Turing).^[111]

Centenary commemoration[link]

To mark the 100th anniversary of Turing's birth, the Turing Centenary Advisory Committee (TCAC) is coordinating the Alan Turing Year, a year-long programme of events around the world honouring Turing's life and achievements. The TCAC working with the University of Manchester faculty members and a broad spectrum of people from Cambridge University and Bletchley Park, is chaired by S. Barry Cooper, with Alan Turing's nephew Sir John Dermot Turing acting as TCAC Honorary President.

Events are scheduled in many countries around the world including the USA, Brazil, China, Czech Republic, the Philippines, New Zealand, Israel, Spain, Switzerland, Norway, Italy, Portugal and Germany. The keystone events will be a three-day conference in Manchester, UK in June examining Turing's mathematical and code-breaking achievements, and a Turing Centenary Conference in Cambridge organised by King's College, Cambridge and the association Computability in Europe.^[112]

On February 23, 2012, the Royal Mail released a stamp featuring Turing as part its "Britons of Distinction" series.^[113]

The Turing Test, an opera by Julian Wagstaff which ran at the Edinburgh fringe in 2007, will also go on a UK tour in October to mark the 100th anniversary year of Turing's birth.^[114] The Turing Test is set in the near future and tells the fictional story of a brilliant young PhD student Stephanie, who is trapped in a bitter battle between two rival scientists racing to build the world's first truly intelligent computer.^[115]

See also[link]

	Biography portal
	Logic portal
	LGBT portal

• Good–Turing frequency estimation
• LU Decomposition
• Turing degree
• Turing completeness
• Turing machine
• Turing machine examples
• Turing pattern
• Turing reduction
• Turing switch
• Turing test
• Unorganized machine

Notes[link]

References[link]

Further reading[link]

• Alan Turing at the Mathematics Genealogy Project
• Jack Copeland, ed. "The Mind and the Computing Machine: Alan Turing and others". The Rutherford Journal. http://www.rutherfordjournal.org/article010111.html. 
• Hodges, Andrew (27 August 2007). "Alan Turing". In Edward N. Zalta. Stanford Encyclopedia of Philosophy (Winter 2009 ed.). Stanford University. http://plato.stanford.edu/entries/turing/. Retrieved 10 January 2011. 
• Gray, Paul (29 March 1999). "Computer Scientist: Alan Turing". TIME. http://www.time.com/time/magazine/article/0,9171,990624,00.html. 
• Gleick, James, The Information: A History, A Theory, A Flood, New York: Pantheon, 2011, ISBN 978-0-375-42372-7
• Leavitt, David, The Man Who Knew Too Much: Alan Turing and the Invention of the Computer, W. W. Norton, 2006

External links[link]

Wikiquote has a collection of quotations related to: Alan Turing

Wikimedia Commons has media related to: Alan Turing

• Alan Turing RKBExplorer
• Alan Turing Year
• CiE 2012: Turing Centenary Conference
• Visual Turing
• Turing Machine calculators at Wolfram Alpha
• Alan Turing site maintained by Andrew Hodges including a short biography
• AlanTuring.net – Turing Archive for the History of Computing by Jack Copeland
• The Turing Archive – contains scans of some unpublished documents and material from the Kings College, Cambridge archive
• Jones, G. James (11 December 2001). "Alan Turing – Towards a Digital Mind: Part 1". System Toolbox (The Binary Freedom Project). http://www.systemtoolbox.com/article.php?history_id=3. 
• Sherborne School Archives – holds papers relating to Alan Turing's time at Sherborne School
• Alan Turing plaques recorded on openplaques.org

Papers[link]

• An extensive list of Turing's papers, reports and lectures, plus translated versions and collections BibNetWiki
• List of publications from Microsoft Academic Search.
• Turing, Alan (October 1950), "Computing Machinery and Intelligence", Mind LIX (236): 433–460, DOI:10.1093/mind/LIX.236.433, ISSN 0026-4423, http://loebner.net/Prizef/TuringArticle.html, retrieved 2008-08-18 
• Oral history interview with Nicholas C. Metropolis, Charles Babbage Institute, University of Minnesota. Metropolis was the first director of computing services at Los Alamos National Laboratory; topics include the relationship between Alan Turing and John von Neumann

Angus MacIntyre
Angus Macintyre in 2009
Institutions	Queen Mary, University of London
Doctoral advisor	Dana Scott

Angus John Macintyre is a British mathematician known for his contributions to Model theory and logic. He is professor of mathematics at the Queen Mary, University of London.

He completed his PhD under the supervision of Dana Scott in 1968 with a thesis entitled "Classifying Pairs of Real-Closed Fields". He was elected a Fellow of the Royal Society in 1993, and in 2003 he was awarded the Pólya Prize by the London Mathematical Society. From 2009 to 2011, he served as the president of the London Mathematical Society.

External links[link]

• Angus Macintyre at the Mathematics Genealogy Project
• Home page at Queen Mary

This article about a United Kingdom mathematician is a stub. You can help Wikipedia by expanding it. v t e

A centenarian is a person who lives to or beyond the age of 100 years. Because current average global life expectancies are less than 100, the term is invariably associated with longevity. A supercentenarian is a person who has lived to the age of 110 or more, something only achieved by about one in 1,000 centenarians. Even rarer is a person who has lived to age 115; as of April 2012^[update], there are only 27 people in recorded history who have indisputably reached this age.^[1][2][3] In 2009, the United Nations estimated that there were 455,000 living centenarians worldwide.^[4]

Current incidence[link]

A photo of the Canadian centenarian Muriel Duckworth, taken in honor of her 100th birthday in 2008.

The United States currently has the greatest number of centenarians of any nation, estimated at 70,490 on September 1, 2010.^[5] This corresponds to a national incidence of one centenarian per 4,400 people.^[6]

Japan has the second-largest number of centenarians, with an estimated 47,756 as of September 2011.^[7] Japan started its surveys in 1963, at which time the number of Japanese centenarians was found to be 153. This number surpassed the 10,000 mark in 1998, 20,000 in 2003, and 40,000 in 2009. According to a UN Demographic survey, Japan is expected to have 272,000 centenarians by 2050.^[8] However, some sources suggest that the number could be closer to 1 million.^[9] Many experts attribute Japan's high life expectancy to the Japanese diet, which is particularly low in refined simple carbohydrates, and to hygienic practices. In addition, the number of centenarians in relation to the total population was, in September 2010, 114% higher in Shimane Prefecture than the ratio for the whole of Japan. This ratio was also 92% higher in Okinawa Prefecture.^[10][11] In addition to diet, there are four other factors that have been found to increase the life expectancy for Okinawans, as noted later in the "research into centenarians" section of this article.^[12] The incidence of centenarians in Japan was one per 3,522 people in 2008,^[13] although Okinawa again exceeded this average, with one per 1,838 people in 2006.

Centenarian controversy in Japan[link]

The number of Japanese centenarians was called into question in 2010, following a series of reports showing that hundreds of thousands of elderly people had gone "missing" in the country. The deaths of many centenarians had not been reported, casting doubt on the country's reputation for having a large population of centenarians.^{[14][15][16][17]}

In July 2010, a centenarian listed as the oldest living male in Tokyo, registered to be aged 111, was found to have died some 30 years before; his body was found mummified in its bed,^[18] resulting in a police investigation into centenarians listed over the age of 105. Soon after the discovery, the Japanese police further found that at least 200 other Japanese centenarians were missing, with the total likely to rise amid a nationwide search that began in early August 2010.^[19] In one case, the remains of a mother thought to be 104 had been stuffed into her son's backpack for nearly a decade.^[20]

There are growing concerns that Japan's welfare system can be exploited by unscrupulous family members keen to continue receiving benefits after the pensioners die.^[19] In one case, a man received around 9.5 million yen in pension payments despite his wife having died six years previously.^[19]

Centenarian populations[link]

The total number of centenarians in the world remains uncertain. It has been estimated by the Population Division of the United Nations as 23,000 in 1950, 110,000 in 1990, 150,000 in 1995, 209,000 in 2000 and 324,000 in 2005.^[21] There were an estimated 455,000 centenarians in the world in 2009.^[4] However, these estimates do not take into account the recent downward adjustments of national estimates made by several countries, such as the United States.^[22] The following table lists estimated centenarian populations by country, including both the latest and the earliest known estimates, where available.

Traditions[link]

An 1895 photograph of a Chaldean man from Mosul, Iraq, said to be 107 years old.

In many countries, people receive a gift or congratulations on their 100th birthday. In the United States, centenarians traditionally receive a letter from the President, congratulating them for their longevity. NBC's The Today Show show has also named new centenarians on air since 1983. In the United Kingdom and the Commonwealth Realms, the Queen sends greetings (formerly as a telegram) on the 100th birthday and on every birthday starting with the 105th. Centenarians born in Ireland receive a €2,540 "Centenarians' Bounty" and a letter from the President of Ireland, even if they are resident abroad.^[50] Japanese centenarians receive a silver cup and a certificate from the Prime Minister of Japan upon their 100th birthday, honouring them for their longevity and prosperity in their lives. Swedish centenarians receive a telegram from the King and Queen of Sweden.^[51] Centenarians born in Italy receive a letter from the President of Italy. In Japan, a "National Respect for the Aged Day" has been celebrated every September since 1966.

An aspect of blessing in many cultures is to offer a wish that the recipient lives to 100. Among Hindus, people who touch the feet of elders are often blessed with "May you live a hundred years". In Sweden, the traditional birthday song states, May he/she live for one hundred years. In Judaism, the term May you live to be 120 years old is a common blessing. In Poland, Sto lat, a wish to live a hundred years, is a traditional form of praise and good wishes, and the song "sto lat, sto lat" is sang on the occasion of the birthday celebrations--arguably, it is the most popular song in Poland and among Poles around the globe. Chinese emperors were hailed to live ten thousand years, while empresses were hailed to live a thousand years. In Italy, "A hundred of these days!" (cento di questi giorni) is an augury for birthdays, to live to celebrate 100 more birthdays.^[52] Some Italians say "Cent'anni!", which means "a hundred years", in that they wish that they could all live happily for a hundred years. In Greece, wishing someone Happy Birthday ends with the expression να τα εκατοστήσεις (na ta ekatostisis), which can be loosely translated as "may you make it one hundred birthdays".

Centenarians in ancient times[link]

While the density of centenarians per capita was much less in ancient times than today, the data suggest that reaching the age of 100 was not unheard of. However, ancient demographics are biased in favor of wealthy or powerful individuals rather than the ordinary person. Grmek and Gourevitch speculate that during the Classical Greek Period, anyone who made it past the age of five years — surviving all the common childhood illness of that day — had a reasonable chance of living to a ripe old age. Life expectancy at 400 B.C. was estimated to be around 30 years of age. One demographer of ancient civilizations reported that Greek men lived to 45 years (based on a sample size of 91), while women lived to 36.2 years (based on a sample size of 55). Curiously, the gender statistics are inverted compared to today, since child-birth was a much more traumatic experience at that time than now, and it certainly skewed female statistics downward. It was common for average citizens to take great care in their hygiene (sanitation), Mediterranean diet (fish, figs, olive oil, wine, etc.), and exercise program (sports/gymnasium), although there was much more male trauma per capita than today, due to military service being virtually universal for citizens. This also biased the statistics for men downward.^[53]

Diogenes Laertius (c. 250) gives one of the earliest references regarding (plausible centenarian) longevity given by a scientist, the astronomer Hipparchus of Nicea (c. 185 – c. 120 B.C.), who, according to the doxographer, assured that the philosopher Democritus of Abdera (c. 470/460 – c. 370/360 B.C.) lived 109 years. All other accounts about Democritus given by the ancients appear to agree on the fact that the philosopher lived over 100 years. Such longevity would not be dramatically out of line with that of other ancient Greek philosophers thought to have lived beyond the age of 90 (e.g.: Xenophanes of Colophon, c. 570/565 – c. 475/470 B.C.; Pyrrho of Ellis, c. 360 - c. 270 B.C.; Eratosthenes of Cirene c. 285 – c. 190 B.C., etc.). The case of Democritus differs from the case of, for example, Epimenides of Crete (7th, 6th centuries B.C.), who is said to have lived an implausible 154, 157 or 290 years, depending on the source.

The sixth dynasty Egyptian ruler Pepi II is believed by some Egyptologists to have lived to the age of 100 or more (c. 2278 BC - c. 2184 BC), as he ruled for 94 years.^[54] However this is under dispute, as others claim the length of his reign was actually 64 years.^[55]

The Indian Sufi poet, Kabir (1398-1518?) is believed by some to have lived to an implausible age of 120 while others believe that he lived for no more than 80 years.

Ultimately, there is no reason to believe that centenarians did not exist 2500 years ago, even if they were not commonplace.^[56]

Hosius of Córdoba, the man who convinced Constantine the Great to call the First Council of Nicaea, reportedly lived to age 102.

The Chronicon of Bernold of Constance records the death in 1097 of Azzo marchio de Longobardia, pater Welfonis ducis de Baiowaria, commenting that he was iam maior centenario.^[57]

Research into centenarians[link]

Research carried out in Italy suggests that healthy centenarians have high levels of vitamin A and vitamin E and that this seems to be important in guaranteeing their extreme longevity.^[58] Other research contradicts this, however, and has found that these findings do not apply to centenarians from Sardinia, for whom other factors probably play a more important role.^[59] A preliminary study carried out in Poland showed that, in comparison with young healthy female adults, centenarians living in Upper Silesia had significantly higher red blood cell glutathione reductase and catalase activities and higher, although insignificantly, serum levels of vitamin E.^[60] Researchers in Denmark have also found that centenarians exhibit a high activity of glutathione reductase in red blood cells. In this study, those centenarians having the best cognitive and physical functional capacity tended to have the highest activity of this enzyme.^[61]

Other research has found that people having parents who became centenarians have an increased number of naïve B cells. It is well known that the children of parents who have a long life are also likely to reach a healthy age, but it is not known why, although the inherited genes are probably important.^[62] A variation in the gene FOXO3A is known to have a positive effect on the life expectancy of humans, and is found much more often in people living to 100 and beyond - moreover, this appears to be true worldwide.^[63]

Men and women who are 100 or older tend to have something else in common, an extraverted personality, says Thomas T. Perls, M.D., M.P.H., the director of the New England Centenarian Study at Boston University. Centenarians will often have many friends, strong ties to relatives and a healthy dose of self-esteem.^[64]

Some research suggests that centenarian offspring are more likely to age in better cardiovascular health than their peers.^[65]

In John W. Santrock's book "A Topical Approach to Life-Span Development", there are five factors that research has suggested that are most important to longevity in centenarians:^[12] 1) heredity and family history 2) health, i.e. weight, diet, whether or not a person smokes, amount of exercise 3) education level 4) personality 5) lifestyle.^[12]

Santrock's book also noted that the largest group of centenarians are women who have never been married.^[12] Also, people who have been through traumatic life events, such as Holocaust survivors, learn to cope better with stress and poverty and are more likely to reach centenarian status.^[12]

In Okinawa, Japan, studies have shown five factors that have contributed to the large number of centenarians in that region:^[12]