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Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician,
computer scientist A computer scientist is a person who is trained in the academic study of computer science. Computer scientists typically work on the theoretical side of computation, as opposed to the hardware side on which computer engineers mainly focus (al ...
,
logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises ...
ian,
cryptanalyst Cryptanalysis (from the Greek ''kryptós'', "hidden", and ''analýein'', "to analyze") refers to the process of analyzing information systems in order to understand hidden aspects of the systems. Cryptanalysis is used to breach cryptographic sec ...
, philosopher, and theoretical biologist. Turing was highly influential in the development of
theoretical computer science Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory. It is difficult to circumsc ...
, providing a formalisation of the concepts of
algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specificat ...
and
computation Computation is any type of arithmetic or non-arithmetic calculation that follows a well-defined model (e.g., an algorithm). Mechanical or electronic devices (or, historically, people) that perform computations are known as ''computers''. An es ...
with the
Turing machine A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algori ...
, which can be considered a model of a
general-purpose computer A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations ( computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These pro ...
. He is widely considered to be the father of theoretical computer science and
artificial intelligence Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animals and humans. Example tasks in which this is done include speech re ...
. Born in
Maida Vale Maida Vale ( ) is an affluent residential district consisting of the northern part of Paddington in West London, west of St John's Wood and south of Kilburn. It is also the name of its main road, on the continuous Edgware Road. Maida Vale is p ...
, London, Turing was raised in
southern England Southern England, or the South of England, also known as the South, is an area of England consisting of its southernmost part, with cultural, economic and political differences from the Midlands and the North. Officially, the area includes G ...
. He graduated at
King's College, Cambridge King's College is a constituent college of the University of Cambridge. Formally The King's College of Our Lady and Saint Nicholas in Cambridge, the college lies beside the River Cam and faces out onto King's Parade in the centre of the city ...
, with a degree in mathematics. Whilst he was a
fellow A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...
at Cambridge, he published a proof demonstrating that some purely mathematical yes–no questions can never be answered by computation and defined a
Turing machine A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algori ...
, and went on to prove that the
halting problem In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever. Alan Turing proved in 1936 that a g ...
for Turing machines is undecidable. In 1938, he obtained his PhD from the
Department of Mathematics Department may refer to: * Departmentalization, division of a larger organization into parts with specific responsibility Government and military *Department (administrative division), a geographical and administrative division within a country, ...
at
Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...
. During the
Second World War World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
, Turing worked for the
Government Code and Cypher School Government Communications Headquarters, commonly known as GCHQ, is an intelligence and security organisation responsible for providing signals intelligence (SIGINT) and information assurance (IA) to the government and armed forces of the Unit ...
(GC&CS) at
Bletchley Park Bletchley Park is an English country house and estate in Bletchley, Milton Keynes ( Buckinghamshire) that became the principal centre of Allied code-breaking during the Second World War. The mansion was constructed during the years following ...
, Britain's
codebreaking Cryptanalysis (from the Greek ''kryptós'', "hidden", and ''analýein'', "to analyze") refers to the process of analyzing information systems in order to understand hidden aspects of the systems. Cryptanalysis is used to breach cryptographic sec ...
centre that produced
Ultra adopted by British military intelligence in June 1941 for wartime signals intelligence obtained by breaking high-level encrypted enemy radio and teleprinter communications at the Government Code and Cypher School (GC&CS) at Bletchley Park. '' ...
intelligence. For a time he led
Hut 8 Hut 8 was a section in the Government Code and Cypher School (GC&CS) at Bletchley Park (the British World War II codebreaking station, located in Buckinghamshire) tasked with solving German naval (Kriegsmarine) Enigma messages. The section was l ...
, the section that was responsible for German naval cryptanalysis. Here, he devised a number of techniques for speeding the breaking of German
cipher In cryptography, a cipher (or cypher) is an algorithm for performing encryption or decryption—a series of well-defined steps that can be followed as a procedure. An alternative, less common term is ''encipherment''. To encipher or encode i ...
s, including improvements to the pre-war Polish bomba method, an
electromechanical In engineering, electromechanics combines processes and procedures drawn from electrical engineering and mechanical engineering. Electromechanics focuses on the interaction of electrical and mechanical systems as a whole and how the two systems ...
machine that could find settings for the Enigma machine. Turing played a crucial role in cracking intercepted coded messages that enabled the Allies to defeat the
Axis powers The Axis powers, ; it, Potenze dell'Asse ; ja, 枢軸国 ''Sūjikukoku'', group=nb originally called the Rome–Berlin Axis, was a military coalition that initiated World War II and fought against the Allies. Its principal members were ...
in many crucial engagements, including the
Battle of the Atlantic The Battle of the Atlantic, the longest continuous military campaign in World War II, ran from 1939 to the defeat of Nazi Germany in 1945, covering a major part of the naval history of World War II. At its core was the Allied naval blockade ...
. After the war, Turing worked at the National Physical Laboratory, where he designed the
Automatic Computing Engine The Automatic Computing Engine (ACE) was a British early electronic serial stored-program computer designed by Alan Turing. It was based on the earlier Pilot ACE. It led to the MOSAIC computer, the Bendix G-15, and other computers. Backg ...
(ACE), one of the first designs for a stored-program computer. In 1948, Turing joined
Max Newman Maxwell Herman Alexander Newman, FRS, (7 February 1897 – 22 February 1984), generally known as Max Newman, was a British mathematician and codebreaker. His work in World War II led to the construction of Colossus, the world's first operatio ...
's
Computing Machine Laboratory The Computing Machine Laboratory at the University of Manchester in the north of England was established by Max Newman shortly after the end of World War II, around 1946. The Laboratory was funded through a grant from the Royal Society, which was ...
, at the
Victoria University of Manchester The Victoria University of Manchester, usually referred to as simply the University of Manchester, was a university in Manchester, England. It was founded in 1851 as Owens College. In 1880, the college joined the federal Victoria University. Afte ...
, where he helped develop the
Manchester computers The Manchester computers were an innovative series of Von Neumann architecture, stored-program Computer, electronic computers developed during the 30-year period between 1947 and 1977 by a small team at the Victoria University of Manchester, Uni ...
and became interested in
mathematical biology Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of the living organisms to investigate the principles that govern the structure, development a ...
. He wrote a paper on the chemical basis of
morphogenesis Morphogenesis (from the Greek ''morphê'' shape and ''genesis'' creation, literally "the generation of form") is the biological process that causes a cell, tissue or organism to develop its shape. It is one of three fundamental aspects of devel ...
and predicted
oscillating Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
chemical reaction A chemical reaction is a process that leads to the IUPAC nomenclature for organic transformations, chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the pos ...
s such as the
Belousov–Zhabotinsky reaction A Belousov–Zhabotinsky reaction, or BZ reaction, is one of a class of reactions that serve as a classical example of non-equilibrium thermodynamics, resulting in the establishment of a nonlinear chemical oscillator. The only common element in ...
, first observed in the 1960s. Despite these accomplishments, Turing was never fully recognised in Britain during his lifetime because much of his work was covered by the
Official Secrets Act An Official Secrets Act (OSA) is legislation that provides for the protection of state secrets and official information, mainly related to national security but in unrevised form (based on the UK Official Secrets Act 1911) can include all infor ...
. Turing was prosecuted in 1952 for
homosexual acts Homosexuality is romantic attraction, sexual attraction, or sexual behavior between members of the same sex or gender. As a sexual orientation, homosexuality is "an enduring pattern of emotional, romantic, and/or sexual attractions" to peo ...
. He accepted hormone treatment with
DES Des is a masculine given name, mostly a short form (hypocorism) of Desmond. People named Des include: People * Des Buckingham, English football manager * Des Corcoran, (1928–2004), Australian politician * Des Dillon (disambiguation), sever ...
, a procedure commonly referred to as
chemical castration Chemical castration is castration via anaphrodisiac drugs, whether to reduce libido and sexual activity, to treat cancer, or otherwise. Unlike surgical castration, where the gonads are removed through an incision in the body, ...
, as an alternative to prison. Turing died on 7 June 1954, 16 days before his 42nd birthday, from
cyanide poisoning Cyanide poisoning is poisoning that results from exposure to any of a number of forms of cyanide. Early symptoms include headache, dizziness, fast heart rate, shortness of breath, and vomiting. This phase may then be followed by seizures, slow h ...
. An inquest determined his death as a suicide, but it has been noted that the known evidence is also consistent with accidental poisoning. Following a public campaign in 2009, the British Prime Minister
Gordon Brown James Gordon Brown (born 20 February 1951) is a British former politician who served as Prime Minister of the United Kingdom and Leader of the Labour Party (UK), Leader of the Labour Party from 2007 to 2010. He previously served as Chance ...
made an official public apology on behalf of the British government for "the appalling way uringwas treated".
Queen Elizabeth II Elizabeth II (Elizabeth Alexandra Mary; 21 April 1926 – 8 September 2022) was Queen of the United Kingdom and other Commonwealth realms from 6 February 1952 until Death and state funeral of Elizabeth II, her death in 2022. She was queen ...
granted a posthumous pardon in 2013. The term "
Alan Turing law The "Alan Turing law" is an informal term for the law in the United Kingdom, contained in the Policing and Crime Act 2017, which serves as an amnesty law to pardon men who were cautioned or convicted under historical legislation that outlawe ...
" is now used informally to refer to a 2017 law in the United Kingdom that retroactively pardoned men cautioned or convicted under historical legislation that outlawed homosexual acts. Turing has an extensive legacy with statues of him and many things named after him, including an annual award for computer science innovations. He appears on the current
Bank of England £50 note The Bank of England £50 note is a sterling banknote. It is the highest denomination of banknote currently issued for public circulation by the Bank of England. The current note, the first of this denomination to be printed in polymer, entered ...
, which was released on 23 June 2021, to coincide with his birthday. A 2019 BBC series, as voted by the audience, named him the greatest person of the 20th century.


Early life and education


Family

Turing was born in
Maida Vale Maida Vale ( ) is an affluent residential district consisting of the northern part of Paddington in West London, west of St John's Wood and south of Kilburn. It is also the name of its main road, on the continuous Edgware Road. Maida Vale is p ...
, London, while his father, Julius Mathison Turing (1873–1947), was on leave from his position with the
Indian Civil Service The Indian Civil Service (ICS), officially known as the Imperial Civil Service, was the higher civil service of the British Empire in India during British rule in the period between 1858 and 1947. Its members ruled over more than 300 million ...
(ICS) of the British Raj government at
Chatrapur Chhatrapur (also spelt as Chhatarpur) is a town and a Notified Area Council since 1955 in Ganjam district in the state of Odisha, India. It is the district headquarters town of Ganjam district. Chhatrapur is a Tehsil / Block (CD) in the Ganja ...
, then in the
Madras Presidency The Madras Presidency, or the Presidency of Fort St. George, also known as Madras Province, was an administrative subdivision (presidency) of British India. At its greatest extent, the presidency included most of southern India, including the ...
and presently in
Odisha Odisha (English: , ), formerly Orissa ( the official name until 2011), is an Indian state located in Eastern India. It is the 8th largest state by area, and the 11th largest by population. The state has the third largest population of ...
state, in India. Turing's father was the son of a clergyman, the Rev. John Robert Turing, from a Scottish family of merchants that had been based in the Netherlands and included a
baronet A baronet ( or ; abbreviated Bart or Bt) or the female equivalent, a baronetess (, , or ; abbreviation Btss), is the holder of a baronetcy, a hereditary title awarded by the British Crown. The title of baronet is mentioned as early as the 14th ...
. Turing's mother, Julius's wife, was Ethel Sara Turing (; 1881–1976), daughter of Edward Waller Stoney, chief engineer of the Madras Railways. The Stoneys were a
Protestant Protestantism is a Christian denomination, branch of Christianity that follows the theological tenets of the Reformation, Protestant Reformation, a movement that began seeking to reform the Catholic Church from within in the 16th century agai ...
Anglo-Irish Anglo-Irish people () denotes an ethnic, social and religious grouping who are mostly the descendants and successors of the English Protestant Ascendancy in Ireland. They mostly belong to the Anglican Church of Ireland, which was the establis ...
gentry Gentry (from Old French ''genterie'', from ''gentil'', "high-born, noble") are "well-born, genteel and well-bred people" of high social class, especially in the past. Word similar to gentle imple and decentfamilies ''Gentry'', in its widest ...
family from both
County Tipperary County Tipperary ( ga, Contae Thiobraid Árann) is a county in Ireland. It is in the province of Munster and the Southern Region. The county is named after the town of Tipperary, and was established in the early 13th century, shortly after th ...
and
County Longford County Longford ( gle, Contae an Longfoirt) is a county in Ireland. It is in the province of Leinster. It is named after the town of Longford. Longford County Council is the local authority for the county. The population of the county was 46,6 ...
, while Ethel herself had spent much of her childhood in
County Clare County Clare ( ga, Contae an Chláir) is a county in Ireland, in the Southern Region and the province of Munster, bordered on the west by the Atlantic Ocean. Clare County Council is the local authority. The county had a population of 118,817 ...
. Julius and Ethel married on 1 October 1907 at Batholomew's church on Clyde Road, in Dublin. Julius's work with the ICS brought the family to British India, where his grandfather had been a general in the
Bengal Army The Bengal Army was the army of the Bengal Presidency, one of the three presidencies of British India within the British Empire. The presidency armies, like the presidencies themselves, belonged to the East India Company (EIC) until the Govern ...
. However, both Julius and Ethel wanted their children to be brought up in Britain, so they moved to
Maida Vale Maida Vale ( ) is an affluent residential district consisting of the northern part of Paddington in West London, west of St John's Wood and south of Kilburn. It is also the name of its main road, on the continuous Edgware Road. Maida Vale is p ...
, London, where Alan Turing was born on 23 June 1912, as recorded by a
blue plaque A blue plaque is a permanent sign installed in a public place in the United Kingdom and elsewhere to commemorate a link between that location and a famous person, event, or former building on the site, serving as a historical marker. The term i ...
on the outside of the house of his birth, later the Colonnade Hotel. Turing had an elder brother, John (the father of Sir John Dermot Turing, 12th Baronet of the Turing baronets). Turing's father's civil service commission was still active and during Turing's childhood years, his parents travelled between
Hastings Hastings () is a large seaside town and borough in East Sussex on the south coast of England, east to the county town of Lewes and south east of London. The town gives its name to the Battle of Hastings, which took place to the north-west ...
in the United Kingdom and India, leaving their two sons to stay with a retired
Army An army (from Old French ''armee'', itself derived from the Latin verb ''armāre'', meaning "to arm", and related to the Latin noun ''arma'', meaning "arms" or "weapons"), ground force or land force is a fighting force that fights primarily on ...
couple. At Hastings, Turing stayed at
Baston Lodge Baston Lodge is a residential villa in St Leonards-on-Sea, Hastings, East Sussex, southern England. The building was designed by Decimus Burton (1800–1881) as a seaside villa for John Ward, a friend, and completed in 1850. The architecture is ...
, Upper Maze Hill,
St Leonards-on-Sea St Leonards-on-Sea (commonly known as St Leonards) is a town and seaside resort in the Borough of Hastings in East Sussex, England. It has been part of the borough since the late 19th century and lies to the west of central Hastings. The origina ...
, now marked with a blue plaque. The plaque was unveiled on 23 June 2012, the centenary of Turing's birth. Very early in life, Turing showed signs of the genius that he was later to display prominently. His parents purchased a house in
Guildford Guildford () is a town in west Surrey, around southwest of central London. As of the 2011 census, the town has a population of about 77,000 and is the seat of the wider Borough of Guildford, which had around inhabitants in . The name "Guildf ...
in 1927, and Turing lived there during school holidays. The location is also marked with a blue plaque.


School

Turing's parents enrolled him at St Michael's, a primary school at 20 Charles Road,
St Leonards-on-Sea St Leonards-on-Sea (commonly known as St Leonards) is a town and seaside resort in the Borough of Hastings in East Sussex, England. It has been part of the borough since the late 19th century and lies to the west of central Hastings. The origina ...
, from the age of six to nine. The headmistress recognised his talent, noting that she has "...had clever boys and hardworking boys, but Alan is a genius." Between January 1922 and 1926, Turing was educated at Hazelhurst Preparatory School, an independent school in the village of
Frant Frant is a village and civil parish in the Wealden District of East Sussex, England, on the Kentish border about three miles (5 km) south of Royal Tunbridge Wells. When the iron industry was at its height, much of the village was owned ...
in Sussex (now
East Sussex East Sussex is a ceremonial and non-metropolitan county in South East England on the English Channel coast. It is bordered by Kent to the north and east, West Sussex to the west, and Surrey to the north-west. The largest settlement in East Su ...
). In 1926, at the age of 13, he went on to
Sherborne School (God and My Right) , established = 705 by Aldhelm, re-founded by King Edward VI 1550 , closed = , type = Public school Independent, boarding school , religion = Church of England , president = , chair_label = Chairman of the governors , ...
, a boarding independent school in the market town of
Sherborne Sherborne is a market town and civil parish in north west Dorset, in South West England. It is sited on the River Yeo, on the edge of the Blackmore Vale, east of Yeovil. The parish includes the hamlets of Nether Coombe and Lower Clatcombe. T ...
in Dorset, where he boarded at Westcott House. The first day of term coincided with the 1926 General Strike, in Britain, but Turing was so determined to attend that he rode his bicycle unaccompanied from
Southampton Southampton () is a port city in the ceremonial county of Hampshire in southern England. It is located approximately south-west of London and west of Portsmouth. The city forms part of the South Hampshire built-up area, which also covers Po ...
to Sherborne, stopping overnight at an inn. Turing's natural inclination towards mathematics and science did not earn him respect from some of the teachers at Sherborne, whose definition of education placed more emphasis on the
classics Classics or classical studies is the study of classical antiquity. In the Western world, classics traditionally refers to the study of Classical Greek and Roman literature and their related original languages, Ancient Greek and Latin. 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". Despite this, Turing continued to show remarkable ability in the studies he loved, solving advanced problems in 1927 without having studied even elementary
calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...
. In 1928, aged 16, Turing encountered
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
's work; not only did he grasp it, but it is possible that he managed to deduce Einstein's questioning of
Newton's laws of motion Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in moti ...
from a text in which this was never made explicit.


Christopher Morcom

At Sherborne, Turing formed a significant friendship with fellow pupil Christopher Collan Morcom (13 July 1911 – 13 February 1930), who has been described as Turing's "first love". Their relationship provided inspiration in Turing's future endeavours, but it was cut short by Morcom's death, in February 1930, from complications of
bovine tuberculosis Bovines ( subfamily Bovinae) comprise a diverse group of 10 genera of medium to large-sized ungulates, including cattle, bison, African buffalo, water buffalos, and the four-horned and spiral-horned antelopes. The evolutionary relationship betw ...
, contracted after drinking infected cow's milk some years previously. The event caused Turing great sorrow. He coped with his grief by working that much harder on the topics of science and mathematics that he had shared with Morcom. In a letter to Morcom's mother, Frances Isobel Morcom (née Swan), Turing wrote: Turing's relationship with Morcom's mother continued long after Morcom's death, with her sending gifts to Turing, and him sending letters, typically on Morcom's birthday. A day before the third anniversary of Morcom's death (13 February 1933), he wrote to Mrs. Morcom: Some have speculated that Morcom's death was the cause of Turing's
atheism Atheism, in the broadest sense, is an absence of belief in the existence of deities. Less broadly, atheism is a rejection of the belief that any deities exist. In an even narrower sense, atheism is specifically the position that there no d ...
and
materialism Materialism is a form of philosophical monism which holds matter to be the fundamental substance in nature, and all things, including mental states and consciousness, are results of material interactions. According to philosophical materiali ...
. Apparently, at this point in his life he still believed in such concepts as a spirit, independent of the body and surviving death. In a later letter, also written to Morcom's mother, Turing wrote:


University and work on computability

After Sherborne, Turing studied as an undergraduate from 1931 to 1934 at
King's College, Cambridge King's College is a constituent college of the University of Cambridge. Formally The King's College of Our Lady and Saint Nicholas in Cambridge, the college lies beside the River Cam and faces out onto King's Parade in the centre of the city ...
, where he was awarded first-class honours in mathematics. In 1935, at the age of 22, he was elected a
Fellow A fellow is a concept whose exact meaning depends on context. In learned or professional societies, it refers to a privileged member who is specially elected in recognition of their work and achievements. Within the context of higher education ...
of King's College on the strength of a dissertation in which he proved a version of the
central limit theorem In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselv ...
. Unknown to Turing, this version of the theorem had already been proven, in 1922, by
Jarl Waldemar Lindeberg Jarl Waldemar Lindeberg (4 August 1876, Helsinki – 24 December 1932, Helsinki) was a Finnish mathematician known for work on the central limit theorem. Life and work Lindeberg was son of a teacher at the Helsinki Polytechnical Institute and at ...
. Despite this, the committee found Turing's methods original and so regarded the work worthy of consideration for the fellowship.
Abram Besicovitch Abram Samoilovitch Besicovitch (or Besikovitch) (russian: link=no, Абра́м Само́йлович Безико́вич; 23 January 1891 – 2 November 1970) was a Russian mathematician, who worked mainly in England. He was born in Berdyansk ...
's report for the committee went so far as to say that if Turing's work had been published before Lindeberg's, it would have been "an important event in the mathematical literature of that year". In 1936, Turing published his paper "
On Computable Numbers, with an Application to the Entscheidungsproblem Turing's proof is a proof by Alan Turing, first published in January 1937 with the title "On Computable Numbers, with an Application to the ". It was the second proof (after Church's theorem) of the negation of Hilbert's ; that is, the conjecture ...
". It was published in the ''Proceedings of the London Mathematical Society'' journal in two parts, the first on 30 November and the second on 23 December. In this paper, Turing reformulated
Kurt Gödel Kurt Friedrich Gödel ( , ; April 28, 1906 – January 14, 1978) was a logician, mathematician, and philosopher. Considered along with Aristotle and Gottlob Frege to be one of the most significant logicians in history, Gödel had an imme ...
's 1931 results on the limits of proof and computation, replacing Gödel's universal arithmetic-based formal language with the formal and simple hypothetical devices that became known as
Turing machine A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algori ...
s. The ''
Entscheidungsproblem In mathematics and computer science, the ' (, ) is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. The problem asks for an algorithm that considers, as input, a statement and answers "Yes" or "No" according to whether the statem ...
'' (decision problem) was originally posed by German mathematician
David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many a ...
in 1928. Turing proved that his "universal computing machine" would be capable of performing any conceivable mathematical computation if it were representable as an
algorithm In mathematics and computer science, an algorithm () is a finite sequence of rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specificat ...
. He went on to prove that there was no solution to the ''decision problem'' by first showing that the
halting problem In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever. Alan Turing proved in 1936 that a g ...
for Turing machines is undecidable: it is not possible to decide algorithmically whether a Turing machine will ever halt. This paper has been called "easily the most influential math paper in history". Although
Turing's proof Turing's proof is a proof by Alan Turing, first published in January 1937 with the title "On Computable Numbers, with an Application to the ". It was the second proof (after Church's theorem) of the negation of Hilbert's ; that is, the conjecture ...
was published shortly after
Alonzo Church Alonzo Church (June 14, 1903 – August 11, 1995) was an American mathematician, computer scientist, logician, philosopher, professor and editor who made major contributions to mathematical logic and the foundations of theoretical computer scienc ...
's equivalent proof using his
lambda calculus Lambda calculus (also written as ''λ''-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation ...
, Turing's approach is considerably more accessible and intuitive than Church's. It also included a notion of a 'Universal Machine' (now known as a
universal Turing machine In computer science, a universal Turing machine (UTM) is a Turing machine that can simulate an arbitrary Turing machine on arbitrary input. The universal machine essentially achieves this by reading both the description of the machine to be simu ...
), with the idea that such a machine could perform the tasks of any other computation machine (as indeed could Church's lambda calculus). According to the
Church–Turing thesis In computability theory, the Church–Turing thesis (also known as computability thesis, the Turing–Church thesis, the Church–Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis) is a thesis about the nature of comp ...
, Turing machines and the lambda calculus are capable of computing anything that is computable.
John von Neumann John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...
acknowledged that the central concept of the modern computer was due to Turing's paper. To this day, Turing machines are a central object of study in
theory of computation In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation, using an algorithm, how efficiently they can be solved or to what degree (e.g., a ...
. From September 1936 to July 1938, Turing spent most of his time studying under Church at
Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...
, in the second year as a Jane Eliza Procter Visiting Fellow. In addition to his purely mathematical work, he studied cryptology and also built three of four stages of an electro-mechanical
binary multiplier A binary multiplier is an electronic circuit used in digital electronics, such as a computer, to multiply two binary numbers. A variety of computer arithmetic techniques can be used to implement a digital multiplier. Most techniques involve compu ...
. In June 1938, he obtained his PhD from the
Department of Mathematics Department may refer to: * Departmentalization, division of a larger organization into parts with specific responsibility Government and military *Department (administrative division), a geographical and administrative division within a country, ...
at Princeton; his dissertation, ''
Systems of Logic Based on Ordinals ''Systems of Logic Based on Ordinals'' was the PhD dissertation of the mathematician Alan Turing. Turing's thesis is not about a new type of formal logic, nor was he interested in so-called ‘ranked logic’ systems derived from ordinal or relat ...
'', introduced the concept of
ordinal logic In mathematics, ordinal logic is a logic associated with an ordinal number by recursively adding elements to a sequence of previous logics.Solomon Feferman, ''Turing in the Land of O(z)'' in "The universal Turing machine: a half-century survey" by R ...
and the notion of relative computing, in which Turing machines are augmented with so-called
oracles An oracle is a person or agency considered to provide wise and insightful counsel or prophetic predictions, most notably including precognition of the future, inspired by deities. As such, it is a form of divination. Description The word '' ...
, allowing the study of problems that cannot be solved by Turing machines. John von Neumann wanted to hire him as his postdoctoral assistant, but he went back to the United Kingdom.


Career and research

When Turing returned to Cambridge, he attended lectures given in 1939 by
Ludwig Wittgenstein Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He is considere ...
about the
foundations of mathematics Foundations of mathematics is the study of the philosophy, philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the natu ...
. The lectures have been reconstructed verbatim, including interjections from Turing and other students, from students' notes. Turing and Wittgenstein argued and disagreed, with Turing defending
formalism Formalism may refer to: * Form (disambiguation) * Formal (disambiguation) * Legal formalism, legal positivist view that the substantive justice of a law is a question for the legislature rather than the judiciary * Formalism (linguistics) * Scient ...
and Wittgenstein propounding his view that mathematics does not discover any absolute truths, but rather invents them.


Cryptanalysis

During the Second World War, Turing was a leading participant in the breaking of German ciphers at
Bletchley Park Bletchley Park is an English country house and estate in Bletchley, Milton Keynes ( Buckinghamshire) that became the principal centre of Allied code-breaking during the Second World War. The mansion was constructed during the years following ...
. The historian and wartime codebreaker
Asa Briggs Asa Briggs, Baron Briggs (7 May 1921 – 15 March 2016) was an English historian. He was a leading specialist on the Victorian era, and the foremost historian of broadcasting in Britain. Briggs achieved international recognition during his lon ...
has said, "You needed exceptional talent, you needed genius at Bletchley and Turing's was that genius." From September 1938, Turing worked part-time with the
Government Code and Cypher School Government Communications Headquarters, commonly known as GCHQ, is an intelligence and security organisation responsible for providing signals intelligence (SIGINT) and information assurance (IA) to the government and armed forces of the Unit ...
(GC&CS), the British codebreaking organisation. He concentrated on cryptanalysis of the Enigma cipher machine used by
Nazi Germany Nazi Germany (lit. "National Socialist State"), ' (lit. "Nazi State") for short; also ' (lit. "National Socialist Germany") (officially known as the German Reich from 1933 until 1943, and the Greater German Reich from 1943 to 1945) was ...
, together with
Dilly Knox Alfred Dillwyn "Dilly" Knox, CMG (23 July 1884 – 27 February 1943) was a British classics scholar and papyrologist at King's College, Cambridge and a codebreaker. As a member of the Room 40 codebreaking unit he helped decrypt the Zimmer ...
, a senior GC&CS codebreaker. Soon after the July 1939 meeting near
Warsaw Warsaw ( pl, Warszawa, ), officially the Capital City of Warsaw,, abbreviation: ''m.st. Warszawa'' is the capital and largest city of Poland. The metropolis stands on the River Vistula in east-central Poland, and its population is officia ...
at which the
Polish Cipher Bureau The Cipher Bureau, in Polish language, Polish: ''Biuro Szyfrów'' (), was the interwar Polish General Staff's Second Department of Polish General Staff, Second Department's unit charged with SIGINT and both cryptography (the ''use'' of ciphers an ...
gave the British and French details of the wiring of Enigma machine's rotors and their method of decrypting Enigma machine's messages, Turing and Knox developed a broader solution. The Polish method relied on an insecure
indicator Indicator may refer to: Biology * Environmental indicator of environmental health (pressures, conditions and responses) * Ecological indicator of ecosystem health (ecological processes) * Health indicator, which is used to describe the health o ...
procedure that the Germans were likely to change, which they in fact did in May 1940. Turing's approach was more general, using crib-based decryption for which he produced the functional specification of the
bombe The bombe () was an electro-mechanical device used by British cryptologists to help decipher German Enigma-machine-encrypted secret messages during World War II. The US Navy and US Army later produced their own machines to the same functiona ...
(an improvement on the Polish Bomba (cryptography), Bomba). On 4 September 1939, the day after the UK declared war on Germany, Turing reported to Bletchley Park, the wartime station of GC&CS.Copeland, 2006 p. 378. Like all others who came to Bletchley, he was required to sign the
Official Secrets Act An Official Secrets Act (OSA) is legislation that provides for the protection of state secrets and official information, mainly related to national security but in unrevised form (based on the UK Official Secrets Act 1911) can include all infor ...
, in which he agreed not to disclose anything about his work at Bletchley, with severe legal penalties for violating the Act. 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 dubbed ''Banburismus'' for making much more efficient use of the bombes; developing a procedure dubbed ''Turingery'' for working out the cam settings of the wheels of the Lorenz SZ 40/42 (''Tunny'') cipher machine and, towards the end of the war, the development of a portable secure voice scrambler at Her Majesty's Government Communications Centre, 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, titled ''The Applications of Probability to Cryptography'' and ''Paper on Statistics of Repetitions'', which were of such value to GC&CS and its successor Government Communications Headquarters, GCHQ that they were not released to the The National Archives (United Kingdom), UK National Archives until April 2012, shortly before the centenary of his birth. A GCHQ mathematician, "who identified himself only as Richard," said at the time that the fact that the contents had been restricted under the Official Secrets Act for some 70 years demonstrated their importance, and their relevance to post-war cryptanalysis: Turing had 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". According to historian Ronald Lewin, I.J. Good, Jack Good, a cryptanalyst who worked with Turing, said of his colleague: Peter Hilton recounted his experience working with Turing in
Hut 8 Hut 8 was a section in the Government Code and Cypher School (GC&CS) at Bletchley Park (the British World War II codebreaking station, located in Buckinghamshire) tasked with solving German naval (Kriegsmarine) Enigma messages. The section was l ...
in his "Reminiscences of Bletchley Park" from ''A Century of Mathematics in America:'' Hilton echoed similar thoughts in the Nova PBS documentary ''Decoding Nazi Secrets''. While working at Bletchley, Turing, who was a talented Long-distance running, long-distance runner, occasionally ran the to London when he was needed for meetings, and he was capable of world-class marathon standards. Turing tried out for the 1948 British Olympic team, but he was hampered by an injury. His tryout time for the marathon was only 11 minutes slower than British silver medallist Thomas Richards' Olympic race time of 2 hours 35 minutes. He was Walton Athletic Club's best runner, a fact discovered when he passed the group while running alone. When asked why he ran so hard in training he replied: Due to the problems of counterfactual history, it is hard to estimate the precise effect Ultra intelligence had on the war. However, official war historian Harry Hinsley estimated that this work shortened the war in Europe by more than two years and saved over 14 million lives. Transcript of a lecture given on Tuesday 19 October 1993 at Cambridge University At the end of the war, a memo was sent to all those who had worked at Bletchley Park, reminding them that the code of silence dictated by the Official Secrets Act did not end with the war but would continue indefinitely. Thus, even though Turing was appointed an Order of the British Empire, Officer of the Order of the British Empire (OBE) in 1946 by King George VI for his wartime services, his work remained secret for many years.


Bombe

Within weeks of arriving at Bletchley Park, Turing had specified an electromechanical machine called the
bombe The bombe () was an electro-mechanical device used by British cryptologists to help decipher German Enigma-machine-encrypted secret messages during World War II. The US Navy and US Army later produced their own machines to the same functiona ...
, which could break Enigma more effectively than the Polish ''bomba (cryptography), 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. 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 (cryptanalysis), crib'': a fragment of probable plaintext. For each possible setting of the rotors (which had on the order of 1019 states, or 1022 states for the four-rotor U-boat variant), the bombe performed a chain of logical deductions based on the crib, implemented Electromechanics, electromechanically. 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. A contradiction would occur when an enciphered letter would be turned back into the same plaintext letter, which was impossible with the Enigma. The first bombe was installed on 18 March 1940.


Action This Day

By late 1941, Turing and his fellow cryptanalysts Gordon Welchman, Conel Hugh O'Donel Alexander, Hugh Alexander and Stuart Milner-Barry were frustrated. Building on the Biuro Szyfrów#Gift to allies, work of the Poles, they had set up a good working system for decrypting Enigma signals, but their limited staff and bombes meant they could not translate all the signals. In the summer, they had considerable success, and shipping losses had fallen to under 100,000 tons a month; however, they badly needed more resources to keep abreast of German adjustments. They had tried to get more people and fund more bombes through the proper channels, but had failed. On 28 October they wrote directly to Winston Churchill explaining their difficulties, with Turing as the first named. They emphasised how small their need was compared with the vast expenditure of men and money by the forces and compared with the level of assistance they could offer to the forces. As Andrew Hodges, biographer of Turing, later wrote, "This letter had an electric effect." Churchill wrote a memo to Hastings Ismay, 1st Baron Ismay, General Ismay, which read: "ACTION THIS DAY. Make sure they have all they want on extreme priority and report to me that this has been done." On 18 November, the chief of the secret service reported that every possible measure was being taken. The cryptographers at Bletchley Park did not know of the Prime Minister's response, but as Milner-Barry recalled, "All that we did notice was that almost from that day the rough ways began miraculously to be made smooth." More than two hundred bombes were in operation by the end of the war.


Hut 8 and the naval Enigma

Turing decided to tackle the particularly difficult problem of Cryptanalysis of the Enigma#German Naval Enigma, German naval Enigma "because no one else was doing anything about it and I could have it to myself". In December 1939, Turing solved the essential part of the naval Enigma machine#Indicator, indicator system, which was more complex than the indicator systems used by the other services. 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 the 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." For this, he invented a measure of weight of evidence that he called the ''Ban (unit), ban''. ''Banburismus'' could rule out certain sequences of the Enigma rotors, substantially reducing the time needed to test settings on the bombes. Later this sequential process of accumulating sufficient weight of evidence using decibans (one tenth of a ban) was used in Cryptanalysis of the Lorenz cipher. Turing travelled to the United States in November 1942 and worked with US Navy cryptanalysts on the naval Enigma and bombe construction in Washington; he also visited their United States Naval Computing Machine Laboratory, Computing Machine Laboratory in Dayton, Ohio. Turing's reaction to the American bombe design was far from enthusiastic: During this trip, he also assisted at Bell Labs with the development of secure speech devices. He returned to Bletchley Park in March 1943. During his absence, Colonel Hugh O'Donel Alexander, 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 of Turing's contribution:


Turingery

In July 1942, Turing devised a technique termed ''Turingery'' (or jokingly ''Turingismus'') for use against the Lorenz cipher messages produced by the Germans' new ''Geheimschreiber'' (secret writer) machine. This was a teleprinter Rotor machine, 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. He also introduced the Tunny team to Tommy Flowers who, under the guidance of
Max Newman Maxwell Herman Alexander Newman, FRS, (7 February 1897 – 22 February 1984), generally known as Max Newman, was a British mathematician and codebreaker. His work in World War II led to the construction of Colossus, the world's first operatio ...
, went on to build the Colossus computer, the world's first programmable digital electronic computer, which replaced a simpler prior machine (the Heath Robinson (codebreaking machine), Heath Robinson), and whose superior speed allowed the statistical decryption techniques to be applied usefully to the messages. 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, but he was not directly involved in the Colossus development.


Delilah

Following his work at Bell Labs in the US, Turing pursued the idea of electronic enciphering of speech in the telephone system. In the latter part of the war, he moved to work for the Secret Service's Radio Security Service (later Her Majesty's Government Communications Centre, HMGCC) at Hanslope Park. At the park, 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 (voice encryption), Delilah''. The machine was intended for different applications, but it lacked the capability for use with long-distance radio transmissions. In any case, Delilah was completed too late to be used during the war. Though the system worked fully, with Turing demonstrating it to officials by encrypting and decrypting a recording of a Winston Churchill speech, Delilah was not adopted for use. 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

Between 1945 and 1947, Turing lived in Hampton, London, Hampton, London, while he worked on the design of the ACE (computer), ACE (Automatic Computing Engine) at the National Physical Laboratory (United Kingdom), National Physical Laboratory (NPL). He presented a paper on 19 February 1946, which was the first detailed design of a stored-program computer. John von Neumann, 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". Although ACE was a feasible design, the effect of the
Official Secrets Act An Official Secrets Act (OSA) is legislation that provides for the protection of state secrets and official information, mainly related to national security but in unrevised form (based on the UK Official Secrets Act 1911) can include all infor ...
surrounding the wartime work at Bletchley Park made it impossible for Turing to explain the basis of his analysis of how a computer installation involving human operators would work. This led to delays in starting the project and he became disillusioned. In late 1947 he returned to Cambridge for a sabbatical year during which he produced a seminal work on ''Intelligent Machinery'' that was not published in his lifetime. While he was at Cambridge, the Pilot ACE was being built in his absence. It executed its first program on 10 May 1950, and a number of later computers around the world owe much to it, including the English Electric DEUCE and the American Bendix G-15. The full version of Turing's ACE was not built until after his death. According to the memoirs of the German computer pioneer Heinz Billing from the Max Planck Institute for Physics, published by Genscher, Düsseldorf, there was a meeting between 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, Turing was appointed Reader (academic rank), reader in the School of Mathematics, University of Manchester, Mathematics Department at the
Victoria University of Manchester The Victoria University of Manchester, usually referred to as simply the University of Manchester, was a university in Manchester, England. It was founded in 1851 as Owens College. In 1880, the college joined the federal Victoria University. Afte ...
. A year later, he became deputy director of the Computing Machine Laboratory, where he worked on software for one of the earliest Von Neumann architecture, stored-program computers—the Manchester Mark 1. Turing wrote the first version of the Programmer's Manual for this machine, and was recruited by Ferranti as a consultant in the development of their commercialised machine, the Ferranti Mark 1. He continued to be paid consultancy fees by Ferranti until his death. During this time, he continued to do more abstract work in mathematics, and in "Computing Machinery and Intelligence" (''Mind (journal), Mind'', October 1950), Turing addressed the problem of
artificial intelligence Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animals and humans. Example tasks in which this is done include speech re ...
, and proposed an experiment that 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. In the paper, Turing suggested that rather than building a program to simulate the adult mind, it would be better to produce a simpler one to simulate a child's mind and then to subject it to a course of education. A Turing test#Reverse Turing test and CAPTCHA, 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. By 1950, the program was completed and dubbed the Turochamp. In 1952, he tried to implement it on a Ferranti Mark 1, but lacking enough power, the computer was unable to execute the program. Instead, Turing "ran" the program by flipping through the pages of the algorithm and carrying out its instructions on a chessboard, taking about half an hour per move. The game was recorded. According to Garry Kasparov, Turing's program "played a recognizable game of chess." The program lost to Turing's colleague Alick Glennie, although it is said that it won a game against Champernowne's wife, Isabel. His Turing test was a significant, characteristically provocative, and lasting contribution to the debate regarding artificial intelligence, which continues after more than half a century.


Pattern formation and mathematical biology

When Turing was 39 years old in 1951, he turned to Mathematical and theoretical biology, mathematical biology, finally publishing his masterpiece "The Chemical Basis of Morphogenesis" in January 1952. He was interested in
morphogenesis Morphogenesis (from the Greek ''morphê'' shape and ''genesis'' creation, literally "the generation of form") is the biological process that causes a cell, tissue or organism to develop its shape. It is one of three fundamental aspects of devel ...
, the development of patterns and shapes in biological organisms. He suggested that a system of chemicals reacting with each other and diffusing across space, termed a reaction–diffusion system, could account for "the main phenomena of morphogenesis". He used systems of partial differential equations to model catalytic chemical reactions. For example, if a catalyst A is required for a certain chemical reaction to take place, and if the reaction produced more of the catalyst A, then we say that the reaction is autocatalytic, and there is positive feedback that can be modelled by nonlinear differential equations. Turing discovered that patterns could be created if the chemical reaction not only produced catalyst A, but also produced an inhibitor B that slowed down the production of A. If A and B then diffused through the container at different rates, then you could have some regions where A dominated and some where B did. To calculate the extent of this, Turing would have needed a powerful computer, but these were not so freely available in 1951, so he had to use linear approximations to solve the equations by hand. These calculations gave the right qualitative results, and produced, for example, a uniform mixture that oddly enough had regularly spaced fixed red spots. The Russian biochemist Boris Pavlovich Belousov, Boris Belousov had performed experiments with similar results, but could not get his papers published because of the contemporary prejudice that any such thing violated the second law of thermodynamics. Belousov was not aware of Turing's paper in the ''Philosophical Transactions of the Royal Society''. Although published before the structure and role of DNA was understood, Turing's work on morphogenesis remains relevant today and is considered a seminal piece of work in mathematical biology. One of the early applications of Turing's paper was the work by James Murray explaining spots and stripes on the fur of cats, large and small. Further research in the area suggests that Turing's work can partially explain the growth of "feathers, hair follicles, the branching pattern of lungs, and even the left-right asymmetry that puts the heart on the left side of the chest." In 2012, Sheth, et al. found that in mice, removal of Hox genes causes an increase in the number of digits without an increase in the overall size of the limb, suggesting that Hox genes control digit formation by tuning the wavelength of a Turing-type mechanism. Later papers were not available until ''Collected Works of A. M. Turing'' was published in 1992.


Personal life


Engagement

In 1941, Turing proposed marriage to Hut 8 colleague 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.


Homosexuality and indecency conviction

In January 1952, Turing was 39 when he started a relationship with Arnold Murray, a 19-year-old unemployed man. Just before Christmas, Turing was walking along Manchester's Wilmslow Road, Oxford Road when he met Murray just outside the Dancehouse, Regal Cinema and invited him to lunch. On 23 January, Turing's house was burgled. Murray told Turing that he and the burglar were acquainted, and Turing reported the crime to the police. During the investigation, he acknowledged a sexual relationship with Murray. Homosexual acts were criminal offences in the United Kingdom at that time, and both men were charged with "gross indecency" under Criminal Law Amendment Act 1885#Section 11, Section 11 of the Criminal Law Amendment Act 1885. Initial committal procedure, committal proceedings for the trial were held on 27 February during which Turing's solicitor "reserved his defence", i.e., did not argue or provide evidence against the allegations. Turing was later convinced by the advice of his brother and his own solicitor, and he entered a plea of guilty. The case, ''Elizabeth II, Regina v. Turing and Murray,'' was brought to trial on 31 March 1952. Turing was convicted and given a choice between imprisonment and probation. His probation would be conditional on his agreement to undergo hormone, hormonal physical changes designed to reduce libido, known as "chemical castration." He accepted the option of injections of what was then called stilboestrol (now known as diethylstilbestrol or DES), a synthetic oestrogen; this feminization of his body was continued for the course of one year. The treatment rendered Turing impotence, impotent and caused gynaecomastia, breast tissue to form, fulfilling in the literal sense Turing's prediction that "no doubt I shall emerge from it all a different man, but quite who I've not found out". Murray was given a conditional discharge. 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 British signals intelligence agency that had evolved from GC&CS in 1946, though he kept his academic job. He was denied entry into the United States after his conviction in 1952, but was free to visit other European countries.


Treasure

In the 1940s, Turing became worried about losing his savings in the event of a German invasion. In order to protect it, he bought two Silver as an investment, silver bars weighing and worth £250 (in 2022, £8,000 adjusted for inflation, £48,000 at spot price) and buried them in a wood near Bletchley Park. Upon returning to dig them up, Turing found that he was unable to break his own code describing where exactly he had hidden them. This, along with the fact that the area had been renovated, meant that he never regained the silver.


Death

On 8 June 1954, at his house at 43 Adlington Road, Wilmslow, Turing's housekeeper found him dead. He had died the previous day at the age of 41. Cyanide poisoning was established as the cause of death. When his body was discovered, an apple lay half-eaten beside his bed, and although the apple was not tested for cyanide, it was speculated that this was the means by which Turing had consumed a fatal dose. An Inquests in England and Wales, inquest determined that he had committed suicide. Andrew Hodges and another biographer, David Leavitt, have both speculated that Turing was re-enacting a scene from the Walt Disney film ''Snow White and the Seven Dwarfs (1937 film), Snow White and the Seven Dwarfs'' (1937), his favourite fairy tale. Both men noted that (in Leavitt's words) he took "an especially keen pleasure in the scene where the Wicked Queen immerses her apple in the poisonous brew". Turing's remains were cremated at Woking Crematorium on 12 June 1954, and his ashes were scattered in the gardens of the crematorium, just as his father's had been. Philosopher Jack Copeland has questioned various aspects of the coroner's historical verdict. He suggested an alternative explanation for the cause of Turing's death: the accidental inhalation of cyanide fumes from an apparatus used to electroplating, electroplate gold onto spoons. The potassium cyanide was used to Gold#Commercial chemistry, dissolve the gold. Turing had such an apparatus set up in his tiny spare room. Copeland noted that the autopsy findings were more consistent with inhalation than with ingestion of the poison. Turing also habitually ate an apple before going to bed, and it was not unusual for the apple to be discarded half-eaten. Furthermore, Turing had reportedly borne his legal setbacks and hormone treatment (which had been discontinued a year previously) "with good humour" and had shown no sign of despondency before his death. He even set down a list of tasks that he intended to complete upon returning to his office after the holiday weekend. Turing's mother believed that the ingestion was accidental, resulting from her son's careless storage of laboratory chemicals. Biographer Andrew Hodges theorised that Turing arranged the delivery of the equipment to deliberately allow his mother plausible deniability with regard to any suicide claims. It has been suggested that Turing's belief in fortune-telling may have caused his depressed mood. As a youth, Turing had been told by a fortune-teller that he would be a genius. In mid-May 1954, shortly before his death, Turing again decided to consult a fortune-teller during a day-trip to Lytham St Annes, St Annes-on-Sea with the Greenbaum family. According to the Greenbaums' daughter, Barbara:


Government apology and pardon

In August 2009, British programmer John Graham-Cumming started a petition urging the British government to apologise for Turing's prosecution as a homosexual. The petition received more than 30,000 signatures. The Prime Minister,
Gordon Brown James Gordon Brown (born 20 February 1951) is a British former politician who served as Prime Minister of the United Kingdom and Leader of the Labour Party (UK), Leader of the Labour Party from 2007 to 2010. He previously served as Chance ...
, acknowledged the petition, releasing a statement on 10 September 2009 apologising and describing the treatment of Turing as "appalling": In December 2011, William Jones and his Member of Parliament, John Leech (politician), John Leech, created an e-petition requesting that the British government pardon Turing for his conviction of "gross indecency": The petition gathered over 37,000 signatures, and was submitted to Parliament by the Manchester MP John Leech (politician), John Leech but the request was discouraged by Justice Minister Tom McNally, Baron McNally#Political career, Lord McNally, who said: John Leech (politician), John Leech, the MP for Manchester Withington (UK Parliament constituency), Manchester Withington (2005–15), submitted several bills to Parliament and led a high-profile campaign to secure the pardon. Leech made the case in the House of Commons that Turing's contribution to the war made him a national hero and that it was "ultimately just embarrassing" that the conviction still stood. Leech continued to take the bill through Parliament and campaigned for several years, gaining the public support of numerous leading scientists, including Stephen Hawking. At the British premiere of a film based on Turing's life, ''The Imitation Game'', the producers thanked Leech for bringing the topic to public attention and securing Turing's pardon. Leech is now regularly described as the "architect" of Turing's pardon and subsequently the Alan Turing Law which went on to secure pardons for 75,000 other men and women convicted of similar crimes. On 26 July 2012, a bill was introduced in the British House of Lords, House of Lords to grant a statutory pardon to Turing for offences under section 11 of the Criminal Law Amendment Act 1885, of which he was convicted on 31 March 1952. Late in the year in a letter to ''The Daily Telegraph'', the physicist Stephen Hawking and 10 other signatories including the Astronomer Royal Martin Rees, Baron Rees of Ludlow, Lord Rees, List of presidents of the Royal Society, President of the Royal Society Sir Paul Nurse, Jean Barker, Baroness Trumpington, Lady Trumpington (who worked for Turing during the war) and John Sharkey, Baron Sharkey, Lord Sharkey (the bill's sponsor) called on Prime Minister David Cameron to act on the pardon request. The government indicated it would support the bill, and it passed its third reading in the House of Lords in October. At the bill's second reading in the House of Commons of the United Kingdom, House of Commons on 29 November 2013, Conservative MP Christopher Chope objected to the bill, delaying its passage. The bill was due to return to the House of Commons on 28 February 2014, but before the bill could be debated in the House of Commons, the government elected to proceed under the royal prerogative of mercy. On 24 December 2013,
Queen Elizabeth II Elizabeth II (Elizabeth Alexandra Mary; 21 April 1926 – 8 September 2022) was Queen of the United Kingdom and other Commonwealth realms from 6 February 1952 until Death and state funeral of Elizabeth II, her death in 2022. She was queen ...
signed a pardon for Turing's conviction for "gross indecency", with immediate effect. Announcing the pardon, Lord Chancellor Chris Grayling said Turing deserved to be "remembered and recognised for his fantastic contribution to the war effort" and not for his later criminal conviction. The Queen officially pronounced Turing pardoned in August 2014. The Queen's action is only the fourth royal pardon granted since the conclusion of the Second World War. Pardons are normally granted only when the person is technically innocent, and a request has been made by the family or other interested party; neither condition was met in regard to Turing's conviction. In September 2016, the government announced its intention to expand this retroactive exoneration to other men convicted of similar historical indecency offences, in what was described as an "
Alan Turing law The "Alan Turing law" is an informal term for the law in the United Kingdom, contained in the Policing and Crime Act 2017, which serves as an amnesty law to pardon men who were cautioned or convicted under historical legislation that outlawe ...
". The Alan Turing law is now an informal term for the law in the United Kingdom, contained in the Policing and Crime Act 2017, which serves as an amnesty law to retroactively pardon men who were cautioned or convicted under historical legislation that outlawed homosexual acts. The law applies in England and Wales.


Legacy


Awards, honours, and tributes

Turing was appointed an officer of the Order of the British Empire in 1946. He was also elected a List of Fellows of the Royal Society elected in 1951, Fellow of the Royal Society (FRS) in 1951. 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". A bridge carrying this road was widened, and carries the name Alan Turing Bridge. A Alan Turing Memorial, statue of Turing was unveiled in Manchester on 23 June 2001 in Sackville Park, between the University of Manchester building on Whitworth Street and Canal Street, Manchester, Canal Street. The memorial statue depicts the "father of computer science" sitting on a bench at a central position in the park. Turing is shown holding an apple. The cast bronze bench carries in relief the text 'Alan Mathison Turing 1912–1954', and the motto 'Founder of Computer Science' as it could appear if encoded by an Enigma machine: 'IEKYF ROMSI ADXUO KVKZC GUBJ'. However, the meaning of the coded message is disputed, as the 'u' in 'computer' matches up with the 'u' in 'ADXUO'. As a letter encoded by an enigma machine cannot appear as itself, the actual message behind the code is uncertain. A plaque at the statue's feet reads 'Father of computer science, mathematician, logician, wartime codebreaker, victim of prejudice'. There is also a Bertrand Russell quotation: "Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture." The sculptor buried his own old Amstrad computer under the plinth as a tribute to "the godfather of all modern computers". In 1999, ''Time (magazine), Time'' magazine named Turing as one of the Time 100: The Most Important People of the Century, 100 Most Important People of the 20th century 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." A blue plaque was unveiled at King's College, Cambridge on the centenary of his birth on 23 June 2012 and is now installed at the college's Keynes Building on King's Parade. A high steel sculpture, designed in Turing's honour by Sir Antony Gormley, is planned to be installed at King's College, but Historic England deemed the sculpture too abstract for the setting, saying that it "would result in harm, of a less than substantial nature, to the significance of the listed buildings and landscape, and by extension the conservation area." On 25 March 2021, the Bank of England publicly unveiled the design for a new Bank of England £50 note, £50 note, featuring Turing's portrait, before its official issue on 23 June, Turing's birthday. Turing was selected as the new face of the note in 2019 following a public nomination process.


Centenary celebrations

To mark the 100th anniversary of Turing's birth, the Turing Centenary Advisory Committee (TCAC) co-ordinated the Alan Turing Year in 2012, a year-long programme of events around the world honouring Turing's life and achievements. The TCAC, chaired by S. Barry Cooper with Turing's nephew Sir John Dermot Turing acting as Honorary President, worked with the University of Manchester faculty members and a broad spectrum of people from Cambridge University and
Bletchley Park Bletchley Park is an English country house and estate in Bletchley, Milton Keynes ( Buckinghamshire) that became the principal centre of Allied code-breaking during the Second World War. The mansion was constructed during the years following ...
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Notes and references


Notes


References


Sources

* * * * * * * * Bruderer, Herbert
''Konrad Zuse und die Schweiz. Wer hat den Computer erfunden? Charles Babbage, Alan Turing und John von Neumann''
Oldenbourg Verlag, München 2012, XXVI, 224 Seiten, * * * * * * * * * ** in * * * * * * * * * * * * * Petzold, Charles (2008). "The Annotated Turing: A Guided Tour through Alan Turing's Historic Paper on Computability and the Turing Machine". Indianapolis: Wiley Publishing. * Smith, Roger (1997). ''Fontana History of the Human Sciences''. London: Fontana. * * Weizenbaum, Joseph (1976). ''Computer Power and Human Reason''. London: W.H. Freeman. * and * Turing's mother, who survived him by many years, wrote this 157-page biography of her son, glorifying his life. It was published in 1959, and so could not cover his war work. Scarcely 300 copies were sold (Sara Turing to Lyn Newman, 1967, Library of St John's College, Cambridge). The six-page foreword by Lyn Irvine includes reminiscences and is more frequently quoted. It was re-published by Cambridge University Press in 2012, to honour the centenary of his birth, and included a new foreword by Martin Davis (mathematician), Martin Davis, as well as a never-before-published memoir by Turing's older brother John F. Turing. * This 1986 Hugh Whitemore play tells the story of Turing's life and death. In the original West End and Broadway runs, Derek Jacobi played Turing and he recreated the role in a 1997 television film based on the play made jointly by the BBC and WGBH-TV, WGBH, Boston. The play is published by Amber Lane Press, Oxford, ASIN: B000B7TM0Q * Williams, Michael R. (1985) ''A History of Computing Technology'', Englewood Cliffs, New Jersey: Prentice-Hall, *


Further reading


Articles

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Books

* * * * * (originally published in 1983); basis of the film ''The Imitation Game'' * (originally published in 1959 by W. Heffer & Sons, Ltd)


External links


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 Turing and
John von Neumann John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...

How Alan Turing Cracked The Enigma Code
Imperial War Museums
Alan Turing Year

CiE 2012: Turing Centenary Conference

Science in the Making
Alan Turing's papers in the Royal Society's archives
Alan Turing
site maintained by Andrew Hodges including
short biography

AlanTuring.net – Turing Archive for the History of Computing
by Jack Copeland
The Turing Archive
nbsp;– contains scans of some unpublished documents and material from the King's College, Cambridge archive
Alan Turing Papers
– University of Manchester Library, Manchester *
Sherborne School Archives
– holds papers relating to Turing's time at Sherborne School
Alan Turing plaques
recorded on openplaques.org
Alan Turing
archive on New Scientist {{DEFAULTSORT:Turing, Alan Mathison Alan Turing, 1912 births 1954 suicides 20th-century English mathematicians 20th-century atheists 20th-century English philosophers Academics of the University of Manchester Academics of the University of Manchester Institute of Science and Technology Alumni of King's College, Cambridge Artificial intelligence researchers Bayesian statisticians Bletchley Park people British anti-fascists British cryptographers British people of World War II Computability theorists Computer designers English atheists English computer scientists English inventors English logicians English male long-distance runners English people of Irish descent English people of Scottish descent Fellows of King's College, Cambridge Fellows of the Royal Society Former Protestants Foreign Office personnel of World War II Gay academics Gay scientists Gay sportsmen GCHQ people History of artificial intelligence History of computing in the United Kingdom LGBT-related suicides LGBT mathematicians LGBT philosophers LGBT scientists from the United Kingdom LGBT sportspeople from England LGBT track and field athletes Officers of the Order of the British Empire People educated at Sherborne School People from Maida Vale People from Wilmslow People convicted for homosexuality in the United Kingdom People who have received posthumous pardons Princeton University alumni Recipients of British royal pardons Theoretical biologists Theoretical computer scientists Deaths by cyanide poisoning Suicides by cyanide poisoning Suicides in England