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Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English
mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces ...

mathematician
,
computer scientist A computer scientist is a person who has acquired the knowledge of computer science Computer science deals with the theoretical foundations of information, algorithms and the architectures of its computation as well as practical techniques ...

computer scientist
,
logic Logic is an interdisciplinary field which studies truth and reasoning. Informal logic seeks to characterize Validity (logic), valid arguments informally, for instance by listing varieties of fallacies. Formal logic represents statements and ar ...

logic
ian,
cryptanalyst cipher machine Cryptanalysis (from the Greek language, Greek ''kryptós'', "hidden", and ''analýein'', "to analyze") is the study of analyzing information systems in order to study the hidden aspects of the systems. Cryptanalysis is used to b ...
,
philosopher A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about Metaphysics, existence, reason, Epistemology, knowledge, Ethics, values, Philosophy of mind, mi ...

philosopher
, and
theoretical biologist Mathematical and theoretical biology or, Biomathematics, is a branch of biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular bi ...
. Turing was highly influential in the development of
theoretical computer science Theoretical computer science (TCS) is a subset of general computer science Computer science deals with the theoretical foundations of information, algorithms and the architectures of its computation as well as practical techniques for the ...

theoretical computer science
, providing a formalisation of the concepts of
algorithm In and , an algorithm () is a finite sequence of , computer-implementable instructions, typically to solve a class of problems or to perform a computation. Algorithms are always and are used as specifications for performing s, , , and other ...

algorithm
and
computation Computation is any type of that includes both al and non-arithmetical steps and which follows a well-defined model (e.g. an ). Mechanical or electronic devices (or, , people) that perform computations are known as ''s''. An especially well-know ...

computation
with the
Turing machine A Turing machine is a mathematical model of computation In computer science, and more specifically in computability theory (computer science), computability theory and computational complexity theory, a model of computation is a model which des ...

Turing machine
, which can be considered a model of a
general-purpose computer A computer is a machine A machine is a man-made device that uses power to apply forces and control movement to perform an action. Machines can be driven by animals and people A people is a plurality of person A person (plural ...
. Turing is widely considered to be the father of theoretical computer science and
artificial intelligence Artificial intelligence (AI) is intelligence Intelligence has been defined in many ways: the capacity for abstraction Abstraction in its main sense is a conceptual process where general rules and concept Concepts are defined as abstra ...

artificial intelligence
. Born in
Maida Vale Maida Vale ( ) is an affluent residential district consisting of the northern part of Paddington Paddington is an within the , in . First a medieval parish then a , it was integrated with Westminster and in 1965. Three important landmarks ...
, 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 The Midlands is the central part of England ...

southern England
. He graduated at
King's College, Cambridge King's College is a constituent college of the University of Cambridge in Cambridge Cambridge ( ) is a College town, university city and the county town of Cambridgeshire, England, on the River Cam approximately north of London. At the Un ...

King's College, Cambridge
with a degree in mathematics. Whilst he was a
fellow A fellow is a broad concept whose exact meaning depends on context. In learned Learning is the process of acquiring new understanding, knowledge, behaviors, skills, value (personal and cultural), values, attitudes, and preferences. The abil ...
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 In computer science, and more specifically in computability theory (computer science), computability theory and computational complexity theory, a model of computation is a model which des ...

Turing machine
, and went on to prove the
halting problem In computability theory Computability theory, also known as recursion theory, is a branch of mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set the ...
for Turing machines is undecidable. In 1938, he obtained his
PhD A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as La ...
from the Department of Mathematics at
Princeton University Princeton University is a private Private or privates may refer to: Music * "In Private "In Private" was the third single in a row to be a charting success for United Kingdom, British singer Dusty Springfield, after an absence of nearly tw ...

Princeton University
. During the
Second World War World War II or the Second World War, often abbreviated as WWII or WW2, was a global war A world war is "a war War is an intense armed conflict between states State may refer to: Arts, entertainment, and media Literatur ...
, Turing worked for the
Government Code and Cypher School Government Communications Headquarters, commonly known as GCHQ, is an intelligence Intelligence has been defined in many ways: the capacity for logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=none, ...
(GC&CS) at
Bletchley Park Bletchley Park is an English country house An English country house is a large house or mansion in the English countryside. Such houses were often owned by individuals who also owned a Townhouse (Great Britain), town house. This allowed ...

Bletchley Park
, Britain's
codebreaking cipher machine Cryptanalysis (from the Greek language, Greek ''kryptós'', "hidden", and ''analýein'', "to analyze") is the study of analyzing information systems in order to study the hidden aspects of the systems. Cryptanalysis is used to bre ...
centre that produced
Ultra Ultra was the designation adopted by British British may refer to: Peoples, culture, and language * British people, nationals or natives of the United Kingdom, British Overseas Territories, and Crown Dependencies. ** Britishness, the Brit ...

Ultra
intelligence. For a time he led
Hut 8 Hut 8 was a section in the Government Code and Cypher School Government Communications Headquarters, commonly known as GCHQ, is an intelligence Intelligence has been defined in many ways: the capacity for logic Logic (from Ancient G ...
, 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 ...

cipher
s, including improvements to the pre-war Polish
bombe The bombe () is an Electromechanics, electro-mechanical device used by the British cryptologists to help decipher German Enigma machine, Enigma-machine-encrypted secret messages during World War II. The United States Navy, US Navy and United S ...
method, an
electromechanical In engineering Engineering is the use of scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad ran ...
machine that could find settings for the
Enigma machine The Enigma machine is a 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 ''en ...

Enigma machine
. Turing played a crucial role in cracking intercepted coded messages that enabled the Allies to defeat the Nazis in many crucial engagements, including the
Battle of the Atlantic The Battle of the Atlantic, the longest continuous military campaign A military campaign is large-scale long-duration significant military strategy Military strategy is a set of ideas implemented by military organization Military orga ...
. Due to the problems of
counterfactual history Counterfactual history, also sometimes referred to as virtual history, is a form of historiography Historiography is the study of the methods of historians in developing history as an academic discipline, and by extension is any body of hist ...
, it is hard to estimate the precise effect Ultra intelligence had on the war, but Professor
Jack Copeland Brian Jack Copeland (born 1950) is Professor of Philosophy at the University of Canterbury, Christchurch, New Zealand, and author of books on the computing pioneer Alan Turing. Overview Jack Copeland's education includes a BPhil and a DPhil fr ...

Jack Copeland
has estimated that this work shortened the war in Europe by more than two years and saved over 14 million lives. 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 Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician A mathematician is s ...
. The Automatic Computing Engine was one of the first designs for a stored-program computer. In 1948, Turing joined
Max Newman Maxwell Herman Alexander Newman, FRS FRS may also refer to: Government and politics * Facility Registry System, a centrally managed Environmental Protection Agency database that identifies places of environmental interest in the United State ...

Max Newman
's Computing Machine Laboratory, at the
Victoria University of Manchester The Victoria University of Manchester, usually referred to as simply the University of Manchester, was a university A university ( la, universitas, 'a whole') is an educational institution, institution of higher education, higher (or Tertiary ...
, where he helped develop the
Manchester computers The Manchester computers were an innovative series of stored-program electronic computers developed during the 30-year period between 1947 and 1977 by a small team at the University of Manchester , mottoeng = Knowledge, Wisdom, Humanity , e ...
and became interested in
mathematical biology Mathematical and theoretical biology or, Biomathematics, is a branch of biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular bi ...
. He wrote a paper on the chemical basis of
morphogenesis Morphogenesis (from the Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is a ...
and predicted
oscillating Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of Mechanical equilibrium, equilibrium) or between two or more different states. The term ''vibration'' is precisely used to describ ...
chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substance A chemical substance is a form of matter In classical physics and general chemistry, matter is any substance that has mass and t ...

chemical reaction
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 t ...
, first observed in the 1960s. Turing was prosecuted in 1952 for homosexual acts; the
Labouchere Amendment Section 11 of the Criminal Law Amendment Act 1885, commonly known as the Labouchere Amendment, made " gross indecency" a crime in the United Kingdom. In practice, the law was used broadly to prosecute male homosexual Homosexuality is roma ...
of 1885 had mandated that "gross indecency" was a criminal offence in the UK. He accepted
chemical castration Chemical castration is castration via anaphrodisiac drugs, whether to reduce libido and sexual activity, management of cancer, to treat cancer, or otherwise. Unlike orchiectomy, surgical castration, where the gonads are removed through an incision ...
treatment, with , as an alternative to prison. Turing died in 1954, 16 days before his 42nd birthday, from
cyanide poisoning Cyanide poisoning is poisoning A poison In biology, poisons are Chemical substance, substances that can cause death, injury or harm to organs, Tissue (biology), tissues, Cell (biology), cells, and DNA usually by chemical reactions or oth ...
. An inquest determined his death as a suicide, but it has been noted that the known evidence is also consistent with accidental poisoning. Despite these accomplishments, he was never fully recognised in his home country 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 OSA 1911) can include all information held by gov ...
. In 2009, following an Internet campaign, British Prime Minister
Gordon Brown James Gordon Brown (born 20 February 1951) is a British politician who served as Prime Minister of the United Kingdom The prime minister of the United Kingdom is the head of government The head of government is either the h ...

Gordon Brown
made an official public apology on behalf of the British government for "the appalling way he was treated".
Queen Elizabeth II Elizabeth II (Elizabeth Alexandra Mary; born 21 April 1926) is Queen of the United Kingdom The monarchy of the United Kingdom, commonly referred to as the British monarchy, is the constitutional monarchy A constitutional mo ...

Queen Elizabeth II
granted Turing a posthumous pardon in 2013. The "
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 The Policing and Crime Act 2017 (c. 3) is an Act of Parliament, act of the Parliament of the United Kingdom. It received r ...
" is now an informal term for 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, many things named after him including an annual award for computer science innovations. He is due to appear on the Bank of England £50 note, to be released in June 2021. 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 Paddington is an within the , in . First a medieval parish then a , it was integrated with Westminster and in 1965. Three important landmarks ...
, 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 British India during British Raj, British rule in the period between 1858 and 1947. Its members ruled over mor ...
(ICS) at
Chatrapur Chhatrapur (also spelt as Chhatarpur) is a town and a Notified Area Council 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 Ganjam District of ...
, then in the
Madras Presidency The Madras Presidency, or the Presidency of Fort St. George, also known as Madras Province, was an Presidencies and provinces of British India, administrative subdivision (presidency) of British India. At its greatest extent, the presidency inc ...
and presently in
Odisha Odisha (English: , ), formerly Orissa (), is an States and union territories of India, Indian state located in East India, Eastern India. It is the List of states and union territories of India by area, 8th largest state by area, and the Li ...

Odisha
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 rare female equivalent, a baronetess (, , or ; abbreviation Btss), is the holder of a baronetcy, a hereditary title awarded by the British Crown The Crown is the in all its aspects within ...

baronet
. 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 form of that originated with the 16th-century , a movement against what its followers perceived to be in the . Protestants originating in the Reformation reject the Roman Catholic doctrine of , but disagree among themselves ...
Anglo-Irish Anglo-Irish () is a term which was more commonly used in the 19th and early 20th centuries to identify an ethnic group An ethnic group or ethnicity is a grouping of people A people is any plurality of person A person (plural people ...
gentry Gentry (from Old French Old French (, , ; Modern French French ( or ) is a Romance language of the Indo-European family. It descended from the Vulgar Latin of the Roman Empire, as did all Romance languages. French evolved from Ga ...
family from both
County Tipperary County Tipperary ( ga, Contae Thiobraid Árann) is a county A county is a geographical region of a country used for administrative or other purposesChambers Dictionary The ''Chambers Dictionary'' (''TCD'') was first published by Willia ...

County Tipperary
and
County Longford County Longford ( gle, Contae an Longfoirt) is a county A county is a geographical region of a country used for administrative or other purposesChambers Dictionary The ''Chambers Dictionary'' (''TCD'') was first published by William Cha ...
, while Ethel herself had spent much of her childhood in
County Clare County Clare ( ga, Contae an Chláir) is a county A county is a geographical region of a country used for administrative or other purposesChambers Dictionary, L. Brookes (ed.), 2005, Chambers Harrap Publishers Ltd, Edinburgh in certain mod ...
. 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 The Bengal Presidency, officially the Presidency of Fort William and later Bengal Province, was a subdivision of the British India, British Empire in India. At the height of its territo ...
. 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 Paddington is an within the , in . First a medieval parish then a , it was integrated with Westminster and in 1965. Three important landmarks ...
, London, where Alan Turing was born on 23 June 1912, as recorded by a blue plaque on the outside of the house of his birth, later the Colonnade Hotel. Turing had an elder brother, John (the father of , 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 seaside town A town is a human settlement. Towns are generally larger than villages and smaller than city, cities, though the criteria to distinguish between them vary considerably in different parts of the world. Origi ...

Hastings
in the United Kingdom and India, leaving their two sons to stay with a retired
Army An army (from Latin ''arma'' "arms, weapons" via Old French ''armée'', "armed" eminine, ground force or land force is a fighting force that fights primarily on land. In the broadest sense, it is the land-based military branch Military branch ...
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 A seaside resort is a resort town, town, village, or hotel that serves as a Resort, vacation resort and is located on a coast. Sometimes the concept includes an aspe ...

St Leonards-on-Sea
, 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 Surrey Surrey () is a county A county is a geographical region of a country used for administrative or other purposesChambers Dictionary The ''Chambers Dictionary'' (''TCD'') was first published by William ...

Guildford
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 day school at 20 Charles Road,
St Leonards-on-Sea St Leonards-on-Sea (commonly known as St Leonards) is a town and seaside resort A seaside resort is a resort town, town, village, or hotel that serves as a Resort, vacation resort and is located on a coast. Sometimes the concept includes an aspe ...

St Leonards-on-Sea
, at the age of six. The headmistress recognised his talent early on, as did many of his subsequent teachers. 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, 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 vill ...
in Sussex (now
East Sussex East Sussex is a county A county is a geographical region of a country used for administrative or other purposesChambers Dictionary The ''Chambers Dictionary'' (''TCD'') was first published by William Chambers (publisher), William and R ...

East Sussex
). In 1926, at the age of 13, he went on to
Sherborne School (God and My Right) , established = 705 by Aldhelm Aldhelm ( ang, Ealdhelm, la, Aldhelmus Malmesberiensis) (c. 63925 May 709), Abbot of Malmesbury Abbey, Bishop of Sherborne, and a writer and scholar of Latin Latin (, or , ) is a classi ...
, a boarding independent school in the market town of
Sherborne Sherborne is a market town A market town is a European that obtained by custom or royal charter, in the , a market right, which allowed it to host a regular ; this distinguished it from a or . In Britain, small rural towns with a hin ...
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 A port is a maritime law, maritime facility comprising one or more Wharf, wharves or loading areas, where ships load and discharge Affreightment, cargo and passengers. Although usually situated on a sea ...
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 Classical antiquity (also the classical era, classical period or classical age) is the period of cultural history History (from Greek#REDIRECT Greek Greek may refer ...

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 mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations ...

calculus
. 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 physicists of all time. Einstein is known for developing the theory of relativity The theo ...

Albert Einstein
'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 law Law is a system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its ...
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 ''Mycobacterium bovis'' (''M. bovis'') is a slow-growing (16- to 20-hour generation time) aerobic bacterium and the causative agent of tuberculosis Tuberculosis (TB) is an infectious disease usually caused by ''Mycobacterium tuberculosi ...
, 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 birthdays. 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 A belief is an attitude Attitude may refer to: Philosophy and psychology * Attitude (psychology) In psychology Psychology is the science of mind and behavior. Psy ...

atheism
and
materialism Materialism is a form of philosophical monism which holds matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimate ...
. 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 in Cambridge Cambridge ( ) is a College town, university city and the county town of Cambridgeshire, England, on the River Cam approximately north of London. At the Un ...

King's College, Cambridge
, 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 broad concept whose exact meaning depends on context. In learned Learning is the process of acquiring new understanding, knowledge, behaviors, skills, value (personal and cultural), values, attitudes, and preferences. The abil ...
of King's College on the strength of a dissertation in which he proved the
central limit theorem In probability theory Probability theory is the branch of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in ...
. Unknown to the committee, the theorem had already been proven, in 1922, by Jarl Waldemar Lindeberg. A blue plaque at the college was unveiled on the centenary of his birth on 23 June 2012 and is now installed at the college's Keynes Building on King's Parade. In 1936, Turing published his paper "
On Computable Numbers, with an Application to the EntscheidungsproblemTuring's proof is a proof by Alan Turing, first published in January 1937 with the title "On Computable Numbers, with an Application to the Entscheidungsproblem." It was the second proof (after Church's theorem) of the conjecture that some purely mat ...
". 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 Logic is an interdisciplinary field which studies truth Truth is the property of being in accord with fact or reality.Merriam-Webster's Online Dict ...
'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 In computer science, and more specifically in computability theory (computer science), computability theory and computational complexity theory, a model of computation is a model which des ...

Turing machine
s. The ''
Entscheidungsproblem In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and ...

Entscheidungsproblem
'' (decision problem) was originally posed by German mathematician
David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician This is a List of German mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Ancient Greek, G ...
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 and , an algorithm () is a finite sequence of , computer-implementable instructions, typically to solve a class of problems or to perform a computation. Algorithms are always and are used as specifications for performing s, , , and other ...

algorithm
. He went on to prove that there was no solution to the ''decision problem'' by first showing that the
halting problem In computability theory Computability theory, also known as recursion theory, is a branch of mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set the ...
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 proofTuring's proof is a proof by Alan Turing Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Ancient Greek ...
was published shortly after
Alonzo Church Alonzo Church (June 14, 1903 – August 11, 1995) was an American American(s) may refer to: * American, something of, from, or related to the United States of America, commonly known as the United States The United States of America (US ...
's equivalent proof using his
lambda calculus Lambda calculus (also written as ''λ''-calculus) is a formal system A formal system is an used for inferring theorems from axioms according to a set of rules. These rules, which are used for carrying out the inference of theorems from axioms, ar ...
, 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 Computer science deals with the theoretical foundations of information, algorithms and the architectures of its computation as well as practical techniques for their application. Computer science is the study of , ...

universal Turing machine
), 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 (computation), 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) i ...
, 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 Hungarian Americans (Hungarian language, Hungarian: ''amerikai magyarok'') are United States, Americans of Hungarian p ...

John von Neumann
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 Theoretical computer science (TCS) is a subset of general computer science Computer science deals with the theoretical foundations of information, algorithms and the architectures of its computation a ...
. From September 1936 to July 1938, Turing spent most of his time studying under Church at
Princeton University Princeton University is a private Private or privates may refer to: Music * "In Private "In Private" was the third single in a row to be a charting success for United Kingdom, British singer Dusty Springfield, after an absence of nearly tw ...

Princeton University
, 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 An electronic circuit is composed of individual electronic component An electronic component is any basic discrete device or physical entity in an electronic system Electronic may refer to: *Ele ...

binary multiplier
. In June 1938, he obtained his PhD from the Department of Mathematics at Princeton; his dissertation, '' Systems of Logic Based on Ordinals'', introduced the concept of ordinal logic and the notion of relative computing, in which Turing machines are augmented with so-called
oracles An oracle is a person or agency Agency may refer to: * a governmental or other institution Institutions, according to Samuel P. Huntington, are "stable, valued, recurring patterns of behavior". Institutions can refer to mechanisms which g ...
, 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 Austrian may refer to: * Austrians, someone from Austria or of Austrian descent ** Someone who is considered an Austrian citizen, see Austrian nationali ...

Ludwig Wittgenstein
about the
foundations of mathematics Foundations of mathematics is the study of the philosophical Philosophy (from , ) is the study of general and fundamental questions, such as those about existence Existence is the ability of an entity to interact with physical or mental r ...
. 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) * Scienti ...
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 An English country house is a large house or mansion in the English countryside. Such houses were often owned by individuals who also owned a Townhouse (Great Britain), town house. This allowed ...

Bletchley Park
. 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 In the history of the United Kingdom, the Victorian era was the wikt:period, period of Queen Victoria's ...
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 Intelligence has been defined in many ways: the capacity for logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, label=none, ...
(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 ...

Nazi Germany
, together with
Dilly Knox Alfred Dillwyn "Dilly" Knox, CMG (23 July 1884 – 27 February 1943) was a British classics Classics or classical studies is the study of classical antiquity, and in the Western world The Western world, also known as the West ...
, a senior GC&CS codebreaker. Soon after the July 1939 meeting near
Warsaw Warsaw, * la, Varsovia (Polish language, Polish: ''Warszawa'' ), officially the Capital City of Warsaw, is the capital and List of cities and towns in Poland, largest city of Poland. The metropolis stands on the Vistula, River Vistula in e ...

Warsaw
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 and ...
gave the British and French details of the wiring of
Enigma machine's rotors Enigma, aenigma, or The Enigma may refer to: * Riddle, someone or something that is mysterious or puzzling Biology * Aenigma (beetle), ''Aenigma'' (beetle), a genus of beetles * ''Zulunigma'' or ''Aenigma'', a genus of jumping spiders from South A ...
and their method of decrypting
Enigma machine The Enigma machine is a 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 ''en ...

Enigma machine
's messages, Turing and Knox developed a broader solution. The Polish method relied on an insecure
indicator Indicator may refer to: Biology * Indicator (genus), ''Indicator'' (genus), a genus of birds in the honeyguide family * Environmental indicator of environmental health (pressures, conditions and responses) * Ecological indicator of ecosystem hea ...

indicator
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 (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. 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 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 Government Communications Headquarters, commonly known as GCHQ, is an intelligence Intelligence has been defined in many ways: the capacity for logic Logic (from Ancient G ...
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. In 1946, Turing was appointed an Order of the British Empire, Officer of the Order of the British Empire (OBE) by King George VI for his wartime services, but his work remained secret for many years.


Bombe

Within weeks of arriving at Bletchley Park, Turing had specified an electromechanical machine called the bombe, 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. 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 FRS may also refer to: Government and politics * Facility Registry System, a centrally managed Environmental Protection Agency database that identifies places of environmental interest in the United State ...

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 (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, UK, 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 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 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 A university ( la, universitas, 'a whole') is an educational institution, institution of higher education, higher (or Tertiary ...
. 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 Intelligence has been defined in many ways: the capacity for abstraction Abstraction in its main sense is a conceptual process where general rules and concept Concepts are defined as abstra ...

artificial intelligence
, 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#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is a ...
, 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.


Conviction for indecency

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. 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. Turing was never accused of espionage but, in common with all who had worked at Bletchley Park, he was prevented 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 OSA 1911) can include all information held by gov ...
from discussing his war work.


Death

On 8 June 1954, Turing's housekeeper found him dead at the age of 41; he had died the previous day. 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. Philosophy professor
Jack Copeland Brian Jack Copeland (born 1950) is Professor of Philosophy at the University of Canterbury, Christchurch, New Zealand, and author of books on the computing pioneer Alan Turing. Overview Jack Copeland's education includes a BPhil and a DPhil fr ...

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. In addition, 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 prior to 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. Conspiracy theory, Conspiracy theorists pointed out that Turing was the cause of intense anxiety to the British authorities at the time of his death. The secret services feared that communists would entrap prominent homosexuals and use them to gather intelligence. Turing was still engaged in highly classified work when he was also a practising homosexual who holidayed in European countries near the Iron Curtain. According to the conspiracy theory, it is possible that the secret services considered him too great a security risk and assassinated one of the most brilliant minds in their employ. 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:
But it was a lovely sunny day and Alan was in a cheerful mood and off we went... Then he thought it would be a good idea to go to the Blackpool Pleasure Beach, Pleasure Beach at Blackpool. We found a fortune-teller's tent[,] and Alan said he'd like to go in[,] so we waited around for him to come back... And this sunny, cheerful visage had shrunk into a pale, shaking, horror-stricken face. Something had happened. We don't know what the fortune-teller said[,] but he obviously was deeply unhappy. I think that was probably the last time we saw him before we heard of his suicide.


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 politician who served as Prime Minister of the United Kingdom The prime minister of the United Kingdom is the head of government The head of government is either the h ...

Gordon Brown
, 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; born 21 April 1926) is Queen of the United Kingdom The monarchy of the United Kingdom, commonly referred to as the British monarchy, is the constitutional monarchy A constitutional mo ...

Queen Elizabeth II
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 a letter to the Prime Minister, David Cameron, human rights advocate Peter Tatchell criticised the decision to single out Turing due to his fame and achievements when thousands of others convicted under the same law have not received pardons. Tatchell also called for a new investigation into Turing's death: 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 The Policing and Crime Act 2017 (c. 3) is an Act of Parliament, act of the Parliament of the United Kingdom. It received r ...
". The
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 The Policing and Crime Act 2017 (c. 3) is an Act of Parliament, act of the Parliament of the United Kingdom. It received r ...
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 The Enigma machine is a 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 ''en ...

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." 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, 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 An English country house is a large house or mansion in the English countryside. Such houses were often owned by individuals who also owned a Townhouse (Great Britain), town house. This allowed ...

Bletchley Park
.


Steel sculpture controversy

In May 2020 it was reported by ''Gay Star News'' that a high steel sculpture, to honour Turing, designed by Sir Antony Gormley, was planned to be installed in
King's College, Cambridge King's College is a constituent college of the University of Cambridge in Cambridge Cambridge ( ) is a College town, university city and the county town of Cambridgeshire, England, on the River Cam approximately north of London. At the Un ...

King's College, Cambridge
. Historic England, however, was quoted as saying that the abstract work of 19 steel slabs "... would be at odds with the existing character of the College. This 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."


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

* * * * * *


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 Hungarian Americans (Hungarian language, Hungarian: ''amerikai magyarok'') are United States, Americans of Hungarian p ...

John von Neumann

How Alan Turing Cracked The Enigma Code
Imperial War Museums
Alan Turing
RKBExplorer
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 Brian Jack Copeland (born 1950) is Professor of Philosophy at the University of Canterbury, Christchurch, New Zealand, and author of books on the computing pioneer Alan Turing. Overview Jack Copeland's education includes a BPhil and a DPhil fr ...

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 mathematicians 20th-century atheists 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 mathematicians 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 GCHQ people History of artificial intelligence LGBT-related suicides LGBT scientists LGBT scientists from the United Kingdom Officers of the Order of the British Empire People educated at Sherborne School People from Maida Vale People from Wilmslow People prosecuted under anti-homosexuality laws People who have received posthumous pardons Princeton University alumni Recipients of British royal pardons Suicides by cyanide poisoning Suicides in England Theoretical computer scientists Gay sportsmen LGBT sportspeople from England LGBT track and field athletes History of computing in the United Kingdom 20th-century British scientists Deaths by poisoning 20th-century English philosophers Doctors and scientists who committed suicide