1912 – 1954 • Father of Computer Science
The mathematician who defined computation, broke the Enigma code, and asked whether machines can think — whose life was cut short by the society he helped save.
Alan Mathison Turing was born on June 23, 1912 in Maida Vale, London. His father Julius was in the Indian Civil Service; Alan and his brother were raised mainly by foster families in England while their parents were abroad.
A shy, solitary boy, Turing showed early fascination with science and numbers. At Sherborne School he was considered eccentric. A pivotal friendship with Christopher Morcom, who died suddenly in 1930, deeply affected him and may have spurred his interest in the nature of mind.
He entered King's College, Cambridge in 1931, where he distinguished himself in mathematics. His fellowship dissertation (1935) independently re-proved the central limit theorem.
In 1936, at age 23, he wrote "On Computable Numbers," the paper that would define the concept of a universal computing machine and resolve Hilbert's Entscheidungsproblem. He then went to Princeton to study under Alonzo Church.
Defined the Turing machine, proved the halting problem undecidable, and introduced the concept of a universal machine that can simulate any other. This paper is the foundation of theoretical computer science.
Led the team that broke the German Enigma code, designing the electromechanical Bombe that searched for rotor settings. His work shortened WWII by an estimated two years and saved millions of lives.
Published the paper proposing the "Turing Test" for machine intelligence. The question "Can machines think?" launched the field of artificial intelligence and philosophy of mind.
Published "The Chemical Basis of Morphogenesis," proposing reaction-diffusion equations to explain biological pattern formation (spots, stripes). Confirmed experimentally decades later.
Hilbert's Entscheidungsproblem (1928) asked: is there an algorithm that can decide the truth of any mathematical statement? This was the last pillar of his program, after Godel had toppled completeness and consistency.
Turing and Church independently answered no in 1936. But to prove it, Turing first had to define what an "algorithm" is — and his definition, the Turing machine, became the foundation of all computing.
The German Enigma machine produced codes with ~10^23 possible settings. Breaking it required combining mathematical insight with engineering at industrial scale. Bletchley Park employed 10,000 people at its peak.
Turing's contributions were kept secret until the 1970s. For decades, the world did not know that one of its greatest wartime heroes was a mathematician.
Computability Codebreaking Artificial Intelligence
A Turing machine consists of an infinite tape divided into cells (each holding a symbol), a read/write head, and a finite state table specifying transitions: given current state and symbol, write a new symbol, move left or right, enter a new state.
Despite its simplicity, a Turing machine can compute anything computable. The Church-Turing thesis asserts that the informal notion of "algorithm" is exactly captured by what a Turing machine can do.
A universal Turing machine can simulate any other Turing machine, given its description as input — the theoretical blueprint for the general-purpose computer.
Turing proved no algorithm can decide, for an arbitrary program and input, whether the program will halt or run forever. The proof uses a diagonal argument (like Cantor's): assuming a halting decider leads to a contradiction via self-reference.
A universal Turing machine U takes as input a description of any Turing machine M and its input, then simulates M. This is the theoretical foundation of the stored-program computer: one machine that can run any program.
The thesis asserts that Turing machines capture the intuitive notion of "effectively computable." This is not a theorem but a definition-proposal that has withstood every challenge, including quantum computing (which is faster but not more capable in terms of computability).
Turing introduced "oracle machines" in his PhD thesis (1938): Turing machines augmented with a black box that answers unsolvable questions. This gave rise to the study of relative computability and the arithmetical hierarchy.
The German Enigma machine used rotating electromechanical rotors to produce polyalphabetic substitution ciphers with approximately 1.6 x 10^20 possible settings. Each day, operators changed settings.
Turing designed the Bombe, an electromechanical device that exploited known-plaintext attacks (cribs) to eliminate impossible rotor settings. By war's end, Bletchley Park was reading Enigma messages routinely.
He also developed the Banburismus procedure for naval Enigma and contributed to breaking the even more complex Lorenz cipher used for high-level communications.
Polish mathematicians Rejewski, Zygalski, and Rozycki broke early Enigma versions in the 1930s. They shared their work with Britain in 1939. Turing built on their methods, adapting them for the more complex wartime machines with additional rotors and plugboard settings.
Turing developed Bayesian statistical methods (Banburismus) to identify likely rotor settings, dramatically reducing the search space before the Bombe was applied. His use of "weight of evidence" (in decibans) anticipated information-theoretic cryptanalysis.
The Colossus machines (1943-44), built to break the Lorenz cipher, were among the world's first electronic digital computers. While Tommy Flowers designed the hardware, the mathematical basis came from the Bletchley Park team including Turing and Tutte.
Historians estimate Turing's work shortened the war by at least two years and saved millions of lives. The Battle of the Atlantic, in particular, was won in part by decrypting U-boat communications. Churchill called Bletchley "the goose that laid the golden egg."
In his final major paper, Turing proposed that biological patterns (stripes on a zebra, spots on a leopard) arise from reaction-diffusion systems: two chemicals diffusing at different rates can create stable spatial patterns from initially uniform conditions.
This was remarkably prescient. Turing patterns have been confirmed experimentally in chemical systems (CIMA reaction) and implicated in biological patterning from fish pigmentation to digit formation.
In "Computing Machinery and Intelligence," Turing replaced the question "Can machines think?" with an operational test: a machine is intelligent if a human interrogator cannot distinguish it from a human through text conversation.
This "imitation game" launched the field of AI and remains the most famous benchmark in philosophy of mind, though modern AI has complicated the picture.
Reaction-Diffusion Artificial Intelligence Philosophy of Mind
Turing combined mathematical abstraction with practical engineering and a willingness to cross disciplinary boundaries. He thought by imagining concrete processes and then abstracting.
What can be computed? What is intelligence?
Imagine a human following rules; abstract to a machine
Derive fundamental results (halting problem, universality)
Design actual machines (Bombe, ACE computer)
In 1952, Turing reported a burglary and, during the investigation, acknowledged a sexual relationship with a man. He was charged with "gross indecency" under the same law that had convicted Oscar Wilde. He chose chemical castration over prison.
His conviction stripped him of his security clearance, ending his ability to work for GCHQ on cryptography. The man who had been essential to winning the war was now considered a security risk by the state he had helped save.
On June 7, 1954, Turing was found dead from cyanide poisoning. A half-eaten apple lay beside him. The inquest ruled suicide, though some have questioned this conclusion. He was 41 years old.
In 2009, Prime Minister Gordon Brown issued a public apology. In 2013, Queen Elizabeth II granted a Royal Pardon. In 2017, the "Turing Law" posthumously pardoned all men convicted of historical homosexuality offences.
Every computer, phone, and smart device implements Turing's universal machine concept. The entire digital world rests on his theoretical foundation.
Modern cryptography descends from Bletchley Park. Turing's statistical methods for codebreaking anticipate Bayesian approaches now used in signal intelligence worldwide.
Turing patterns explain pigmentation in fish, digit formation in limb buds, and hair follicle spacing. His reaction-diffusion model is now a standard tool in mathematical biology.
The Turing test remains a cultural touchstone for AI. His 1950 paper anticipated neural networks, genetic algorithms, and machine learning decades before their development.
The halting problem's undecidability sets fundamental limits on what automated tools can verify about programs, shaping the design of programming languages and verification tools.
Turing instabilities in reaction-diffusion systems are used to design self-organizing nanostructures and pattern functional materials at the microscale.
Andrew Hodges (1983). The definitive biography, combining mathematical depth with personal narrative. The basis for the film "The Imitation Game."
George Dyson (2012). The story of how Turing's ideas were implemented in the first computers at the IAS, weaving together the histories of computing and the bomb.
Turing's original paper. Remarkably readable for a foundational work. Available freely online. Every computer scientist should read it at least once.
Charles Petzold (2008). A line-by-line walkthrough of "On Computable Numbers" with extensive commentary, making the original paper accessible to modern readers.
"We can only see a short distance ahead, but we can see plenty there that needs to be done."
— Alan Turing, "Computing Machinery and Intelligence," 19501912 – 1954