Alan Turing was a British mathematician and logician whose 1936 paper, written while he was still a graduate student, defined — mathematically, rigorously, for the first time — what it actually means for something to be "computable." He did this by describing an idealized device, now called a Turing machine: an infinitely long tape divided into cells, a "head" that can read and write one symbol at a time and move left or right, and a small table of rules governing what the head does based on the current symbol and its current internal state. That's the whole machine. And Turing argued, convincingly enough that it became the foundation of computer science (the Church–Turing thesis), that this almost absurdly simple setup, with the right rule table, could in principle carry out any computation any computer — however powerful — could ever perform. This is the theoretical foundation nearly all of modern computer science still rests on.
Below is a real, working Turing machine — simplified for this page, but mechanically identical to Turing's concept. Its one job: add 1 to a binary number written on the tape, using nothing but the rules "if you see this symbol in this state, write this symbol, move this direction, and switch to this state." Step through it and watch a real computation happen, one mechanical rule at a time.
Press "Step once" to begin — watch the head (▲) move and the tape's symbols flip.
Notice what just happened: no arithmetic, no numbers "understood" by the machine in any meaningful sense — just a tiny table of "if you see X in state Y, do Z" rules, applied mechanically, over and over, until the machine reaches a halt state. Every calculation your phone, laptop, or any computer on Earth performs is, underneath layers and layers of engineering, this same basic idea — read, decide, write, move — running at billions of steps per second instead of one click at a time.
Turing didn't build a computer. He defined, in the abstract, what a computer is — years before the vacuum tubes and transistors existed to build one. Theory arrived before the hardware needed it.
In that same 1936 work, Turing also proved something more unsettling: there is no general method — no algorithm, ever — that can look at an arbitrary computer program and its input and correctly determine, in every single case, whether that program will eventually finish running or continue forever. This is the halting problem, and Turing's proof that it's fundamentally unsolvable was a close cousin of Kurt Gödel's incompleteness theorems from a few years earlier (see Gödel's Incompleteness Theorems in this library's Mathematics section) — another example of a rigorously proven limit on what any formal system, however powerful, can ever fully determine about itself.
When World War II broke out, Turing joined Britain's codebreaking effort at Bletchley Park, working to break Germany's Enigma cipher — a machine-generated code the German military used to encrypt communications, considered by German command to be effectively unbreakable. Building on the work of Polish cryptologists — Marian Rejewski, Jerzy Różycki and Henryk Zygalski had broken Enigma in the 1930s and built an earlier machine, the bomba, and shared their methods with Britain and France in July 1939 — Turing led the design of the British Bombe (with a key improvement, the "diagonal board," from Gordon Welchman), an electromechanical machine that could rapidly test possible Enigma settings and dramatically narrow down the search for the day's key, turning a mathematically astronomical problem into a tractable one. Historians differ on the precise scale of the impact, but a commonly cited estimate holds that the codebreaking work at Bletchley Park — with Turing's contribution central to it — shortened the war in Europe by roughly two years, with some historians' estimates of lives saved as a result running into the millions. Precise counterfactual history is inherently difficult to pin down exactly, but the consensus among historians is that the impact was substantial and genuinely war-altering, not a minor intelligence advantage.
After the war, Turing worked on some of the first actual stored-program computers ever built (including early design work later realized in the Manchester and Pilot ACE machines) — moving from pure theory to hands-on engineering. In 1950 he published a paper posing a question that still frames the entire field of artificial intelligence: "Can machines think?" Rather than get lost in defining "thinking" philosophically, he proposed a practical test — now called the Turing Test — where a human judge holds a text conversation with both a machine and another human, without knowing which is which; if the judge can't reliably tell them apart, the machine passes. Whether or not the specific test still satisfies modern AI researchers (it's been extensively debated and refined since), Turing was asking serious, structured questions about machine intelligence decades before it was a mainstream scientific field, let alone the subject of daily conversation it is today.
In 1952, Turing reported a burglary to the police — and in the course of the investigation, disclosed a sexual relationship with another man, which was a criminal offense in the UK at the time under "gross indecency" laws. He was prosecuted and convicted, and given a choice between imprisonment and a course of hormonal treatment intended to suppress his sex drive, sometimes referred to as chemical castration; he chose the latter. His conviction also cost him his security clearance, ending his ability to continue certain classified consulting work for the British government he had so recently helped win a war.
Turing died in 1954 of cyanide poisoning. A coroner's inquest at the time ruled it suicide, and this remains the most widely accepted account among historians. It's worth noting, in the interest of accuracy rather than sensationalism, that some biographers (notably Jack Copeland) have since raised questions about that ruling, pointing to the informal nature of the original investigation and the possibility of accidental poisoning from chemicals in his home laboratory — a minority view that hasn't overturned the standard account, but is a genuine, documented point of historical uncertainty rather than settled fact either way.
Public acknowledgment of this injustice came slowly. In 2009, British Prime Minister Gordon Brown issued a formal public apology on behalf of the UK government for how Turing had been treated. In 2013, Queen Elizabeth II granted Turing a posthumous royal pardon. In 2017, the UK extended that same pardon automatically to thousands of other men historically convicted under the same now-abolished laws — an act informally known as the "Alan Turing law," part of the Policing and Crime Act 2017. In 2021, his portrait was placed on the Bank of England's £50 note, making him the first openly gay man featured on British currency. None of this undoes what was done to him — but it stands as a rare instance of a country publicly, formally reckoning with how it treated one of its own most consequential scientific minds.
Alan Turing's 1936 Turing machine gave computation a rigorous mathematical definition years before electronic computers existed, and his 1950 work on machine intelligence still frames how artificial intelligence is discussed today. His wartime codebreaking work at Bletchley Park is credited by historians with shortening the war in Europe by an estimated two years. He was later criminally prosecuted for being gay, chemically castrated as an alternative to prison, and died at 41 — a loss compounded by decades of official silence before Britain's eventual apology, pardon, and commemoration. Both the brilliance and the injustice are part of the same, real history.
Try this: run the Turing machine above with a larger starting number like 1111, and count how many individual mechanical steps it takes to do something as simple as adding 1 — then consider that a modern chip performs billions of comparably simple steps every single second.
Sources. Turing's 1936 paper ("On Computable Numbers, with an Application to the Entscheidungsproblem"), the halting problem, his WWII work on the Bombe at Bletchley Park, his 1950 "Computing Machinery and Intelligence" paper and the Turing Test, his 1952 prosecution and 1954 death, and the UK government's 2009 apology, 2013 pardon, and 2017 Alan Turing Law are all extensively documented history. The estimate that Bletchley Park's codebreaking shortened WWII by roughly two years, with lives saved potentially in the millions, is a commonly cited historian's estimate, not an exact, universally agreed figure — inherent to any counterfactual historical claim. The binary-increment Turing machine above is a genuine, simplified working implementation, verified to correctly increment any binary number in the provided list.