In 1936, a 24-year-old Cambridge mathematician named Alan Turing published a paper titled On Computable Numbers. To answer a question David Hilbert had posed about the foundations of mathematics, Turing did something no one had done before: he gave a precise mathematical definition of what it means to compute anything. The model — an infinite paper tape, a movable head, a finite table of rules — was deliberately austere. It was also sufficient. Every computation any physical machine could ever perform could, in principle, be performed by a Turing machine. The conceptual machine that would underlie the digital age was sketched in a paper read by perhaps two dozen people.
Turing's paper proved three results of permanent importance. First, the universal Turing machine: a single Turing machine could simulate any other Turing machine, given the latter's description as input. Hardware and software became separable — a machine plus a program. This is the core abstraction of every modern computer. Second, the halting problem: there is no algorithm that, given an arbitrary program and input, can decide whether the program will halt or run forever. The proof uses a diagonal argument identical in spirit to Gödel's incompleteness proof, and establishes a hard limit on what any computational system can determine about itself. Third, the Church-Turing thesis (jointly with Alonzo Church, who had independently arrived at lambda calculus): any function that can be effectively calculated at all can be calculated by a Turing machine. The thesis is not a theorem (effective calculation is not formally defined) but has resisted every attempted counter-example for nearly a century, including with quantum computers.
Every computer is a Turing machine — physically more elaborate, finite in storage, vastly faster, but conceptually identical. Computational complexity theory (P vs. NP, etc.) is built on Turing's framework. The current debate about whether artificial general intelligence can be implemented on classical hardware is, technically, a question about whether human cognition is Turing-computable — most working AI researchers assume it is, and the empirical performance of large transformer models (descendants of attention-based architectures running on Turing-computable hardware) has so far supported that assumption. Turing himself was prosecuted for homosexuality in 1952 and died by cyanide in 1954 at age 41.