On Computable Numbers Alive
The founding document — the universal machine described to answer Hilbert, proving some numbers cannot be computed and in doing so defining what a computer is.
Turing's paper appeared in the Proceedings of the London Mathematical Society in 1936–37. To answer Hilbert's Entscheidungsproblem he invented an imaginary machine — an infinite tape, a read/write head, a finite table of states — then proved a single 'universal' machine could simulate any other, and that no machine could decide all mathematical truth.
The universal machine is the conceptual schema of every stored-program computer: one device, many programs. Turing wrote the paper at age 23, largely unaware of Church's parallel result; his appendix proving the two models equivalent became the first statement of the Church–Turing thesis.