What year did Alan Turing publish the paper defining the Turing machine?

1936 → tub · match.

Turing's 1936 paper "On Computable Numbers" introduced the abstract Turing machine — an imaginary device reading and writing symbols on an infinite tape — to answer a deep question posed by David Hilbert: is there a mechanical procedure to decide every mathematical statement? Turing proved there is not, showing some problems (like the halting problem) can never be solved by any algorithm. Alonzo Church reached the same conclusion the same year via his lambda calculus, and the two results together — the Church–Turing thesis — pin down what "computable" even means. That paper is the theoretical bedrock of all computer science. Peg 19 · 36 → tub · match: a match floating in a tub.