Alan Turing published “On Computable Numbers, with an Application to the Entscheidungsproblem” in 1936. The paper appeared in the Proceedings of the London Mathematical Society and became one of the foundations of theoretical computer science.
In it, Turing described an abstract model of computation now called the Turing machine. He used this model to investigate which mathematical procedures can be carried out mechanically. The paper also addressed the Entscheidungsproblem, or “decision problem,” associated with David Hilbert’s question about whether a universal method could determine the truth of every mathematical statement in a formal system.
Turing showed that no such all-purpose decision procedure exists. The work also introduced the idea of a universal machine that could imitate other machines when given their descriptions. Some references mention 1937 because a revised version and related publication history extended into that year, but the original paper was published in 1936. That is the standard answer to this quiz question.