The theory was published in 1936, in the article "On Computable Numbers, with an Application on the Entscheidungsproblem," in response to treatment of the decision problem, formulated by Hilbert.

What did Alan Turing's 1936 paper on computable numbers prove?

Turing's proof is a proof by Alan Turing, first published in January 1937 with the title "On Computable Numbers, with an Application to the Entscheidungsproblem." It was the second proof (after Church's theorem) of the conjecture that some purely mathematical yes–no questions can never be answered by computation; more ...

Are real numbers Uncomputable?

Most real numbers can never be calculated, they're uncomputable, which suggests that mathematics is full of things that we can't know, that we can't calculate. This is related to something famous called Gödel's incompleteness theorem from 1931, five years before Turing.