What is the full title of Alan Turing's 1936 paper that introduced the Turing machine?

Alan Turing’s 1936 paper was titled “On Computable Numbers, with an Application to the Entscheidungsproblem.” The paper introduced the abstract computing device now called a Turing machine and used it to analyze the limits of mechanical calculation.

The Entscheidungsproblem, or “decision problem,” asked whether a general algorithm could determine whether any mathematical statement is formally provable. Turing showed that no such universal method exists. His argument helped establish the modern concept of computability and demonstrated that some precisely defined problems cannot be solved by any algorithm.

The paper was published in the Proceedings of the London Mathematical Society across two issues in 1936. Turing’s machine was not a physical computer: it was a mathematical model consisting of an unbounded tape, a read-write head, and a finite set of rules. Those simple ingredients were enough to describe general-purpose computation.

A common mix-up is to call the paper “The Entscheidungsproblem” or “On Computable Numbers.” Both phrases appear within the title or describe its subject, but neither is the complete canonical title.