Which essay won Alan Turing a Smith's Prize in 1936?

The essay that won Alan Turing a Smith’s Prize in 1936 was “On the Gaussian Error Function.” The work explored probability theory and was closely connected with Turing’s independent rediscovery of a version of the central limit theorem.

Turing originally wrote the work as a Fellowship dissertation for King’s College, Cambridge. He completed and submitted it in the mid-1930s, and the dissertation helped secure his election as a Fellow of King’s. The manuscript was not published as a conventional paper, but it was important in establishing his mathematical reputation.

Turing’s result had an unusual history: he later learned that a closely related theorem had already been proved by Jarl Waldemar Lindeberg in 1922. Even so, Cambridge mathematicians considered Turing’s approach sufficiently original and impressive. The title can be confused with “On Computable Numbers,” his landmark 1936 paper on computability, but that was a different work and not the essay associated with the Smith’s Prize.