Turing's Work on the Riemann Hypothesis

Alan Turing (right) with two engineers at the console of the Ferranti Mark I computer in 1951 (Photo: New Atlas)

Alan Turing (1912-54) is a well-known name for a variety of reasons. To the general public, he is probably best known for his work on the cryptanalysis of the Enigma ciphering system during the World War II. To mathematicians, however, he is perhaps best known for being one of the founders of computer science. He was the person who formalized the core concepts of computation and algorithms via his invention of the Turing machine. He also solved Hilbert’s Entscheidungsproblem (see essay below).

The Entscheidungsproblem (1930s)

Few, however, are aware of his significant contributions to analytic number theory via his work on the non-trivial zeros of the Riemann zeta function and, by extension, the Riemann hypothesis.

The Problem

The first essay I ever wrote about mathematics was on the Riemann zeta function and its association with the distribution of prime number, the so-called Riemann hypothesis (see technical…