Turing and the Riemann Hypothesis
AR Booker · Bristol Research (University of Bristol) · 2006
a numerical method for verifying the Riemann hypothesis and its implementation on the Manchester Mark I, one of the earliest general purpose digital computers. Turing writes in his introduction The calculations had been planned some time in advance, but had in fact to be carried out in great haste. If it had not been for the fact that the computer remained in serviceable condition for an unusually long period from 3 p.m. one afternoon to 8 a.m. the following morning it is probable that the calculations would never have been done at all. As it was, the interval 2π.63 2 < t<2π.64 2 was investigated during that period, and very little more was accomplished. The modesty of this last sentence notwithstanding, Turing’s paper is an important contribution to number theory that continues to have relevance today; indeed, we are fortunate that the Manchester computer remained serviceable for so long on that day, for otherwise Turing may never have published his results! The goal of this article is to Andrew R. Booker is a lecturer at the University of Bristol. His email address is [email protected].