Alan Turing and Number Theory
Beside well-known revolutionary contributions,
Alan Turing had a number of significant results in "traditional"
mathematics. In particular he was very much interested in the
famous Riemann Hypothesis. This hypothesis, stated by Berhard
Riemann in 1859 and included by David Hilbert in his 8th problem
in 1900, still remains open, being now one of the Millennium
Problems. The Riemann Hypothesis predicts positions of zeros
of so called zeta function, and Alan Turing developed a rigorous
method for verifying the Hypothesis for the initial zeros.
He also invented a machine for calculating the values of
the zeta function. In contrast to celebrated imaginable
Turing machines, Turing started to implement this machine
but never finished because of the War. |