The unreasonable effectiveness of number theory in science and communication (1987 Rayleigh Lecture)

A brief overview is given of the role of integers and integer relationships in the science. The effectiveness of discrete mathematics in physics, music, and communication (and its negation, cryptography) is examined. The discussion covers: numbers and musical scales; concert halls and quadratic residues; wave diffraction and primitive roots; forbidding property of Fermat primes; Euler totients and cryptography; uses of finite fields; error correction codes from Galois fields; correlation and Fourier properties of Galois sequences; Galois sequences and the fourth effect of general relativity; and Chinese remainders feed fast algorithm.