Physics and the queen of mathematics

Abstract

‘Mathematics is the queen of the sciences and the theory of numbers is the queen of mathematics’. The role of the monarch has changed since assertion. Queens are no longer allowed to live in isolated splendour. Indeed, they are now expected to mingle with their subjects and even to provide some public service in return for their upkeep. So number theory, once considered by mathematicians to be a field with no application to the other sciences, is now proving to be of considerable use to physicists, both as a working tool and as a guide to possible directions of future research. It may even be the case that physics can help in the solution of some of the important problems in this, one of the purest areas of pure mathematics. Number theory is concerned with properties of the integers. Some topics of interest are, for example: the distribution of prime numbers, the distribution of integers which are the sum of two squares (e.g. 29 = 22 + 52), and the evaluation or estimation of functions of the integers.