The aim is to show the central position mathematics holds in our culture between the scientific method on the one hand and the creative spirit of the humanities on the other. It first considers the achievements of men like Archimedes, Pascal and Newton and so traces the development of mathematical ideas from primitive notions of number to modern abstract concepts like set and vector. It then examines in detail the idea of algebraic structure and shows how the Boolean algebra of sets may be used to design a computer as well as to solve problems in proportional logic. Finally, the idea of a mathematical model is explained by referring to applications taken from probability, statistics, linear programming and cybernetics.

The abstract ideas of modern mathematics have been related to real-life situations, showing how they have evolved from, and throw light on, traditional school mathematics. And although the book makes a sound basis for a classroom course, it forms a self-contained introduction to modern topics which makes it equally suitable for the interested sixth-former or the adult looking for a readable approach to present-day mathematics.