Form and Content

After an introduction indicating the general plan of the book and some specific questions to be discussed, Mathematics for the Million is organized as a historical narrative of the development of mathematics and its role as a tool for solving practical problems, particularly those dealing with measurement. Thus, a concept will be discussed as of the time that it was first studied, and only later does the reader see how it was developed by later thinkers, to the level at which it is understood today. In the course of the book, the reader is introduced to many of the main areas of mathematical study, including arithmetic, algebra, geometry, trigonometry, calculus, matrix algebra, and probability. The book is profusely illustrated, with drawings and diagrams of the problems. Each chapter concludes with a substantial series of test problems and a summary list of major concepts and rules to be memorized.

The narrative begins with a discussion of the first number systems and a look at the sort of questions that mathematicians have tried to solve. This information is followed by an analysis of Euclid’s geometry, which is seen not as a pure axiomatic system but as a way of applying observations about size and shape in a systematic fashion. Eschewing the rigors of formal proof, Lancelot Hogben demonstrates that Euclid’s major results do in fact match the experience of measurement in the real world,

The discussion of Euclid is followed by a treatment of the trigonometric functions, also seen as tools for measurement, leading to a discussion of the...

(The entire section is 644 words.)