Mathematics and Its History

This textbook presents a unified view of mathematics and its historical development. It is aimed at senior undergraduates who have mastered the basic topics but wish to gain a better grasp of mathematics as a whole. Reasons for the emergence of the main fields of modern mathematics are identified, and connections between them are explained, by tracing the course of a few mathematical themes from ancient times down to the 20th century. The emphasis is on history as a method for unifying and motivating mathematics, rather than as an end in itself. No historical expertise is assumed, and classical mathematics is rephrased in modern terms whenever original sources are used.