1 The Theorem of Pythagoras.- 2 Greek Geometry.- 3 Greek Number Theory.- 4 Infinity in Greek Mathematics.- 5 Polynomial Equations.- 6 Analytic Geometry.- 7 Projective Geometry.- 8 Calculus.- 9 Infinite Series.- 10 The Revival of Number Theory.- 11 Elliptic Functions.- 12 Mechanics.- 13 Complex Numbers in Algebra.- 14 Complex Numbers and Curves.- 15 Complex Numbers and Functions.- 16 Differential Geometry.- 17 Noneuclidean Geometry.- 18 Group Theory.- 19 Topology.- 20 Sets, Logic, and Computation.- References.

A concise, unified view of mathematics together with its historical development. Aiming at mathematicians who have mastered the basic topics but wish to gain a better grasp of mathematics as a whole, the author gives the reasons for the emergence of the main fields of modern mathematics, and explains the connections between them by tracing the course of a few mathematical themes from ancient times down to the 20th century. The emphasis here is on history as a method for unifying and motivating mathematics, rather than as an end in itself, and there is more mathematical detail than in other general histories. However, no historical expertise is assumed, and classical mathematics is rephrased in modern terms where needed. Nevertheless, there are copious references to original sources for readers wishing to explore the classics for themselves. In summary, readers will be able to add to their mathematical knowledge as well as gaining a new perspective on what they already know.