Table of Contents

Mathematics of the Egyptians; Mathematics of the Babylonians; Prime numbers; Mathematics of the Greeks-The beginnings; Pythagoras-The Pythagorean school; Heraclitus, Parmenides, Zeno, Empedocles, and Democritus; The mathematical school of Athens; Plato and Aristotle; Groups; The impossibility of solving the three classical problems of antiquity; Euclid; Hilbert's foundation of Euclidean geometry; Basic properties of axiomatic systems; Spaces and geometries; Non-Euclidean geometries; The geometry of experience; Aristarchus, Archimedes, Apollonius, and Eratosthenes; The period from 200 B.C. to 500 A.D. in Alexandria; A brief review of the history of Greek mathematics; Mathematics of China and India; Mathematics of the Arabs; Europe during the middle ages; Renaissance (1400-1600); The seventeenth century; The eighteenth century; Revival of synthetic geometry; The system of real numbers; The system of complex numbers and the quaternions; The fundamental theorem of algebra; Set theory; Logic; Functional analysis; Topology; Functions of real variables; Abstract algebra; Categories and functors; Recent discoveries and achievements; Language; The fast Fourier transform; The theory of wavelets; A short curriculum vitae of the author; Bibliography; Chronological table; Subject index; Name index