From Here to Infinity
Ian Stewart
 After an introductory chapter The Nature of Mathematics, Stewart devotes each of the following 18 chapters to an exposition of a particular problem that has given rise to new mathematics or an area of research in modern mathematics. *Chapter 2 - The Price of Primality - primality tests and integer factorisation *Chapter 3 - Marginal Interest - Fermat's last theorem *Chapter 4 - Parallel Thinking - non-Euclidean geometry *Chapter 5 - The Miraculous Jar - Cantor's theorem and cardinal numbers *Chapter 6 - Ghosts of Departed Quantities - calculus and non-standard analysis *Chapter 7 - The Duellist and the Monster - the classification of finite simple groups *Chapter 8 - The Purple Wallflower - the four colour theorem *Chapter 9 - Much Ado About Knotting - topology and the Poincaré conjecture *Chapter 10 - More Ado About Knotting - knot polynomials *Chapter 11 - Squarerooting the Unsquarerootable - complex numbers and the Riemann hypothesis *Chapter 12 - Squaring the Unsquarable - the Banach-Tarski paradox *Chapter 13 - Strumpet Fortune - probability and random walks *Chapter 14 - The Mathematics of Nature - the stability of the Solar System *Chapter 15 - The Patterns of Chaos - chaos theory and strange attractors *Chapter 16 - The Two-and-a-halfth Dimension - fractals *Chapter 17 - Dixit Algorizmi - algorithms and NP-complete problems *Chapter 18 - The Limits of Computability - Turing machines and computable numbers *Chapter 19 - The Ultimate in Technology Transfer - experimental mathematics and the relationship between mathematics and science