How Big is Infinity?

Introduction. What is mathematics for? - An introduction to purposes and prospects. Where do numbers come from? - From notches on bones to hexadecimals. Why are primes the atoms of mathematics? - Building blocks and the fundamental theorem of arithmetic. Which are the strangest numbers? - Real, irrational and transcendental numbers. Are imaginary numbers truly imaginary? - From the imaginary 'I' to octonions. How big is infinity? - Set theory and the infinity revolution. Where do parallel lines meet? - The birth of new geometries. What is the mathematics of the universe? - The Calculus miracle. Are statistics lies? - Data, proof and 'damned lies'. Can mathematics guarantee riches? - Uncertainty, chance and probability theory. Is there a formula for everything? - Mathematical recipes and the search for knowledge. Why are three dimensions not enough? - Higher dimensions, monster curves and fractals. Can a butterfly's wings really cause a hurricane? - Chaos theory, weather equations and strange attractors. Can we create an unbreakable code? - Ciphers, the Enigma machine and quantum computers. Is mathematics beautiful? - Music, art, golden numbers and the Fibonacci sequence. Can mathematics predict the future? - Mathematical models, simulations and game theory. What shape is the universe? - Topology, manifolds and the Poincare conjecture. What is symmetry? - Patterns, dualities and the fundamental nature of reality. Is mathematics true? - From Plato's reality to Godel's incompleteness theorems. Is there anything left to solve? - The great unsolved problems and the future of mathematics. Glossary. Index.