The Universe in Zero Words

Preface 6
Introduction: The Abacist versus the Algorist 10
Part One: Equations of Antiquity 16
1.Why we believe in arithmetic: the world's simplest equation 20
2.Resisting a new concept: the discovery of zero 26
3.The square of the hypotenuse: the Pythagorean theorem 30
4.The circle game: the discovery of p 40
5.From Zeno's paradoxes to the idea of infinity 46
6.A matter of leverage: laws of levers 52
Part Two: Equations in the age of exploration 56
7.The stammerer's secret: Cardano's formula 60
8.Order in the heavens: Kepler's laws of planetary motion 68
9.Writing for eternity: Fermat's Last Theorem 74
10.An unexplored continent: the fundamental theorem of calculus 80
11.Of apples, legends. and comets: Newton's laws 90
12.The great explorer: Euler's theorems 96
Part Three: Equations in a promethean age 104
13.The new algebra: Hamilton and quaternions 108
14.Two shooting stars: group theory 114
15.The geometry of whales and ants: non-Euclidean geometry 122
16.In primes we trust: the prime number theorem 128
17.The idea of spectra: Fourier series 134
18.A god's-eye view of light: Maxwell's equations 142
Part Four: Equations in our own time 150
19.The photoelectric effect: quanta and relativity 154
20.From a bad cigar to Westminster Abbey: Dirac's formula 164
21.The empire-builder: the Chern-Gauss-Bonnet equation 174
22.A little bit infinite: the Continuum Hypothesis 182
23.Theories of chaos: Lorenz equations 194
24.Taming the tiger: the Black-Scholes equation 204
Conclusion: What of the future? 214
Acknowledgments 218
Bibliography 219
Index 222