The Universe in Zero Words

Dana Mackenzie is a frequent contributor to Science, Discover, and New Scientist, and writes the biennial series What's Happening in the Mathematical Sciences for the American Mathematical Society. In 2012, he received the prestigious Communications Award from the Joint Policy Board for Mathematics. He has a PhD in mathematics from Princeton and was a mathematics professor for thirteen years before becoming a full-time writer.

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 pi 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