TABLE OF CONTENTS: 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
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