The Universe in Zero Words: The Story of Mathematics as Told through Equations

The Universe in Zero Words: The Story of Mathematics as Told through Equations

by Dana Mackenzie


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Product Details

ISBN-13: 9780691160160
Publisher: Princeton University Press
Publication date: 08/25/2013
Pages: 224
Sales rank: 677,451
Product dimensions: 9.10(w) x 6.50(h) x 0.70(d)

About the Author

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.

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 π 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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