Mackenzie, D: 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 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

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.

Dana Mackenzie, Winner of the 2012 Joint Policy Board for Mathematics Communications Award "Quietly learned and beautifully illustrated, Mackenzie's book is a celebration of the succinct and the singular in human expression."--Nature "The equations Mackenzie exhibits in this wonderful book represent 24 of the most profound discoveries in the history of Mathematics... Mackenzie's writing is understated and clear. The complex ideas he explains so lucidly are beautiful in themselves, but this book is physically beautiful too, imaginatively illustrated and stylishly designed to complement its subject."--Irish Times "[M]ackenzie provides interesting insights regarding the equations, such as relating whale communications to a model of a non-Euclidean geometry or the role of cigar smoke in the quantization of angular momentum of quantum particles... The book is an enjoyable read ..."--Choice "This well-designed and accessible book will delight and inform the student, mathematician or historian in your life and it may also help you rediscover your forbidden love for mathematics."--Devorah Bennu, GrrlScentist "With a book that is both short and very easy to read, Mackenzie manages to introduce a very wide scope of ideas, and to produce a condensate of the history of mathematics that is at the same time enlightening and engaging. He succeeds in discussing highly advanced science while remaining very comprehensible, and in popularizing mathematics and physics while also giving food for thought to the specialist. His Universe in Zero Words will therefore seduce any scientist, but also anyone with some curiosity and desire to get more familiar with the history of human thinking and knowledge."--Jean-Baptiste Gramain, London Mathematical Society Newsletter "[V]ery absorbing reading... Two hundred pages, twenty-four equations, one endearing and well told story. I wholeheartedly recommend the book."--Alexander Bogomolny, CTK Insights "A fascinating and informative look behind the