Most popular books about science, and even about mathematics, tiptoe around equations as if they were something to be hidden from the reader's tender eyes. Dana Mackenzie starts from the opposite premise: He celebrates equations. No history of art would be complete without pictures. Why, then, should a history of mathematics – the universal language of science – keep the masterpieces of the subject hidden behind a veil?
The Universe in Zero Words tells the history of twenty-four great and beautiful equations that have shaped mathematics, science, and society – from the elementary (1 + 1 = 2) to the sophisticated (the Black-Scholes formula for financial derivatives), and from the famous (E = mc2) to the arcane (Hamilton's quaternion equations). Mackenzie, who has been called "a popular-science ace" by Booklist magazine, lucidly explains what each equation means, who discovered it (and how), and how it has affected our lives.
Illustrated in color throughout, The Universe in Zero Words tells the human and often-surprising stories behind the invention or discovery of the equations, from how a bad cigar changed the course of quantum mechanics to why whales (if they could communicate with us) would teach us a totally different concept of geometry. At the same time, The Universe in Zero Words shows why these equations have something timeless to say about the universe, and how they do it with an economy (zero words) that no other form of human expression can match.
The Universe in Zero Words is the ultimate introduction and guide to equations that have changed the world.
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
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. He has a PhD in mathematics from Princeton and was a mathematics professor for thirteen years before becoming a full-time writer.
"A fascinating and informative look behind the equations."
– Lucy Sussex, Sydney Morning Herald
"[The book] reads well and quick: I took it with me in the metro one morning and was half-way through it the same evening, as The Universe in Zero Words remains on the light side, especially for readers with a high school training in math [...] The Universe in Zero Words makes for an easy and pleasant read, as well as a wonderful gift for mathematically inclined teenagers."
– Chance Magazine
"MacKenzie has the knack of getting and keeping your attention, and writes with fluency and wit, and he is a good story-teller."
– Anthony G. O'Farrell, Irish Mathematical Society Bulletin
"[This] is brilliantly written, and this reviewer who has taught historical aspects of mathematics for a number of years enjoyed the book and learned some details that were unfamiliar. The author possesses a wonderful skill in presenting technical material to those without the facility to understand the mathematics [...] In summary, a refreshing look at highlights from the History of Mathematics and a welcome addition to the literature, written in a very accessible style."
– Phil Dyke, Leonardo Reviews
"Mackenzie has written an accessible account of mathematical equations through the ages, giving strong insights in a historical context and with a wider interpretation that does justice to the title."
– Wallace A Ferguson, Mathematics Today
"The book is written in a very transparent and elegant manner; it is both enjoyable and informative reading. The reader will absolutely love exciting historical facts and excellent illustrations, diagrams, pictures carefully selected by the author. The volume concludes with a useful bibliography and a helpful index. A very entertaining text that appeals not only to mathematics enthusiasts, but also to a wide audience with a quite limited mathematical background."
– Yuri V. Rogovchenko, Zentralblatt MATH
"Demanding very little prior mathematical knowledge, this is one of the best popular histories of mathematics in recent years. Dana Mackenzie's prose is lively and easy to read, and his mix of historical background and personal biographies of the main characters is engaging."
– Eli Maor, author of The Pythagorean Theorem: A 4,000-Year History and e: The Story of a Number
"Dana Mackenzie is a very good writer. I was constantly amazed at his ability to describe complicated mathematics in a few sentences in a way that the average reader – not the average mathematician or the average math major, but the average reader – can understand. This is a very entertaining book."
– David S. Richeson, author of Euler's Gem: The Polyhedron Formula and the Birth of Topology
"[A] terrific book [...] [A] brilliant history of mathematics as told through equations."
– Dick Lipton, Professor of Computer Science at Georgia Tech