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The Universe in Zero Words

Book Description

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 book 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 book 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.

Table of Contents

  1. Cover Page
  2. Title Page
  3. Copyright Page
  4. Contents
  5. Preface
  6. Introduction: The abacist versus the algorist
  7. Part One: Equations of antiquity
    1. 1. Why we believe in arithmetic: the world’s simplest equation
    2. 2. Resisting a new concept: the discovery of zero
    3. 3. The square of the hypotenuse: the Pythagorean theorem
    4. 4. The circle game: the discovery of π
    5. 5. From Zeno’s paradoxes to the idea of infinity
    6. 6. A matter of leverage: laws of levers
  8. Part Two: Equations in the age of exploration
    1. 7. The stammerer’s secret: Cardano’s formula
    2. 8. Order in the heavens: Kepler’s laws of planetary motion
    3. 9. Writing for eternity: Fermat’s Last Theorem
    4. 10. An unexplored continent: the fundamental theorem of calculus
    5. 11. Of apples, legends … and comets: Newton’s laws
    6. 12. The great explorer: Euler’s theorems
  9. Part Three: Equations in a promethean age
    1. 13. The new algebra: Hamilton and quaternions
    2. 14. Two shooting stars: group theory
    3. 15. The geometry of whales and ants: non-Euclidean geometry
    4. 16. In primes we trust: the prime number theorem
    5. 17. The idea of spectra: Fourier series
    6. 18. A god’s-eye view of light: Maxwell’s equations
  10. Part Four: Equations in our own time
    1. 19. The photoelectric effect: quanta and relativity
    2. 20. From a bad cigar to Westminster Abbey: Dirac’s formula
    3. 21. The empire-builder: the Chern-Gauss-Bonnet equation
    4. 22. A little bit infinite: the Continuum Hypothesis
    5. 23. Theories of chaos: Lorenz equations
    6. 24. Taming the tiger: the Black-Scholes equation
  11. Conclusion: What of the future?
  12. Acknowledgments
  13. Bibliography
  14. Index