The universe in zero words The story of mathematics as told through equations

Dana Mackenzie

Book - 2012

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Subjects
Published
Princeton, N.J. : Princeton University Press 2012.
Language
English
Main Author
Dana Mackenzie (-)
Physical Description
224 p. : ill. (some col.) ; 25 cm
Bibliography
Includes bibliographical references (p. 219-221) and index.
ISBN
9780691152820
  • preface
  • introduction: the abacist versus the algorist
  • Part 1. equations of antiquity
  • 1. Why we believe in arithmetic: the world's simplest equation
  • 2. Resisting a new concept: the discovery of zero
  • 3. The square of the hypotenuse: the Pythagorean theorem
  • 4. The circle game: the discovery of ¿
  • 5. From Zeno's paradoxes to the idea of infinity
  • 6. A matter of leverage: laws of levers
  • Part 2. equations in the age of exploration
  • 7. The stammerer's secret: Cardano's formula
  • 8. Order in the heavens: Kepler's laws of planetary motion
  • 9. Writing for eternity: Fermat's Last Theorem
  • 10. An unexplored continent: the fundamental theorem of calculus
  • 11. Of apples, legends... and comets: Newton's laws
  • 12. The great explorer: Euler's theorems
  • Part 3. equations in a promethean age
  • 13. The new algebra: Hamilton and quaternions
  • 14. Two shooting stars: group theory
  • 15. The geometry of whales and ants: non-Euclidean geometry
  • 16. In primes we trust: the prime number theorem
  • 17. The idea of spectra: Fourier series
  • 18. A god's-eye view of light: Maxwell's equations
  • Part 4. equations in our own time
  • 19. The photoelectric effect: quanta and relativity
  • 20. From a bad cigar to Westminster Abbey: Dirac's formula
  • 21. The empire-builder: the Chern-Gauss-Bonnet equation
  • 22. A little bit infinite: the Continuum Hypothesis
  • 23. Theories of chaos: Lorenz equations
  • 24. Taming the tiger: the Black-Scholes equation
  • conclusion: what of the future?
  • acknowledgments
  • bibliography
  • index
Review by Choice Review

Using 24 great equations, Mackenzie (freelance writer, former mathematics academic) tours the history of mathematics. Four criteria measure an equation's greatness: surprises, aesthetic conciseness, significant consequences, and timeless universality. The equations are presented within four broad divisions of mathematical history. Many are expected, e.g., Pythagorean theorem, fundamental theorem of calculus, Newton's laws, prime number theorem, Fourier series, Maxwell's equations, Einstein's relativity equation. But some equations are surprises themselves and seem forced, such as the discovery of zero (1 - 1 = 0), Cardano's formula for solving cubics, Hamilton's quaternions, Fermat's last theorem, Abel's proof of the quintic, and the Black-Scholes equation for financial derivatives. Nonetheless, Mackenzie 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. Yes, Euler's gem of an equation (e^D]i^D]^D*p + 1 = 0) appears, but as a generalization of De Moivre's theorem. The reference list provides options for readers to dig deeper into the mathematics behind the equations. The book is an enjoyable read, but should not be mistaken for a history of mathematics. At best, it is a guided tour of important sights. Summing Up: Recommended. Lower-division undergraduates through researchers/faculty; general readers. J. Johnson Western Washington University

Copyright American Library Association, used with permission.