The Equation that Couldn't Be Solved

How Mathematical Genius Discovered the Language of Symmetry

Mario Livio

• Publisher: Simon & Schuster
• Year: 2005
• Print ISBN:
  9780743258210
• eBook ISBN:
  9780743274623
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

What do Bach's compositions, Rubik's Cube, the way we choose our mates, and the physics of subatomic particles have in common? All are governed by the laws of symmetry, which elegantly unify scientific and artistic principles. Yet the mathematical language of symmetry-known as group theory-did not emerge from the study of symmetry at all, but from an equation that couldn't be solved. For thousands of years mathematicians solved progressively more difficult algebraic equations, until they encountered the quintic equation, which resisted solution for three centuries. Working independently, two great prodigies ultimately proved that the quintic cannot be solved by a simple formula. These geniuses, a Norwegian named Niels Henrik Abel and a romantic Frenchman named Évariste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory. The first extensive, popular account of the mathematics of symmetry and order, The Equation That Couldn't Be Solved is told not through abstract formulas but in a beautifully written and dramatic account of the lives and work of some of the greatest and most intriguing mathematicians in history.

Table of contents

• Cover
• Colophon
• Also by Mario Livio
• Title Page
• Copyright
• Dedication
• Contents
• Preface
• 1. Symmetry
• 2. eyE s’dniM eht ni yrtemmyS
• 3. Never Forget This in the Midst of Your Equations
• 4. The Poverty-Stricken Mathematician
• 5. The Romantic Mathematician
• 6. Groups
• 7. Symmetry Rules
• 8. Who’s the Most Symmetrical of Them All?
• 9. Requiem for a Romantic Genius
• Appendix 1. Card Puzzle
• Appendix 2. Solving a System of Two Linear Equations
• Appendix 3. Diophantus’s Solution
• Appendix 4. A Diophantine Equation
• Appendix 5. Tartaglia’s Verses and Formula
• Appendix 6. Adriaan van Roomen’s Challenge
• Appendix 7. Properties of the Roots of Quadratic Equations
• Appendix 8. The Galois Family Tree
• Appendix 9. The 14–15 Puzzle
• Appendix 10. Solution to the Matches Problem
• Notes
• References
• Credits
• Index