The Equation That Couldn't Be Solved by Livio, Mario -- Read -- Imperial Library of Trantor

Index

Also by Mario Livio Contents Preface One Symmetry

Immunity to Changes The Frolic Architecture of Snow Morris, Mozart, and Company All are Equal, But…

Two eyE s’dniM eht ni yrtemmyS

The Rules of the Game The Mother of all Symmetries

Three Never Forget This in the Midst of Your Equations

“US” and “AHA” The Protectors of the Public The Fathers of Algebra The Cubic The Plot Thickens Will Tell Aloud Your Greatest Failing

Four The Poverty-Stricken Mathematician

Abel—The Early Years A Struggling Genius The Quintic A European Experience Paris Coming Home

Five The Romantic Mathematician

Galois—The Early Years The Birth of a Mathematician Disaster Strikes Twice Liberté, ÉgalitÉ, Fraternité A Turbulent Life Imprisoned A Romantic in Love A Mysterious Death Conspiracy Theories Galore The Death of a Romantic Posthumous Fame

Six Groups

Groups and Permutations Galois’s Brilliant Proof The Dating Game Shaken, Not Stirred The Supreme Art of Abstraction What is Geometry? The Return of the Quintic

Seven Symmetry Rules

Spacetime A Weighty Symmetry Into the Quantum World Quark, Quark, Group The Harmony of the Strings Not Just Symmetry—Supersymmetry

Eight Who’s the Most Symmetrical of Them All?

Fearful Symmetry Birds Do it, Bees Do it, Even Educated Fleas Do it What’s Love Got to Do With it? Does Symmetry Really Rule? What Passion Cannot Music Raise and Quell? The “Thirty Years’ War,” or the Taming of the Monster

Nine Requiem for a Romantic Genius

The Secrets of a Creative Mind The Story of Two Brains Indivisible

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 CHAPTER 1: SYMMETRY CHAPTER 2: EYE S’DNIM EHT NI YRTEMMYS CHAPTER 3: NEVER FORGET THIS IN THE MIDST OF YOUR EQUATIONS CHAPTER 4: THE POVERTY-STRICKEN MATHEMATICIAN CHAPTER 5: THE ROMANTIC MATHEMATICIAN CHAPTER 6: GROUPS CHAPTER 7: SYMMETRY RULES CHAPTER 8: WHO’S THE MOST SYMMETRICAL OF THEM ALL? CHAPTER 9: REQUIEM FOR A ROMANTIC GENIUS References Credits Index