## The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of SymmetryWhat 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. |

### Contents

1 | |

2 eyE sdniM eht ni yrtemmyS | 29 |

3 Never Forget This in the Midst of Your Equations | 51 |

4 The PovertyStricken Mathematician | 90 |

5 The Romantic Mathematician | 112 |

6 Groups | 158 |

7 Symmetry Rules | 198 |

8 Whos the Most Symmetrical of Them All? | 233 |

Appendix 4 A Diophantine Equation | 281 |

Appendix 5 Tartaglias Verses and Formula | 282 |

Appendix 6 Adriaan van Roomens Challenge | 285 |

Appendix 7 Properties of the Roots of Quadratic Equations | 286 |

Appendix 8 The Galois Family Tree | 288 |

Appendix 9 The 1415 Puzzle | 291 |

Appendix 10 Solution to the Matches Problem | 292 |

Notes | 293 |

9 Requiem for a Romantic Genius | 262 |

Appendix 1 Card Puzzle | 277 |

Appendix 2 Solving a System of Two Linear Equations | 278 |

Appendix 3 Diophantuss Solution | 280 |

309 | |

337 | |

### Other editions - View all

The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the ... Mario Livio No preview available - 2006 |

The Equation that Couldn't be Solved: How Mathematical Genius Discovered the ... Mario Livio No preview available - 2005 |

### Common terms and phrases

Abel Abel’s algebra appeared bilateral symmetry brain Cardano Cauchy century chapter creative Crelly cube cubic degrees Demante denoted described discovered Earth’s École Einstein electrons entire Évariste Galois Évariste’s examination fact famous father Ferrari Ferro figure followed force formula French Galois group Galois’s genius geometry gravity group of permutations group theory Guigniault human ideas identity instance inverse Klein known later laws of nature letter Lie groups mathe mathematician mathematics memoir metry O’Connor and Robertson objects operation paper Paris particles patterns perception physicists physics precisely problem proof properties proton psychologist published puzzle quadratic equations quantum mechanics quarks quintic equation reflection relativity result rotation Ruffini Scipione dal Ferro showed simple groups solution solvable solve spacetime special relativity speed of light spin Stéphanie’s string theory subgroup supersymmetry symmetry transformations Tartaglia theorem tion translation University whole number Woerden words young