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 symmetryknown as group theorydid 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. 
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LibraryThing Review
User Review  jefware  LibraryThingWhile the concept of symmetry is fascinating I think that it's application to particle physics may be like applying circles to planetary motions. Nature just isn't symmetric. This book includes a great history of the mathematics of Group Theory. Read full review
LibraryThing Review
User Review  shushokan  LibraryThingThis book would make a good biography of Abel and Galois but is really a book about maths and not a maths book (if you can see the distinction). We get the intimate details of the two mathematicians ... Read full review
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