Synopses & Reviews
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. andlt;BRandgt; andlt;BRandgt; 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 and#201;variste Galois, both died tragically young. Their incredible labor, however, produced the origins of group theory. andlt;BRandgt; andlt;BRandgt; The first extensive, popular account of the mathematics of symmetry and order, andlt;iandgt;The Equation That Couldn't Be Solvedandlt;/iandgt; 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.
"A lively and fascinating read for a broad audience." -- andlt;iandgt;Natureandlt;/iandgt;
"A lively and fascinating read for a broad audience."
"Mario Livio tells the story of symmetry with insight and literary skill, producing a highly readable and illuminating book."
--Sir Michael Atiyah, Fields Medalist 1966, and Abel Prize in Mathematics Laureate 2004
"Mario Livio tells a gripping tale of humanity's discovery of the language of symmetry, with its colorful, romantic characters and dramatic historical incident. Essential reading for anyone who wants to understand how the apparently remote concerns of pure mathematics can lead to deep and practical insights into the natural world."
--Ian Stewart, author of Does God Play Dice? The New Mathematics of Chaos and professor of mathematics, University of Warwick, UK
"Mario Livio has done a marvelous job combining the gripping human saga of the lives of two mathematical geniuses who died young with the key mathematical ideas of symmetry and structure. He explains important mathematical concepts with both clarity and precision, making them understandable to every reader. This is one of the best books about mathematics I have ever read."
--Amir D. Aczel, author of Chance: A Guide to Gambling, Love, the Stock Market, and Just About Everything Else and Fermat's Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem
"A wide-ranging exploration of the phenomenon of symmetry....There's math, yes, but there are also tales of love, violence, history -- and the whole, in this case, turns out to be greater than the sum of those parts." -- Mary Carmichael, andlt;iandgt;Newsweekandlt;/iandgt;
"Fascinating. . . . [Livio] writes passionately about the role of symmetry in human perception and the arts." -- andlt;iandgt;The Economistandlt;/iandgt;
From the author of the bestseller "The Golden Ratio" comes the story of the 4,000-year-long mathematical quest that uncovered the laws of symmetry in nature and the arts.
About the Author
Mario Livio is an internationally known astrophysicist at the Space Telescope Science Institute (STScI). He is the author of andlt;i andgt;The Golden Ratioandlt;/iandgt;, a highly acclaimed book for which he received the International Pythagoras Prize and the Peano Prize; andlt;i andgt;The Equation That Couldnand#8217;t Be Solvedandlt;/iandgt;; the national bestseller andlt;i andgt;Brilliant Blundersandlt;/iandgt;; and andlt;i andgt;The Accelerating Universeandlt;/iandgt;. He lives in Baltimore, Maryland.
Table of Contents
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
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