The Equation That Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry - Hardcover

Livio, Mario

Hardcover

ISBN 10: 0743258207 ISBN 13: 9780743258203

Publisher: Simon & Schuster, 2005

Synopsis

Traces the four-thousand-year-old mathematical effort to discover and define the laws of symmetry in nature and the arts, citing the achievements of doomed geniuses Niels Henrick Abel and Evariste Galois to solve the quintic equation and give birth to group theory. By the author of The Golden Ratio. 50,000 first printing.

About this title

About the Author

Mario Livio is a Senior Astronomer and the former Head of the Science Division at the Space Telescope Science Institute (STScI), the institute that conducts the scientific program of the Hubble Space Telescope. He received his Ph.D. in theoretical astrophysics from Tel Aviv University in Israel and was a professor in the Physics Department at the Technion-Israel Institute of Technology from 1981 to 1991, when he joined STScI. Dr. Livio has published more than 400 scientific papers and has received numerous awards for research and for excellence in teaching. He is the author of The Golden Ratio, a highly acclaimed book about mathematics and art for which he received the International Pythagoras Prize and the Peano Prize, and The Accelerating Universe.

Reviews

The idea of symmetry has been heavily deployed in recent science popularizations to introduce advanced subjects in math and physics. This approach usually backfires—mathematical symmetry is much too difficult for most laypeople to understand. But this engaging treatise soft-pedals it in a crowd-pleasing way. The title's formula is the "quintic" equation (involving x raised to the fifth power), the analysis of which gave rise to "group theory," the mathematical apparatus scientists use to explore symmetry. Inevitably, the author's attempts to explain group theory and its applications in particle physics and string theory to a general audience fall sadly short, so readers will just have to take his word for the Mozartean beauty of it all. Fortunately, astrophysicist Livio (The Golden Ratio) keeps the hard stuff to a minimum, concentrating instead on interesting digressions into human interest (e.g., the founder of group theory, Evariste Galois, was a revolutionary firebrand who died in 1832 at age 20 in a duel over "an infamous coquette"), pop psychology (women have more orgasms when their partners have symmetrical faces), strategies for finding a soul mate and some easy math puzzles readers might actually solve. The result is a somewhat shapeless but intriguing excursion. Photos.
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The so-called quintic equation resisted solution for three centuries, until two brilliant young mathematicians independently discovered that it could not be solved by any of the usual methods — and thereby opened the door to a new branch of mathematics known as group theory. This book is the story of these two early 19th-century mathematicians— a Norwegian, Niels Henrik Abel, and a Frenchman, Evariste Galois, both of whom died tragically, Galois in a duel at the age of 20. Livio, an astrophysicist now at the Space Telescope Science Institute and author of The Golden Ratio, interweaves their story with fascinating examples of how mathematics illuminates a wide swath of our world.

Editors of Scientific American

From the second-degree, or quadratic, equation taught in algebra, scale up to the fifth-degree, or quintic, equation to grasp astrophysicist Livio's topic. Because the general solution to quintic equations opened up the study of symmetry, which itself enlightens the study of biology, music, visual art, and particle physics, Livio is loaded with story material, none more interesting than biographies of two young mathematicians: Niels Henrik Abel (1802-29) and Evariste Galois (1811-32). Prodigies both, each suffered tragically, Abel dying of tuberculosis, Galois in a duel. Relating the stories of centuries of mathematicians defeated by the quintic equation, Livio captures the brilliant intuitions of Abel and Galois, who courageously dumped the fruitlessness of previous algebraic methods and mastered the quintic through ideas subsumed into group theory. This admirable presentation of a mathematical revolution will challenge general readers but will deliver ample rewards. Gilbert Taylor
Copyright © American Library Association. All rights reserved

Edition details

• Publisher: Simon & Schuster
• Publication date: 2005
• Language: English
• ISBN 10: 0743258207
• ISBN 13: 9780743258203
• Binding: Hardcover
• Edition number: 1
• Number of pages: 368