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From Publishers Weekly

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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From Scientific American

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