The Equation that Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry.

THE EQUATION THAT COULDN'T BE SOLVED: HOW Mathematical Genius Discovered the Language of Symmetry MARIO LIVIO 

Symmetry is easily recognized in art, music, and biology, writes Livio, an astrophysicist. Mathematically, however, symmetry is complex. Many mathematicians have spent their lives attempting to unlock the secrets of symmetry. This book opens with a review of some of these efforts, including the development of algebra and the discovery of the quintic equation, which resisted solution for centuries. The equation ultimately yielded to group theory, which Livio calls the "language of symmetry," Group theory was developed by two 19th-century mathematicians, Niels Henrik Abel and Evariste Galois, both of whom managed their achievements during tragically short lives, Abel died of tuberculosis at 26 and Galois was killed in a duel at age 20, Livio devotes special attention to Galois, whose proof would create a new branch of algebra, The author also delves deep into groups and permutations, and describes how symmetry applies to fields as diverse as physics and psychology. Simon & Schuster, 2005, 268 p., b&w illus. and photos, hardcover, $26.95.