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Not Even Wrong

Mario Livio

The equation that couldn't be solved

Symmetry has always played a large part in the development of mathematics. This book shows how ideas of symmetry were used to settle a long standing question - for which polynomial equations could a formula be found for their roots? The book gives biographical details of the mathematicians working on this problem, and in particular the tragic story of Evariste Galois who was killed in a duel at the age of twenty, having spent the night before hurriedly writing down some of his most important mathematical ideas. Thus Livio makes an abstract mathematical topic accessible to the reader with no previous knowledge of the subject.

Galois work was the start of Group theory, which is the mathematical description of symmetry. Livio goes on to show the important part this theory has come to play in the study of physics, for instance Noether's theorem which relates symmetries to conservation laws, and the use of group theory in particle physics.

My one criticism of the book is that sometimes Livio seems to discuss a subject just of the sake of it. Of course symmetry gives a wide scope for discussion, and some people might enjoy the variety, but I felt that a more focussed approach would have been better.

Amazon.com info
Hardcover 368 pages  
ISBN: 0743258207
Salesrank: 1222042
Weight:1.32 lbs
Published: 2005 Simon & Schuster
Amazon price $6.00
Marketplace:New from $6.00:Used from $1.53
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Amazon.co.uk info
Hardcover 368 pages  
ISBN: 0285637436
Salesrank: 1630455
Weight:1.23 lbs
Published: 2006 Souvenir Press Ltd
Marketplace:New from £26.00:Used from £0.71
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Amazon.ca info
Hardcover 368 pages  
ISBN: 0743258207
Salesrank: 1835009
Weight:1.32 lbs
Published: 2005 Simon & Schuster
Marketplace:New from CDN$ 27.88:Used from CDN$ 1.23
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Product Description
What do the music of J. S. Bach, the basic forces of nature, Rubik's Cube, and the selection of mates have in common? They are all characterized by certain symmetries. Symmetry is the concept that bridges the gap between science and art, between the world of theoretical physics and the everyday world we see around us. Yet the "language" of symmetry--group theory in mathematics--emerged from a most unlikely source: an equation that couldn't be solved.Over the millennia, mathematicians solved progressively more difficult algebraic equations until they came to what is known as the quintic equation. For several centuries it resisted solution, until two mathematical prodigies independently discovered that it could not be solved by the usual methods, thereby opening the door to group theory. These young geniuses, a Norwegian named Niels Henrik Abel and a Frenchman named Evariste Galois, both died tragically. Galois, in fact, spent the night before his fatal duel (at the age of twenty) scribbling another brief summary of his proof, at one point writing in the margin of his notebook "I have no time."The story of the equation that couldn't be solved is a story of brilliant mathematicians and a fascinating account of how mathematics illuminates a wide variety of disciplines. In this lively, engaging book, Mario Livio shows in an easily accessible way how group theory explains the symmetry and order of both the natural and the human-made worlds.