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Why Beauty Is Truth: The History of Symmetry Hardcover – April 10, 2007

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Editorial Reviews

From Publishers Weekly

Anyone who thinks math is dull will be delightfully surprised by this history of the concept of symmetry. Stewart, a professor of mathematics at the University of Warwick (Does God Play Dice?), presents a time line of discovery that begins in ancient Babylon and travels forward to today's cutting-edge theoretical physics. He defines basic symmetry as a transformation, "a way to move an object" that leaves the object essentially unchanged in appearance. And while the math behind symmetry is important, the heart of this history lies in its characters, from a hypothetical Babylonian scribe with a serious case of math anxiety, through Évariste Galois (inventor of "group theory"), killed at 21 in a duel, and William Hamilton, whose eureka moment came in "a flash of intuition that caused him to vandalize a bridge," to Albert Einstein and the quantum physicists who used group theory and symmetry to describe the universe. Stewart does use equations, but nothing too scary; a suggested reading list is offered for more rigorous details. Stewart does a fine job of balancing history and mathematical theory in a book as easy to enjoy as it is to understand.Line drawings. (Apr.)
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From Booklist

*Starred Review* Werner Heisenberg recognized the numerical harmonies at the heart of the universe: "I am strongly attracted by the simplicity and beauty of the mathematical schemes which nature presents us." An accomplished mathematician, Stewart here delves into these harmonies as he explores the way that the search for symmetry has revolutionized science. Beginning with the early struggles of the Babylonians to solve quadratics, Stewart guides his readers through the often-tangled history of symmetry, illuminating for nonspecialists how a concept easily recognized in geometry acquired new meanings in algebra. Embedded in a narrative that piquantly contrasts the clean elegance of mathematical theory with the messy lives of gambling, cheating, and dueling mathematicians, the principles of symmetry emerge in radiant clarity. Readers contemplate in particular how the daunting algebra of quintics finally opened a conceptual door for Evaniste Galois, the French genius who laid the foundations for group theory, so empowering scientists with a new calculus of symmetry. Readers will marvel at how much this calculus has done to advance research in quantum mechanics, relativity, and cosmology, even inspiring hope that the supersymmetries of string theory will combine all of astrophysics into one elegant paradigm. An exciting foray for any armchair physicist! Bryce Christensen
Copyright © American Library Association. All rights reserved
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Product Details

  • Hardcover: 304 pages
  • Publisher: Basic Books; First Edition edition (April 10, 2007)
  • Language: English
  • ISBN-10: 046508236X
  • ISBN-13: 978-0465082360
  • Product Dimensions: 6.1 x 0.7 x 9.2 inches
  • Shipping Weight: 1.2 pounds
  • Average Customer Review: 4.0 out of 5 stars  See all reviews (29 customer reviews)
  • Amazon Best Sellers Rank: #968,598 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

81 of 84 people found the following review helpful By Edward F. Strasser on May 21, 2007
Format: Hardcover
"Beauty" in Stewart's title refers to symmetry in mathematics and physics, and to the mathematical structures called groups, which express this symmetry. "Truth" refers to the fact that the fundamental laws of the universe are described by such symmetries.

Before Stewart goes into this, he builds up for about 100 pages, giving the historical background of the ideas leavened with some biographical sketches. Then he gives two simple examples which form a basis for going into the later topics. I can't match Stewart's simplicity in a brief review, but I hope I can give you an idea of the nature of the examples.

Symmetry here has a somewhat more general meaning than in ordinary language. Ordinarily we say that something is symmetric if it looks the same as its mirror reflection. It is often said that a starfish has "radial symmetry" because, if it is rotated by 72 degrees (1/5 of a circle), it still looks the same, right down to the legs pointing in the same directions. Stewart considers the rotations and reflections of an equilateral triangle and defines a sort of "multiplication" of these turnings. The turnings together with the "multiplication" have a structure known as a "group". (It is called "multiplication" because it follows the same rules as multiplication of numbers. Any set of things which follow these rules is a group.)

There is also purely mathematical symmetry. For example, suppose you have a formula containing 3 numbers. If you rearrange those numbers in any order and the value of the formula is still the same, that rearrangement is called a symmetry. Instead of preserving the shape of an object, it preserves the value of an expression.
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36 of 37 people found the following review helpful By Bruce R. Gilson on July 16, 2007
Format: Hardcover
Some of the reviews of this book seem to feel it doesn't present enough group theory. I think they are looking for a more technical book than Stewart meant to write, and so they are downgrading the book for reasons that are not fair to the book.

I reviewed a book by Mario Livio called "The Equation that Couldn't Be Solved," and gave it 5 stars. After reading this book, I almost want to go back and lower my rating of Livio's book, but of course, I shouldn't do that just because a better book has come out since. Livio's book concentrates on a shorter timespan than this, but both feature the same things -- mathematicians' attempts to solve equations of higher and higher degrees, from quadratics to cubics to quartics, and failure to find a solution to the quintic, only to find (due to the work of Abel and Galois) that it couldn't be done; and Galois' invention of group theory to make his proof, followed by other mathematicians' revelation that group theory is just what the doctor ordered to explain symmetry.

Stewart's book goes further back in time than Livio's, and also devotes more space to the modern uses of symmetry in physics. So it puts everything in more context. And, simply put, Stewart is a captivating writer. I enjoyed Livio's book, but I could hardly put down Stewart's. This book gets a high 5-star rating from me.

But it IS a book for the non-specialist. It isn't a course in group theory, or the Galois theory of equations; it is an attempt to give a non-mathematician some idea of these subjects. It should not be rated on a set of criteria that ignore what Stewart was trying to do. The negative comments really are unjustified; but yes, I'll warn you away from this if you expect it to teach you all the group theory you'll need to do particle physics, or crystallography, or any of the subjects that depend on group theoretic concepts of symmetry these days.
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19 of 19 people found the following review helpful By viktor_57 on May 5, 2007
Format: Hardcover
I have always enjoyed Professor Ian Stewart's works for general audiences, including "Letters to a Young Mathematician" and "Flatterland", among others. In "Why Beauty Is Truth: A History of Symmetry", Stewart continues to explain seemingly esoteric and difficult mathematical topics with a clarity and humanity that illuminate not only the topics themselves, but also the people who developed them and the importance of their work to us in the present day.

In his latest book, "Why Beauty Is Truth", Stewart recounts the history of a concept most of us understand intuitively, symmetry, by describing the lives of people who made important contributions to the mathematics of this seemingly simply concept which turned out to have extraordinary implications. From the development of ancient number systems and algebra to the discovery of Lie groups, Stewart explains the mathematics and concepts in an intuitive way, sprinkling in equations when necessary, but mostly relying on his ability to imagine how a non-mathematician might best understand even the most abstract concepts, whether by example, metaphor, or even some fictional drama.

Stewart is the rare mathematician who seems equally at home with the technical aspects of his subject and its history, including the biographies of those who made important contributions. Stewart is also a fine writer and enthusiastic popularizer, showing how the development of symmetry from the beginnings of counting has led to some of the most important developments in physics, including general relativity and string theory. Math and physics enthusiasts will undoubtedly enjoy "Why Beauty Is Truth", as will the curious lay reader who enjoys new discoveries and lively, engaging and intelligent writing.
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