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Fearless Symmetry: Exposing the Hidden Patterns of Numbers

3.78 ( 9 Ratings by Goodreads)
Fearless Symmetry: Exposing the Hidden Patterns of Numbers

Fearless Symmetry: Exposing the Hidden Patterns of Numbers

(Author) (Author)
3.78 (9 Ratings by Goodreads)
hardback
Published: 11 June, 2006
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Description

Mathematicians solve equations, or try to. But sometimes the solutions are not as interesting as the beautiful symmetric patterns that lead to them. Written in a friendly style for a general audience, Fearless Symmetry is the first popular math book to discuss these elegant and mysterious patterns and the ingenious techniques mathematicians use to uncover them. Hidden symmetries were first discovered nearly two-hundred years ago by French mathematician Evariste Galois. They have been used extensively in the oldest and largest branch of mathematics - number theory - for such diverse applications as acoustics, radar, and codes and ciphers. They have also been employed in the study of Fibonacci numbers and to attack well-known problems such as Fermat's Last Theorem, Pythagorean Triples, and the ever-elusive Riemann Hypothesis. Mathematicians are still devising techniques for teasing out these mysterious patterns, and their uses are limited only by the imagination. The first popular book to address representation theory and reciprocity laws, Fearless Symmetry focuses on how mathematicians solve equations and prove theorems. It discusses rules of math and why they are just as important as those in any games one might play. The book starts with basic properties of integers and permutations and reaches current research in number theory. Along the way, it takes delightful historical and philosophical digressions. Required reading for all math buffs, the book will appeal to anyone curious about popular mathematics and its myriad contributions to everyday life.
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More Details

Type Book
ISBN13 9780691124926
ISBN10 0691124922
Number Of Pages 304
Item Weight 634 g
Product Dimensions 163 x 30 x 236 mm
Publisher / Reseller Princeton University Press
Format hardback
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Media Reviews

The authors are to be admired for taking a very difficult topic and making it ... certainly more accessible than it was before. -- Timothy Gowers Nature The authors ... outline current research in mathematics and tell why it should hold interest even for people outside scientific and technological fields. Science News The book ... does a remarkable job in making the work it describes accessible to an audience without technical training in mathematics, while at the same time remaining faithful to the richness and power of this work. I recommend it to mathematicians and nonmathematicians alike with any interest in this subject. -- William M. McGovern SIAM Review This unique book paints a picture of modern algebraic number theory, culminating in a discussion of Wiles' proof of Fermat's Last Theorem... The focus on reciprocity laws sets this book apart from other expositions of Wiles' proof... [T]his book is an amazing attempt to provide to a mathematically unsophisticated reader a realistic impression of the immense vitality of this area of mathematics. -- Lindsay N. Childs Mathematical Reviews To borrow one of the authors' favorite words, this book is an amazing attempt to provide to a mathematically unsophisticated reader a realistic impression of the immense vitality of this area of mathematics. But I think the book has another useful role. With a very broad brush, it paints a beautiful picture of one of the main themes of the Langlands program. -- Lindsay N. Childs MathSciNet

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Author's Bio

Avner Ash is Professor of Mathematics at Boston College. He is the author (with D. Mumford, M. Rapoport, and Y. Tai) of Smooth Compactification of Locally Symmetric Varieties . Robert Gross is Associate Professor of Mathematics at Boston College.

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