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. Fearless Symmetry starts with basic properties of integers and permutations and reaches current research in number theory.
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Along the way, it takes delightful historical and philosophical digressions. Required reading for all math buffs, Fearless Symmetry will appeal to anyone curious about popular mathematics and its myriad contributions to everyday life. Will This Go On Forever? He is the author with D. Mumford, M. Rapoport, and Y. I recommend it to mathematicians and nonmathematicians alike with any interest in this subject. 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.
Fearless Symmetry: Exposing the Hidden Patterns of Numbers | NHBS Academic & Professional Books
With a very broad brush, it paints a beautiful picture of one of the main themes of the Langlands program. Childs, MathSciNet "All too often, abstract mathematics, one of the most beautiful of human intellectual creations, is ground into the dry dust of drills and proofs. Useful, yes; exciting, no. Avner Ash and Robert Gross have done something different — by focusing on the ideas that modern mathematicians actually care about.
Fearless Symmetry is a book about detecting hidden patterns, about finding definitions that clarify, about the study of numbers that has entranced some of our great thinkers for thousands of years.
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It is a book that takes on number theory in a way that a nonmathematician can follow-systematically but without a barrage of technicalities. Ash and Gross are two terrific guides who take the reader, scientist or layman, on a wonderful hike through concepts that matter, culminating in the extraordinary peaks that surround the irresistible, beckoning claim of Fermat's Last Theorem. Newsletter Google 4.
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Fearless Symmetry: Exposing the Hidden Patterns of Numbers
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About this book Mathematicians solve equations, or try to. Popular Science. Media reviews.
Fearless Symmetry:Exposing the Hidden Patterns of Numbers
Current promotions. This book is devoted to methods in number theory connected with hidden symmetries, their realizations by means of groups and their representations. The book is designed for a wide audience of non-specialists. The authors were willing to make an attempt to explain exciting discoveries in mathematics for a larger public without special training in mathematics.
They did a splendid job. They are able to describe an eminent role of symmetries in number theory by carefully explaining what it means to represent something a group by something else. The first part of the book reviews basic algebraic notions and introduces the Legendre symbol and the law of quadratic reciprocity. The Galois group and its role in number theory is the main topic of the second part. The last part treats various reciprocity laws.