Yearning for the Impossible: The Surprising Truths of Mathematics

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Overview

This book explores the history of mathematics from the perspective of the creative tension between common sense and the "impossible" as the author follows the discovery or invention of new concepts that have marked mathematical progress: - Irrational and Imaginary Numbers - The Fourth Dimension - Curved Space - Infinity and others The author puts these creations into a broader context involving related "impossibilities" from art, literature, philosophy, and physics. By imbedding mathematics into a broader cultural context and through his clever and enthusiastic explication of mathematical ideas the author broadens the horizon of students beyond the narrow confines of rote memorization and engages those who are curious about the place of mathematics in our intellectual landscape.

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Editorial Reviews

From the Publisher
Like the White Queen in Lewis Carroll's Through the Looking-Glass, mathematicians are called upon to believe in things that, at first glance, defy common sense and appear impossible. . . . As Stillwell puts it, 'Mathematics is a story of close encounters with the impossible because all its great discoveries are close to the impossible.'
—Ivars Peterson, Science News , July 2006

Stillwell weaves historical details into his writing seamlessly, helping to give the reader the true feeling that mathematics is more than just a bunch of people playing games with symbols, but rather a rich and rewarding intellectual endeavor important to the human enterprise.
—Marcus E. Barnes, MAA Reviews, August 2006

Yearning for the Impossible is as much of a celebration of the greater understanding mathematics has brought to the world as it is a history and discussion of innovative concepts. and is highly recommended for library and personal reading shelves.
—Wisconsin Bookwatch, August 2006

Rises nobly to the challenge of describing these topics to a genuine novice...There is much to admire in Stillwell's attempt... he's accomplishing something very important and difficult here in demonstrating that there's some real struggle present in the process of mathematical discovery.
—Daniel Biss, Notices, June 2007

Yearning for the Impossible offers a fascinating, historical look at some popular mathematical concepts used in music, art and philosophy. . . This book is an interesting find and provides a readable approach to some higher-level mathematics. The chapters can be read independently, and the reader can dig deeper into textbooks and history books for additional problems and details. I give a high recommendation for this book!
—Lynn Godshall, Convergence Magazine (MAA), June 2007

A wonderful journey through mathematical discoveries... this book is an excellent vehicle for giving mathematics students new research ideas and, most important, for planting the seed in their minds to 'yearn for the impossible' as they investigate new truths.
Mathematics Teacher, August 2007

Stillwell has achieved what many might well have come to believe to be nearly impossible in mathematical exposition for the masses...[he] succeeds, in every topic treated, in bringing a fresh eye to questions even mathematicians might think have been mined in the past to boring exhaustion [and] shows there is still a lot of gold to be found, if one only thinks about things in a new way. Stillwell brings new, unorthodox insights to his writing that will stimulate readers (from high schoolers to emeritus professors) to think about old topics in new, nonstale ways... Yearning for the Impossible will be a treat for teachers, too, who are looking for new ways to bring stimulating, fresh examples into their courses.
SIAM Review, May 2007

Stillwell does an excellent job laying the historical foundations for these discoveries; he is to be commended for his historical accuracy.
—Recreational Math, March 2007

Mathematics may be described as a story of close encounters with the impossible because all great discoveries are close to the impossible. The aim of this book is to tell this story, briefly and with few prerequisites, by presenting some representative encounters across the breadth of mathematics.
CMS Notes, May 2007

This book explores history through a lens focused on the creative tension between common sense and the 'impossible' . . . Drawing connections to art, literature, philosophy, and physics, this book examines the place of mathematics in our intellectual landscape.
L'Enseignement Mathématique, January 2006

2009 Alpha Sigma Nu Book Award in the Discipline of Mathematics/Computer Science
—The Association of Jesuit Colleges & Universities, November 2009

Mathematics Teacher
A wonderful journey through mathematical discoveries . . . this book is an excellent vehicle for giving mathematics students new research ideas and, most important, for planting the seed in their minds to "yearn for the impossible" as they investigate new truths.
MAA Reviews
Stillwell weaves historical details into his writing seamlessly, helping to give the reader the true feeling that mathematics is more than just a bunch of people playing games with symbols, but rather a rich and rewarding intellectual endeavor important to the human enterprise.
Wisconsin Bookwatch
Yearning For The Impossible is as much of a celebration of the greater understanding mathematics has brought to the world as it is a history and discussion of innovative concepts. and is highly recommended for library and personal reading shelves.
Science News
"Like the White Queen in Lewis Carroll's Through the Looking-Glass, mathematicians are called upon to believe in things that, at first glance, defy common sense and appear impossible . . . . As Stillwell puts it, "Mathematics is a story of close encounters with the impossible because all its great discoveries are close to the impossible.
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Product Details

  • ISBN-13: 9781568812540
  • Publisher: Taylor & Francis
  • Publication date: 6/15/2006
  • Edition description: New Edition
  • Pages: 244
  • Sales rank: 1,464,390
  • Product dimensions: 6.00 (w) x 9.10 (h) x 0.90 (d)

Meet the Author

John Stillwell, originally from Melbourne, Australia, is a Professor of Mathematics at the University of San Francisco. He earned his MSc in 1965 from the University of Melbourne and his PhD from MIT in 1970. His writing covers a wide spectrum of mathematics, including translations of classic texts by Dirichlet, Dedekind, Poincaré, and Dehn. He is also the author of Mathematics and Its History, The Four Pillars of Geometry, and Elements of Number Theory, among others. In 2005, he was awarded the Chauvenet Prize of the Mathematical Association of America for his expository writing.
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Table of Contents

1 The irrational 1
2 The imaginary 25
3 The horizon 47
4 The infinitesimal 77
5 Curved space 101
6 The fourth dimension 129
7 The ideal 155
8 Periodic space 177
9 The infinite 197
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Sort by: Showing 1 Customer Reviews
  • Anonymous

    Posted August 6, 2006

    Highly recommended

    Mathematics professor John Stillwell (University of San Francisco) presents Yearning For The Impossible: The Surprising Truth Of Mathematics, a fascinating tour through the history of mathematics and the resounding impact new conceptual discoveries have made upon human civilization. Mathematical achievements such as concepts of irrational numbers, imaginary numbers, the infinitesimal, the fourth dimension, periodic space, and more are explored in terms accessible to lay readers, and their intersection with art, literature, philosophy, and physics among other disciplines is laid bare. Yearning For The Impossible is as much of a celebration of the greater understanding mathematics has brought to the world as it is a history and discussion of innovative concepts, and is highly recommended for library and personal reading shelves.

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