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 Mathematique, January 2006 2009 Alpha Sigma Nu Book Award in the Discipline of Mathematics/Computer Science -The Association of Jesuit Colleges & Universities, November 2009
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.