Review
The author has achieved a remarkable feat, introducing a nave reader to a rich history without compromising the insights and without leaving out a delicious detail. Furthermore, he describes the development of topology from a suggestion by Gottfried Leibniz to its algebraic formulation by Emmy Noether, relating all to Euler's formula. This book will be valuable to every library with patrons looking for an awe-inspiring experience. -- Choice
This is an excellent book about a great man and a timeless formula. -- Charles Ashbacher, Journal of Recreational Mathematics
I liked Richeson's style of writing. He is enthusiastic and humorous. It was a pleasure reading this book, and I recommend it to everyone who is not afraid of mathematical arguments and has ever wondered what this field of 'rubbersheet geometry' is about. You will not be disappointed. -- Jeanine Daems, Mathematical Intelligencer
The book is a pleasure to read for professional mathematicians, students of mathematicians or anyone with a general interest in mathematics. -- European Mathematical Society Newsletter
I found much more to like than to criticize in
Euler's Gem. At its best, the book succeeds at showing the reader a lot of attractive mathematics with a well-chosen level of technical detail. I recommend it both to professional mathematicians and to their seatmates. -- Jeremy L. Martin, Notices of the AMS
I highly recommend this book for teachers interested in geometry or topology, particularly for university faculty. The examples, proofs, and historical anecdotes are interesting, informative, and useful for encouraging classroom discussions. Advanced students will also glimpse the broad horizons of mathematics by reading (and working through) the book. -- Dustin L. Jones, Mathematics Teacher
From the Inside Flap
"Euler's Gem is a thoroughly satisfying meditation on one of mathematics' loveliest formulas. The author begins with Euler's act of seeing what no one previously had, and returns repeatedly to the resulting formula with ever more careful emendations and ever-widening points of view. This highly nuanced narrative sweeps the reader into the cascade of interlocking ideas which undergird modern topology and lend it its power and beauty."--Donal O'Shea, author of The Poincar Conjecture: In Search of the Shape of the Universe
"Beginning with Euler's famous polyhedron formula, continuing to modern concepts of 'rubber geometry,' and advancing all the way to the proof of Poincar's Conjecture, Richeson's well-written and well-illustrated book is a gentle tour de force of topology."--George G. Szpiro, author of Poincar's Prize: The Hundred-Year Quest to Solve One of Math's Greatest Puzzles
"A fascinating and accessible excursion through two thousand years of mathematics. From Plato's Academy, via the bridges of Knigsberg, to the world of knots, soccer balls, and geodesic domes, the author's enthusiasm shines through. This attractive introduction to the origins of topology deserves to be widely read."--Robin Wilson, author of Four Colors Suffice: How the Map Problem Was Solved
"Appealing and accessible to a general audience, this well-organized, well-supported, and well-written book contains vast amounts of information not found elsewhere. Euler's Gem is a significant and timely contribution to the field."--Edward Sandifer, Western Connecticut State University
"Euler's Gem is a very good book. It succeeds in explaining complicated concepts in engaging layman's terms. Richeson is keenly aware of where the difficult twists and turns are located, and he covers them to satisfaction. This book is engaging and a joy to read."--Alejandro Lpez-Ortiz, University of Waterloo
