The Art of the Infinite: The Pleasures of Mathematics - Robert & Ellen Kaplan [epub]

The Art of the Infinite takes infinity, in its countless guises, as a touchstone for understanding mathematical thinking. Robert and Ellen Kaplan guide us through the "Republic of Numbers," where we meet both its upstanding citizens and its more shadowy dwellers; and transport us across the plane of geometry into the unlikely realm where parallel lines meet. The journey is enriched by deft character studies of great mathematicians (and equally colorful lesser ones). And as we go deeper into infinity, we explore the most profound mystery of mathematics: Are its principles eternal truths that we discover? Or ones that we invent?

**

From Publishers Weekly

While Kaplan (The Nothing That Is: A Natural History of Zero) and his wife intend this volume to delight the numerophobic into seeing the beauty in math, the "art" they describe is hidden in a thicket of dry proofs. And yet they've written a lovely and erudite history of the subject in spite of that, one that will absorb anyone who already fancies numbers and all their possibilities. Hand-drawn diagrams accompany dense explanatory prose in this exploration of infinity, as the authors chart mathematical discoveries and great thinkers throughout history. Frequent references to luminaries from the humanities (Shakespeare, Baudelaire, Gaudi, Robert Graves) would earn this book comfortable shelving in a liberal arts library if the math weren't so devilishly hard to grasp. (A typical passage compares the way great changes happen in mathematics with the way important figures enter the action in Proust.) The authors acknowledge that even math basics can be tricky: that the product of two negatives is a positive, for instance, is a puzzle that the Kaplans say "put too many people off math forever, convinced that its dicta were arbitrary or spiteful." The authors write that "mathematics is permanent revolution," and indeed, some may find their heads spinning. Nevertheless, a patient reader who loves thinking about thinking will be rewarded by the book's end; by the final pages, he or she will have personally experienced, via these diagrams and problems, many of the great discoveries in mathematics. Graphs and illustrations throughout.


From School Library Journal

Adult/High School-This is mathematics with a plot and characters, as well as diagrams and formulas. In the process of discussing numbers, natural and rational, real and complex, the Kaplans introduce readers to the historical figures who were challenged by their mysteries. The authors explore math in ways that will be new to students whose education has been confined to the classroom. Readers learn not only that a number can be squared, but also that it can be "triangled," and that the sum of two adjacent triangular numbers always makes a square one. The book shows how all the concepts of different types of numbers lead to the notion of infinity, and how one can prove things through geometry that would normally appear to have nothing to do with shapes and lines. Most of the math discussed can be followed by anyone with a smattering of algebra and geometry, and always it is accompanied by stories of how people first discovered the mathematical principles, with illustrations of the protagonists. These accounts vary from tragic to laugh-out-loud funny. Those who love math won't want to miss this one, and those who would like to love it but never have should give the book a try.