Review by Choice Review
Robert Kaplan's earlier work, The Nothing That Is: A Natural History of Zero (CH, Feb'00), looked at mathematics from the standpoint of nothing. Now, the Kaplans look at mathematics through the theme of the infinite. From ancient ideas such as the development of counting to recent ideas involving different orders of infinity (Cantor), the Kaplans present the infinite as an inevitable consequence in mathematical thinking. Through their presentation, they help readers understand many mathematical basics, such as why the product of two negatives is a positive and the nature of proof by contradiction. This book is quality at its best; it will become a classic among efforts to explain mathematics. The textual expression is exquisite, filled with metaphors; historical references fill the pages; simple hand-prepared sketches are easily understood. Weighty proofs are deferred to an appendix to keep readers from becoming bogged down. The publisher's technical production is superb. A must for libraries supporting baccalaureate or graduate programs in mathematics, public libraries that can afford to cater to those with serious mathematical interests, and personal mathematics libraries everywhere. Excellent for a capstone readings course for college mathematics majors. Good bibliography; excellent index. ^BSumming Up: Essential. General readers; upper-division undergraduates through faculty. W. R. Lee Iowa State University
Copyright American Library Association, used with permission.
Review by Booklist Review
In contrast to many popular math books that use narrative to produce admiration for a famous mathematician, theorem, or number (as Robert Kaplan did for zero in The Nothing That Is, 1999), the Kaplans' new work proposes to inspire readers to actually do math. The authors hope to instill the feeling that arises from inwardly knowing, rather than outwardly reading, that something is true eternally and infinitely. Proof, in other words, is the proposition the Kaplans place on the table. Readers able to quell their initial panic will find a vista of companionable curiosity as the authors commence by playing around with counting numbers, using axioms that form "bridges of equality" to the blackboard pronouncements of school math. Thus liberated from accepting things on authority, the avid reader discovers, guided by the Kaplans, provable properties of irrational, imaginary, and prime numbers; infinite series; plane geometry; trigonometry; and sets. Incorporating biographical asides about various mathematicians, the Kaplans prove themselves enlightening and entertaining ambassadors to the world of mathematics. --Gilbert Taylor
From Booklist, Copyright (c) American Library Association. Used with permission.
Review by Publisher's Weekly Review
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 "[m]athematics 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. (Apr.) (c) Copyright PWxyz, LLC. All rights reserved
(c) Copyright PWxyz, LLC. All rights reserved
Review by Library Journal Review
The Kaplans are founders of the Math Circle, a school that teaches the enjoyment of mathematics, and Robert is the author of The Nothing That Is: A Natural History of Zero. In this new book, the authors cover some of the elements of such areas as plane geometry, algebra, and trigonometry. The contents are chosen and arranged so as to lead into a concluding discussion of Georg Cantor's remarkable discoveries/inventions concerning the nature of infinity. All of this is related in a cheerful conversational tone with frequent allusions to, and quotations from, many other fields of knowledge, including literature, history, and philosophy. At times, a meander through a different discipline distracts from the main argument, but overall the Kaplans' approach makes for very enjoyable reading. This volume should appeal to a broad spectrum of readers interested in learning more about the beauty of mathematics. Recommended for all public and academic libraries.-Jack W. Weigel, Ann Arbor, MI (c) Copyright 2010. Library Journals LLC, a wholly owned subsidiary of Media Source, Inc. No redistribution permitted.
(c) Copyright Library Journals LLC, a wholly owned subsidiary of Media Source, Inc. No redistribution permitted.
Review by School Library Journal Review
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.-Paul Brink, Fairfax County Public Library, VA (c) Copyright 2010. Library Journals LLC, a wholly owned subsidiary of Media Source, Inc. No redistribution permitted.
(c) Copyright Library Journals LLC, a wholly owned subsidiary of Media Source, Inc. No redistribution permitted.
