The Art of the Infinite

PUBLISHERS WEEKLY 1 MAY 2003

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.