Review by Choice Review
Wallace treats the notion of infinity--a grand story beginning with Zeno's paradox and the Greeks and climaxing with Georg Cantor's work. The sea of details between these includes the development of mathematical analysis and the theory of the real numbers, deep and difficult notions for all students of mathematics. One wishes to like this book from an artful writer who knows the power of an abstract image. But it suffers from some unfortunate choices--(seemingly) endless abbreviations, wiseacre tone, and dependence on secondary sources replaced in recent years by better scholarship. Is it a caricature of mathematical writing that he tries by using abbreviations, or does he intend a technical voice, clanking along, to achieve a higher authority than smooth prose? Mathematical history is difficult to write; the intended audience is often hard to imagine before putting pen to paper. Although the thoroughness of his treatment is praiseworthy, the audience must be tough as nails to hear the long story to its end. For infinity, Eli Maor's To Infinity and Beyond (CH, Jul'87) is a better introduction. Ivor Grattan-Guinness's The Norton History of the Mathematical Sciences: The Rainbow of Mathematics (CH, May'99) is better for the growth of ideas in analysis. ^BSumming Up: Optional. General readers; lower-division undergraduates. J. McCleary Vassar College
Copyright American Library Association, used with permission.
Review by Booklist Review
\rtf1\ansi\deff0In his previous books\emdash Infinite Jest 0 (1996), A Supposedly Fun Thing I'll Never Do Again0 (1997)\emdash Wallace has displayed dazzling intellect, keen wit, and a fondness for footnotes. But not even his biggest fans could have suspected that Wallace could write a clever, extensively footnoted, and shockingly readable introduction to the philosophical, historical, and mathematical significance of the concept of infinity. He begins with ancient understandings of infinity, paying special attention to Xeno and Aristotle, the latter of whom he describes as being sort of grandly and breathtakingly wrong, always and everywhere, when it comes to infinity. As the story culminates in Georg Cantor's worldview-shattering breakthroughs, the math becomes devilishly abstract, but Wallace's colloquial style makes it a relatively easy transition from the simple abstraction of numbers (i.e., that five represents something more than five apples or five oranges) into the mind-bending abstractions of transfinite numbers. Though readers with some college math will certainly find this less intimidating, the prose is so engaging, and the underlying metaphysical arguments so fascinating, that even this reviewer (who gave up on math entirely after a C-minus in pre-calc) got lost only a few times. A brilliant antidote both to boring math textbooks and to pop-culture math books that emphasize the discoverer over the discovery. --John Green Copyright 2003 Booklist
From Booklist, Copyright (c) American Library Association. Used with permission.
Review by Publisher's Weekly Review
The subject of infinity would probably strike most readers familiar with Wallace as perfectly suited to his recursive style, and this book is as weird and wonderful as you'd expect. There are footnotes galore, frequently prefaced by the acronym IYI ("If You're Interested"), which can signal either pure digression or the first hint of an idea more fully developed in later chapters. Among other textual idiosyncrasies is the constant use of the lemniscate instead of the word "infinity," emphasizing that this is "not just an incredibly, unbelievably enormous number" but an abstraction beyond what we normally conceive of when we contemplate numbers. Abstraction is one of Wallace's main themes, particularly how the mathematics of infinity goes squarely against our instinct to avoid abstract thought. The ancient Greeks couldn't handle infinity, he points out, because they loathed abstraction. Later mathematicians fared better, and though the emphasis is on Georg Cantor, all the milestones are treated in turn. Wallace appreciates that infinity can be a "skullclutcher," and though the book isn't exactly easy going, he guides readers through the math gently, including emergency glossaries when necessary. He has an obvious enthusiasm for the subject, inspired by a high school teacher whose presence is felt at irregular intervals. Had he not pursued a career in literary fiction, it's not difficult to imagine Wallace as a historian of science, producing quirky and challenging volumes such as this every few years. (Oct.) FYI: This title, along with Sherwin Nuland's The Doctor's Plague, is launching James Atlas's Great Discoveries series for Norton. (c) Copyright PWxyz, LLC. All rights reserved
(c) Copyright PWxyz, LLC. All rights reserved
Review by Library Journal Review
No fiction here, either: the author of Infinite Jest tracks our efforts to understand infinity. (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.
