Before discussing the merits of David Foster Wallace's Everything and More: A Compact History of Infinity, it is essential to define what the book is not. This volume in the "Great Discoveries" series is not a history of the personalities and social conditions that led to the "discovery" of infinity. Nor is it a narrative fixated on the cultish fear of--and obsession with--the infinite that has seemingly driven mathematicians insane over the centuries. Rather, Everything and More is a surprisingly rigorous march through the 2000 plus years of mathematical research that began with Aristotle; continued through Galileo, Isaac Newton, G.W. Leibniz, Karl Weierstrass, and J.W.R. Dedekind; and culminated in Georg Cantor and his Set Theory. The task Wallace (author of the bestseller Infinite Jest and other fiction) has set himself is enormously challenging: without radically compromising the complexity of the philosophy, metaphysics, or mathematics that underlies the evolving concept of infinity, present the material to a lay audience in a manner that is entertaining. To propel his narrative, Wallace even develops a style that mirrors the mathematical language he probes. One difficulty in his focus on concepts and not a strict human chronology, though, is that his structure is dependent on frequent digressions (especially early on). Patience is required. Wallace demands that his reader walk through the equations, study the graphs and charts, and relearn college-level concepts to follow along on the exploration. Indeed, after one wrenching dip into Zeno’s paradoxes, Wallace spouts at his imagined complaining audience: "Deal." But the book should be deemed a success. If one grants him the attention he requires, Wallace has made the trip richly rewarding. --Patrick O’Kelley


From Publishers Weekly
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.Copyright 2003 Reed Business Information, Inc.


From Booklist
*Starred Review* In his previous books--Infinite Jest (1996), A Supposedly Fun Thing I'll Never Do Again (1997)--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 © American Library Association. All rights reserved


From Book News, Inc.
California novelist and essayist Wallace contributes to the series of popular technical writing by examining a set of mathematical achievements that he finds to be extremely abstract and technical but also extremely profound, interesting, and beautiful. He writes for readers who have no technical background, and includes sections--clearly marked--for those who do. He has not indexed his work.Copyright © 2004 Book News, Inc., Portland, OR


New York Times Book Review
A gripping guide to the modern taming of the infinite.


Anthony Doerr, Boston Globe
It's a thoughtful and witty 300-page testimonial to the qualities I never fully understood that mathematics possessed.


John Allen Paulos, The American Scholar
[Wallace] brings to his task a refreshingly conversational style as well as a surprisingly authoritative command of mathematics....A success.


Booklist
Shockingly readable....A brilliant antidote both to boring math textbooks and to pop-culture-math books that emphasize the discoverer over the discovery.


Book Description
The best-selling author of Infinite Jest on the two-thousand-year-old quest to understand infinity. One of the outstanding voices of his generation, David Foster Wallace has won a large and devoted following for the intellectual ambition and bravura style of his fiction and essays. Now he brings his considerable talents to the history of one of math's most enduring puzzles: the seemingly paradoxical nature of infinity. Is infinity a valid mathematical property or a meaningless abstraction? The nineteenth-century mathematical genius Georg Cantor's answer to this question not only surprised him but also shook the very foundations upon which math had been built. Cantor's counterintuitive discovery of a progression of larger and larger infinities created controversy in his time and may have hastened his mental breakdown, but it also helped lead to the development of set theory, analytic philosophy, and even computer technology. Smart, challenging, and thoroughly rewarding, Wallace's tour de force brings immediate and high-profile recognition to the bizarre and fascinating world of higher mathematics. About the series:Great Discoveries brings together renowned writers from diverse backgrounds to tell the stories of crucial scientific breakthroughs—the great discoveries that have gone on to transform our view of the world.


About the Author
David Foster Wallace is the award-winning author of Infinite Jest and other books. He lives in Southern California.