Rating: 
Summary: Good, but flawed
Review: Good subject, interesting (although sometimes tangled) presentation. But the mathematical mistakes just spoil everything. Like the proof of dichotomy convergence using Weierstrass delta-epsilon thing for continuity. What was that? Looked like the author himself didn't quite understand what he was trying to do, so he just crumpled the proof: "Hence... Hence...".
Rating: 
Summary: A Little Look at Infinity
Review: Have you thought about infinity recently? If so, it was possibly bound up in religious ideas, in some of which it is integral ("Where will YOU spend eternity?" says one local billboard). Religious infinities have lapped over into mathematical ideas in surprising ways, and if you hanker to do some serious reading about mathematical infinities and their history, you should consider _Everything and More: A Compact History of Infinity_ (Norton) by David Foster Wallace. Wallace is a novelist, author of the huge and well regarded _Infinite Jest_. He isn't a mathematician, except by avocation, but his enthusiasm for his subject is apparent on every page. It's a good thing that this is so; this is definitely not a superficial look at the subject, and Wallace calls upon some high-powered math that you may not even have done in college. The result is a penetrating book from a serious amateur on some of the most important ideas from nineteenth and twentieth century mathematics. Wallace starts his good-humored and sympathetic tone from the beginning: His "Small But Necessary Foreword" begins, "Unfortunately, this is a Foreword you have to read." There are plenty of footnotes, but half of them are marked "IYI": "If You're Interested," as are many of the paragraphs in the main text (along with "Semi-IYI"). In a history composed of increasing mathematical rigor, Wallace jokes and uses slang. Much of the history has to do with trying to solve the paradoxes of Zeno, like the one about how you can ever get to the other side of the street when you first have to go halfway, then half of the rest of the way, then half of that, and so on. The paradoxes were curious, but when supremely useful calculus came along, the infinitesimals used had never been rigorously defined. It was not until Georg Cantor showed how to deal with infinities as real mathematical entities that calculus had a mathematical foundation. He showed that infinities could be compared, and some infinities were larger than others. The proofs of these ideas (about one of which a mathematician said, "I see it, but I don't believe it!") gave calculus roots, but also gave rise to questions that eventually shook all of mathematics to its foundations. Wallace doesn't get much into Gödel and his eventual Incompleteness Theorem, and it is just as well. There is enough excitement here, at least exciting for anyone who finds paradoxes a charming way to make the neurons spin. Admittedly, he has included equations and propositions full of Greek letters and advanced functions that only math buffs will absorb. He says of Weierstrass's demonstration of continuity, for instance: "There's a reason this all looks so hideously abstract: it _is_ hideously abstract." The substance is tough going, but there is enough style here, in jokes, curious illustrations, and piquant asides, to make this a fascinating show of intellectual prowess.
Rating: 
Summary: A fellow of infinite jest?
Review: I found this a well-researched book by a knowledgeable author, marred only by his putting it into words. The presentation is perhaps that of an overdue term paper at three a.m., when the un-numbered pages have collapsed into a pile on the floor. The arrogant mannerisms, cliches and hackneyed phrases, ideosyncratic abbreviations, and lack of linear structure make it a book that, once you put it down, is hard to pick up again. I bought this book hoping to bring away from it some fresh perspectives on infinity, to benefit the calculus students I am teaching. I left it empty-handed.
Rating:
Summary: A fellow of infinite jest?
Review: I found this a well-researched book by a knowledgeable author, marred only by his putting it into words. The presentation is perhaps that of an overdue term paper at three a.m., when the un-numbered pages have collapsed into a pile on the floor. The arrogant mannerisms, cliches and hackneyed phrases, ideosyncratic abbreviations, and lack of linear structure make it a book that, once you put it down, is hard to pick up again. I bought this book hoping to bring away from it some fresh perspectives on infinity, to benefit the calculus students I am teaching. I left it empty-handed.
Rating:
Summary: The Truth Comes Out
Review: I have tried to read this book for three months now, but I am interrupted whenever I throw it across the room. It lacks the clarity and insight that grace your typical freshman calculus book, although it does have a lot more cutesy footnotes, and footnotes to the footnotes, all designed to cloak Wallace's resounding ineptitude. Having worn out his welcome in the literary world, Foster Wallace has turned to math and science for credibility. Unfortunately, even the mighty realm of mathematics is unable to suport his vast, bloated ego, as alluded to by the numerous Ph.D.'s, students, librarians, and lovers of wisdom who have seen this book for what it is--the once venerable WW Norton's attempt to print money. Unfortunately, the aging Wallace is no longer hip. Like the boy who cried "wolf" one too many times, Wallace and his group of insiders can no longer pull off literary Enrons.
Rating:
Summary: aleph alpha nought nought one
Review: i've been pretty excited to get my hands on this for some time now, so admittedly my expectations were pretty high. the book feels in many ways as if it were a patch-work job. excerpts of writing blaze (like screaming, but for the eyes) with wallace's style, yet other bits want for lucidity and are, rather surprisingly, not exactly enjoyable. for example, there are various non-independent-clause/sentances. this i expect (and find fitting) from delillo, but wallace doesn't seem to make very good use of such a construct (and generally it is cause for a rather harsh break in any fluidity built up to said clause-as-sentence). now it's probably of some import here that i'm a graduate mathematics student and was really just hoping to read one of my favourite writers thoughts on a subject that i enjoy, but mathematically this book is less-than-ideal. i don't know if someone without the "college math" he so often refers to will be able to get much from his explication of the various mathematical ideas he is presenting (even some of the very early examples meant to ellucidate the paradoxical situations that arise when dealing with infinity as a cardinal are (unnecessarily) confusing). so, basically, read the book. it's wallace at times, and those times make it worthwhile. if you want an introduction to set theory, look elsewhere (even to cantor himself), and then come back and read this because it really is a nice book at times (i mean (tautologically), when he's on, he's on). p.s. something i'd meant to mention the first time around: wallace discusses some (of the many) ways in which infinity gives us trouble, and he speaks (often at length) about various interesting aspects of these difficulties, but he fails entirely to mention a most important fact: we have no "direct" word for the infinite. our only means of describing these objects is to call them non-finite. this linguistic/conceptual failing occurs not once, but twice, in that we have various infinities of two basic types: countable (the "smaller" of the two) and (you guessed it) uncountable. that he failed to cover this is, i think, quite representative of the failings of this book. but again, i highly recommend the book, 100% (ummmm, you see, "100%" is one of the shining moments of this book, but until you've read it, you won't really get to enjoy that. a shame, no?)
Rating: 
Summary: Paradoxically flawed
Review: Inspired by praise for David Foster Wallace's "Everything and More" in publications including The Onion and Wired, I bought it hoping to revive in myself and instill in my kids an enduring excitement about mathematics. Wallace begins with a series of anecdotes that promised to fill the bill, leavened with plain talk and a bracing occasional bit of scatology. But the book's reliance on advanced notation -- much of it impenetrable even to this reader, despite four years of college math (up to differential equations!) -- soon kills the narrative flow. Wallace's parenthetical asides and copious footnotes sometimes provide illumination, but the book's scattershot structure belies the dust jacket's promise of "a literary masterpiece." Even Wallace himself acknowledges the book's shortcomings, apologizing at several points for convoluted sentences, bewildering explanations and jumbled storytelling. A good editor could have helped him cut those knots, isolating the advanced math or otherwise rendering it intelligible, allowing him to deliver what author James Gleick hails in his promotional blurb as "exquisitely (and hilariously) original science writing." (Did Gleick and the other reviewers survive the entire book? Or did they just get the funny parts?) Reading "Everything and More" was like being trapped in a literary version of Zeno's Paradox: Finishing half the book, then struggling to complete half of what remained, then half of that ... I finally just gave up, disillusioned.
Rating:
Summary: Paradoxically flawed
Review: Inspired by praise for David Foster Wallace's "Everything and More" in publications including The Onion and Wired, I bought it hoping to revive in myself and instill in my kids an enduring excitement about mathematics. Wallace begins with a series of anecdotes that promised to fill the bill, leavened with plain talk and a bracing occasional bit of scatology. But the book's reliance on advanced notation -- much of it impenetrable even to this reader, despite four years of college math (up to differential equations!) -- soon kills the narrative flow. Wallace's parenthetical asides and copious footnotes sometimes provide illumination, but the book's scattershot structure belies the dust jacket's promise of "a literary masterpiece." Even Wallace himself acknowledges the book's shortcomings, apologizing at several points for convoluted sentences, bewildering explanations and jumbled storytelling. A good editor could have helped him cut those knots, isolating the advanced math or otherwise rendering it intelligible, allowing him to deliver what author James Gleick hails in his promotional blurb as "exquisitely (and hilariously) original science writing." (Did Gleick and the other reviewers survive the entire book? Or did they just get the funny parts?) Reading "Everything and More" was like being trapped in a literary version of Zeno's Paradox: Finishing half the book, then struggling to complete half of what remained, then half of that ... I finally just gave up, disillusioned.
Rating:
Summary: I'm loving It
Review: So the purpose of the Great Discoveries series is to "[bring] together renowned writers from diverse backgrounds to tell the stories of crucial scientific breakthroughs."* Am I wrong in assuming that a "renowned writer" from a "diverse background" probably isn't going to apply an analytical full Nelson on the subject at hand? I would be more disappointed if the "telling a story" bit failed (which it doesn't in this instance). DFW writes prose that is a pleasure to read (especialy in conjunction with the ultimately interesting, yet more often than not, grossly tedious, subject matter (and I'm a Math Major**)). I haven't finished the book yet, but unless DFW punks out and pins it on the butler in the final section, this book will go down as one of the more entertaining pieces of literature*** I've read in a while. * - see "About the series" in E.R. supra
** - as if that title and other similar ones (Ph.D., Prof., etc.) endows one with a "cloak of inscrutability"
*** - the number of which per individual while is monotonically increasing
Rating:
Summary: awful, awful, awful
Review: The author's worst tendencies are on display here. He takes a simple, elegant subject and reduces it to a disorganized mess. Practically unreadable, for both the layperson and mathematician alike. I could carve a better book out of a banana.
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