Since DFW has committed suicide, we will not see an edition revised by him. In re-reading the reviews, it appears that style means a lot. I personally found the book witty. It was a little slow sometimes because of the convolutions he introduced in style, but mostly I kept plowing (and chuckling) through. The librarian who sent back the book did a disservice to some readers. Not everyone likes to learn in the same way. With that kind of attitude, many years ago I would have had Rudin's books removed as too concise to be useful. Of course, there are many mathematicians who love those books for just that reason, and I would have done them a disservice.

I am a physicist with a math minor. To me, the best part of this book was his explanation of why mathematicians insist on the epsilon-deltas of mathematical rigor. No one ever did that before. If I could have read this in high school, I probably would have finished my math major as well as my physics major. Instead, the whole epsilon-delta thing seemed ad-hoc and inexplicable in purpose. I could never accept the need for rigor demanded in advanced analysis.(a drunken prof and Rudin's book didn't help either) DFW showed how a crisis in dealing with the infinite and with infinitesmals led to the development of the what we call the foundations of analysis. Just excellent.

I envied him his high school math teacher, who seems responsible for much of the really good parts of this book. No, DFW wasn't a mathematician and he (in spite of what some reviewers seem to think) knew it. He made clear that he wouldn't be able to do justice to Godel. But incompleteness is moderate difficult. DFW didn't know much about Fourier series, but did know they were important enough to mention.
For some students, that's the way to get them interested, just mention something and let them go dig (so much easier now with the internet).

Remember the subtitle -- a compact history of infinity. So it is more history oriented than a mathematical tome. I had recently read Lillian R. Lieber's Infinity (which I see has been reprinted) and it has her sparse, but excellent development of the concepts. It doesn't have much historical detail though. So everything and more was a pleasure.

Mostly, this book is a "Story"(to use the author's occasionally occurring term) of some fascinating individuals in the history of math, culminating in G. F. L. P. Cantor. The Story's told, in large part, through those individuals' complicated (at least, for this reader) mathematical concepts, worked out in intricate, intriguing movements of the mind.

If you are a math novice and you allow it, the book can introduce you to that whole other way of expressing and exploring a reality outside your immediate perception. Sometimes the effect on me was like Bach played by a master pianist--beautiful without knowing what's going on musically in the progression of notes, chord structures, etc.

I suppose understanding the still not comprehended math of infinity was supposed to be the point, but it need not be. Just as I don't need to be able to read music, much less a musical score, to enjoy listening to Bach, I had a peculiar, quasi-aesthetic experience reading this Story. I didn't need to understand it all. It's even okay with me if he was elaborately putting me on.

I thoroughly enjoyed this text. It was used in a seminar class at the college I attend, and I found it both accessible and exact. Wallace dives into some deep philosophical and metaphysical aspects of math, yet his focus is primarily on the mathematical aspects of infinity. This was also one of the funniest math texts I've ever read - who knew math was "sexy"?

I greatly enjoyed this book, but it's not for everyone. To appreciate it, there are two requirements: (1) You must enjoy, or at least tolerate, Wallace's quirky writing style, with its mixture of the conversationsal and the erudite, its frequent footnotes, abbreviations, and discursions. (2) You must have a certain level of mathematical sophistication. This is not one of those popularizations of math for those who never got past high school algebra. It could perhaps be described as a history of calculus, analysis, and set theory, and specifically of their attempts to come to grips with the infinite and the infinitessimal and make them mathematically valid. The focus is on theory and rigor--which maybe makes it sound dry, but it's not, if you like that sort of thing. It's not that Wallace himself gives lots of rigorous arguments, but that he talks a lot ABOUT the search for mathematical rigor.

Reading this book is a little like sitting in on a class taught by an inspiring yet quirky professor (and, indeed, Wallace makes frequent reference to an inspiring, quirky teacher of his own). Such a class would have a prerequisite--I'm not quite sure what, maybe at least a semester or two of calculus. Probably, the more you know about calculus and related subjects, the more you'll get out of this book.

I was certainly looking forward to reading this book. While I haven't read any of the other books written by this author; his reputation preceeds him. Unfortunately, I was wholly unimpressed by his approach.

I find the writing style very unnatural for mathematics. It can be difficult to follow the long, rambling sentences with his strange turns of phrase. While I can appreciate that this is modern writing, the style is inappropriate for the subject. Mathematics must be presented clearly and accurately. I left the book thinking that the author didn't understand the subject very well himself.

It's an interesting topic and therefore there is something to be gained here. Sadly, there are much better alternatives to this one. If you have a mathematical background the book may irritate you with it's style. A pity though, it is a wonderfully rich and interesting subject.

David Foster Wallace could easily have come as close as anyone could to achieving the aim of this book - to give an understanding of the mathematical concept of infinity to the educated layman. He clearly understands the material, and has a clear way of presenting the material.

However, his stylistic excesses are so annoying and distracting that they detracted from my ability to understand what he was trying to say. In his fiction efforts, these idiosyncracies can increase reading pleasuer and serve a purpose. Here, they do not.

Love him or hate him, DFW is a prodigious talent. Except for the disturbing "Conversations with Hideous Men" I have found his previous material to be so hilariously, intelligently, on-target that I was willing to overlook a multitude of stylistic transgressions (chiefly, the overly cutesy tone, gratuitous flaunting of the author's erudition, the footnote fetish).

So I was reasonably disposed to like this book and was looking forward to reading it. Sadly, it turns out that this was a case where DFW's various idiosyncrasies combine to produce a book which is fundamentally unreadable. Normally, once I start a book, I feel enormous guilt if I don't finish. No guilt here - just exasperation. One can reasonably argue that DFW's enormous talent might justify certain peculiarities of style, but every author needs the discipline of a good editor. W.W. Norton seems to have dispensed with editors altogether, certainly with the sentient kind. A pity, because somebody should have explained to DFW that prefacing any section of text with the title

"Soft-news interpolation, placed here ante rem because this is the last place to do it without disrupting the juggernaut-like momentum of the pre-Cantor mathematical context"

is not just completely unhelpful. It is an irritating distraction, the sorry result of the inability of this talented writer to vanquish the demons which continue to plague his undisciplined style. Unfortunately, this kind of self-indulgent stylistic mannerism recurs with infuriating frequncy.

As a result, this book is a complete train wreck.

When DFW isn't using undefined acronyms, or rubbing his absurdly large vocabulary in your face, the book achieves what I believe to be its goal, that is, to explain the origins and problems associated with infinity. The puzzles he uses are very interesting and provide a good look into the problems the notion of infinite can put forth.

However, the book is unneccesarily complicated and the meaning of many words/phrases/ideas continue to be used throughout the book without explaination. The book attemps to be accessable to "readers who do not have pro-grade technical backgrounds" but fails (at least for me) considering I was often confused although I had taken calc 1 in high school a year before reading it.

There are two books here, that should complement each other, but, in reality, turn out to be mutually exclusive. Which is unfortunate, since they're both pretty good books in their own right.

The first book is your standard David Foster Wallace long essay/argument/explication. If you've read and enjoyed 'A Supposedly Fun A Thing . . .etc., etc. etc.' you'll recognize this easily. It's in DFW's distinctive voice, awash in digressions and asides and continually undercutting itself. And using little tricks like breaking up sentences into fragments which you'd think is just a clever trick but, to me, is just really enjoyable. (And, if you haven't noticed already, DFW's style is, to me, kind of infectious ' a lot of my writing is kind of influenced by it.) Anyway, this first book is a long chatty essay about infinity in general and Cantor's struggles with it in particular.

This is where the second book pops up. It's basically a math textbook. A focused one, yes, but a textbook nonetheless. Meaning that there are a lot of equations and Greek letters and the like. DFW continually claims that most of this math should be accessible to anyone with some high-school math and maybe a semester or two of college calculus. I fit that description to a T, and I should admit that I struggled at times.

But I think the reason I struggled was that the two books ' chatty essay and dry textbook ' undermine each other. The equations are stumbling blocks in the flow of DFW's prose. And the second guessing and asides in DFW's prose (which work just fine in an essay about pomo lit and television or state fairs or such) really get on your nerves. Because when you hit the hundredth iteration of DFW saying, 'well, what I'm about to explain isn't entirely accurate but . . .' you just want to scream 'where in hell can I find a book that explains this all accurately'' (Which, given the complexity of all this, might be a tall order.)

Frankly, I think this could have been a hell of a book if DFW's editors had let him blow it up to Infinite Jest size. Then he could have had room for more historical context, actual biographical details. As well as the space to go through the assorted proofs and equations in a more complete way. As well as the space for an index, table of contents and glossary (because the emergency glossaries, while well intentioned, don't quite cut it.)

But as it is, you basically have to read this thing twice. Once for pleasure and once for the math. If that sounds like your cup of tea (and you're a DFW fan), give this a read.

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...".

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.

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.

The topic matter at hand here -- infinity -- is very subtle. The book is appropriately detailed, at times hilarious, and very colorful. Occasionally requires re-reading of certain parts (at least for me!), but the overall experience is most enjoyable.

Mr. David Foster Wallace's writing style -- sometimes hard to decipher, sometimes too detailed, sometimes not detailed enough -- required a little bit of adjustment from me, as a reader. I'm certain, however, that the style is appropriate to the subject, if not a byproduct of infinity's complexity as a concept and as a historical development. Some of these copmlexities -- such as the wonderful footnotes and quasi-sidebar discussions -- add even more color and detail to the story.

This book is very approachable, even though it requires a little patience at times. It's accessible for even those who (like me) don't have a very strong mathematical background. This is a fascinating topic, and a very well written book. Buy it and enjoy it.

I was always perplexed by the rave reviews for mediocre books, but I recently read in THE NEW YORK TIMES that the author's friends have been writing them in order to help sell the lackluster tomes.

This book is awful. It makes no sense. It rambles. Wallace is no mathematician, but rather than admitting his resounding ignorance, he hides it behind footnotes and cutesy gimmickery. There are hundreds, if not thousands of better math books such as Prime Obession and A New Kind of Science.

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.

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.

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

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 G�del 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.

Hi, I'm a set theorist. This book is ambitious. For many pages and sections, I really wanted to give it a lot of stars just for effort. There are some good approaches to some hard material. But the errors got to be just too heinous (I'm not at all referring to oversimplifying for the sake of exposition; of course that's necessary. In fact, I reckon the *level* of rigor in this book is just about ideal). If you want to skip right to a cringe-and-sputter bad part, check out his interpretations of the axioms of set theory starting p. 286. Trust me: Bad. And unlike DFW, I'm not gonna tell you to "trust me" unless I know I know what I'm talking about.

He knows a lot of math for a creative writing prof, but he often doesn't know what he does and doesn't know. There was a lot of history and philosophy in the book that I didn't know about, and so I didn't find many errors in those kinds of sections. I probably learned something about that stuff, but unfortunately having seen so much mathematical incompetence I have to distrust DFW as a non-fiction writer.

DFW writes with a dangerous tone. Not a compliment in this case. The tone is: "This is a lot of difficult (but gorgeous) material, but *I've* got it all figured out. So you just trust me to guide you through it (and even when I'm telling you stuff that appears unjustified and kooky, you know it is correct and worth reading because I'm so well-educated and clever)." It's pompous and it's fun and it's fine if you're right. If you take that tone and you're wrong, you suck. Sorry, DFW.

Other reviewers hate the footnotes and other style/organizational whatnot. I agree with a *little* of that. Mostly I thought his willingness to entertain tangents and interpolations and sidebars an appropriate way of handling the material.

DFW refers a lot to items he learned in "college math" and "sophomore math" and so on. The book acknowledges that these math-items may not be familiar to you, but implies they would be if you took math in college and remembered it. That's often probably not quite true; DFW went to Harvard and appears to have had a college math experience atypical even amongst the rather well educated in America. Does he not know this, or did he make a Command Decision that this book is only for people for whom college = Ivy League?

Can you do a 2nd ed. sometime, DFW? It is story that ought to be told well, and I think you have a great draft here.

David Wallace's style evidently had a large effect on the reviews here. To get some feel for the style, you might imagine that you're in a Boston bar where Matt Damon's character in 1997's "Good Will Hunting" is expounding on the subject of infinity. I give a few examples of the style below.
As for subject matter, the book works through over 2000 years of infinity-related math. It digs into much of the math that isn't "too hairy", or too long to "unwrap". It contrasts important breakthroughs with then-current conventional mathematical thinking. It gives brief bios of the key players. Bits of this include: "Gallileo's 'Two New Sciences' was in certain respects one long raspberry at the inquisition". Also: "All sources agree that Georg W [G. Cantor's father] personnally supervised his children's religious development in a hardass way".
While not staid, the book is serious in its offbeat (for the subject) way. It never stoops to gratuitous humor. If you have a BS in some technical subject then you probably were exposed in school to most of the mathematics, but not all unless you majored in math. If you just want an overview, expect to be skimming past much of the material.
The book is not broken into chapters (so has no table of contents); there is instead a continuous flow of sections. There is a bibliography and a concise section of "Citations for Quoted and/or Cribbed Material". There is no index. The book is crammed full of footnotes that expand the main text.
As best I can tell from my perspective (enginering BS), the author did a good job of "unwrapping" 2000 plus years of infinity-related mathematics. I was kind of amused by his style -- except where he kept writting "factoid" (ugh) instead of "fact".

This books seems at the same time too difficult and too simple. Speaking as someone with a graduate degree in Chemistry who took more than my share of Math(3 semester Calc, Diff Eq, Matrix Algebra, Group Theory) and Physics(the usual 1st & second year stuff along with a senior level class or two) because I kinda LIKED them, I threw my hands up around page 200 because I just couldn't follow it any more(I'm listing my credits to show I should in fact be able to wade through "college level math" about as well as anyone who isn't actually a math major). Not that I am not CAPABLE, but with all the tangents, unclear clarifications and jumping around going on it just wasn't engaging enough to make it worth my effort. I got the feeling that there was a lot of explanation going on that wasn't necessary(& was just sort of showing off) and a lot of things that demanded more time that were skipped. My guess is that you probably already have to understand the theory & know the story to get much from this one.

If Wallace were only as smart as he thinks he is . . . I fear this attempt by "D.F.W." at mathematics only highlights his ability to fog some of the readers with cute wordsmithing; to give still others the notion that "gee, aren't we smart - just look at the "math" we're doing here"; he doesn't shed much light on Cantor, or infinity. This is a topic that cannot be given a glossed-over treatment - I'm surprised Norton went ahead with it. So what's next from Wallace - a "puff - piece" on string theory?

As a librarian working in a univeristy science library, I had to return this book. I cannot let tax and tuition dollars support this dumbed-down farce propagated by greedy pomo publishers. I can remember the day when such books would never have made it past WW Norton's editors, but alas, the new breed was raised on MTV.

Infinity is infinity is infinity, and its glory remains untouched by this trifling, ludicrous, incompitent, meandering, and fundamentally dishonest effort. Visit your library, or my library, and read the books on mathematics penned by articulate mathematicians--there are plenty of them. Don't believe the pomo hype.

Several previous reviewers have touched on the technical weaknesses of this book and those weaknesses can be quite frustrating. However, this is a book intended for broad, public consumption and hence has to take a few liberties. If you ignore the actual math bits and focus on the history bits you will probably find quite a bit to like. That being said, I was still left unsatisfied.

The "Wallacisms" are distracting and wearying in this context (as opposed to his fiction). The swarming acronyms, the inside jokes, the IYI sections that should either have been stuck in an appendix or better integrated into the main text (or eliminated entirely). After a couple hundred pages it just feels as if Wallace is using his talents as a wordsmith to distract the reader from his treatment of the material.

If you're interested in the math here, rather than the history, then reading actual math books (and the original papers and books) would be a better choice. Dover publishes Contributions to the Founding of the Theory of Transfinite Numbers by Cantor and Essays on the Theory of Numbers by Dedekind. Also try From Frege to Godel by Jean Van Heijenoort and The Joy of Sets by Keith Devlin.

This book is incomprehnesible, incomplete, and incoherent. I bought it, then returned it the next day. Never mind your pedigree; you will find that what this book lacks in substance it does not make up for with structure. It's as if David Foster Wallace went on a few hundred page journey regarding his misconceptions of infinity, and somebody decided to publish and promote it under the guise of a "pop-sci" book. This book does nothing to popularize science and math, and everything to desecrate the exalted fields. Truly, David Foster Wallace should stick to what he knows best; pomo ponzi schemes.

Perhaps the most important effort a reader should make while beginning to read this book is to try to feel what it is about while resisting the urge to pigeon-hole it by categorizing; try not to view it as a Sci-Pop, literary, academic or whatever bin it is supposed to fit in, but an amalgamate of facts, thoughts and prose that is fun and flexible as in a long and enjoyable conversation, which is bi-directional by nature being your own enlightening, wonder, doubt and criticism completing the full-duplex of the communication.
The book takes you on a ride of ideas about ideas, their meaning, consequences but also the ways we should or shouldn't perceive them; like in a friendly (and intelligent) chat, you should enjoy the input but also delight in producing your own extension, doubt, even disagreement, to what is being said and/or how it is being put to you.
To fully achieve this interchange, the reader should not only feel comfortable in early college level Math but also be interested in the history of Philosophy (including both physical and metaphysical) to an extent.
The author takes some poetic licenses here and there (not only with words but also conceptual) that some may not like but, while blunders in a couple cases, sometimes saves us from convoluted boredom. The author's prose is not bland or patronizing as in most Sci-Pop books, but demanding and fulfilling in most of the philosophical passages. The abuse of the footnotes, as some have already mentioned, is a bit distracting indeed when used inside a conceptual unit, but one does get used to it. It also gets a bit unfocused here and there due to its intentional flexibility but quickly recovers.
In all, it is a book that, when read with proper unprejudiced frame of mind, brings satisfaction and contribution. It will find a place in your thoughts even after you have finished reading it.

As a logic graduate student who really loved Infinite Jest, once I heard this book existed, I had to read it. In particular, I wanted to see if DFW had gotten anything out of his one year of philosophy study at Harvard. It seems like he got something out of that year certainly, but not real philosophical/mathematical rigor. I definitely recommend reading this book if you're a fan of his fiction and haven't done any math beyond calculus, but the more math you've done and the less you like his fiction, the less you'll enjoy this book.

He's done an excellent job of "popularizing" the philosophy and mathematics of the infinite (if his readership can really be considered popular), but with the emphasis much more on the history than the philosophy or mathematics. Even with all the background I have, I learned a lot about the history, particularly with the early analysts, and what prompted Cantor to do his stuff. But this book could have used an editor with a mathematical background. While he states the Extreme Value Theorem pretty much correctly, every time he uses it, it is applied both unnecessarily and completely incorrectly. Slightly more egregious is his misstatement of the Continuum Hypothesis and confusion between cardinal exponentiation and successorship. (This is perfectly understandable in someone just learning the subject, as DFW obviously was, but in writing a book on it, he should at least state this central problem clearly.) Also, where his idiosyncratic footnotes and acronyms were great in his fiction, they seem a bit tacky in a more mathematical work - especially where they clash with perfectly standard notation that is at least as clear and just as concise. I often got the feeling that I was reading a draft, rather than a finished book.

But whenever he switched back to a more philosophical stance from a mathematical one, he was much more on top of things. And if you like his style, then this book's for you. But after you've read it, I'd also recommend reading a reputable book on the subject to get some of the mathematical facts straight. If you understood them that is, rather than just reading it as a work of art, which seems fairly appropriate.

I love David Foster Wallace. His writing sparks interest and creates understanding on topics ranging from 5-Star Cruises to Tennis, to drug abuse and AA.

I agree with J.C. below that DFW's expositiion on math leaves "a lot" of holes. But I challenge that, like the RNL (real number line), there are an infinite number of holes to fill. I agree that there is a dearth of discourse on "modern mathematics" (math in the last 40 years), but I counter that this is not what the book is about. And it is exactly what the author stated in his lengthy and helpful forward.

DFW is all about style: Cantor is the protagonist here and infinity is the subject. It's a fascinating read for the liquidity of the predicate-nominative form by itself.

If you are anticipating an authoritative review of the infinity, you will probably have to write your own book.

OK, so I figured I'd give this book a chance.

First of all, it doesn't have an index. This is a major omission, but not as glaring as the omission of the contemporry debate regarding whether spacetime is continuous. Nor does David Foster Wallace so much as mention the most pertinent realm where inifinity is being contemplated these days--quantum gravity. To write a book on infinity without mentioning black holes, singularities, and the nature of quantum space-time is akin to writing a book on the history of rock'n'roll without mentioning the Rolling Stones.

Perhaps the editors left out an index so as to conceal David Foster Wallace's major omissions, but then again, it is hard to tell what the editors were thinkling in publishing a book like this in the first place.

The only defenses of David Foster Wallace I can glean from the reviews are, "hey--he never said he was an expert in mathematics," and also, "mathematicians with Ph.D.'s are uptight because they strive for clarity, brevity, and meaning." Neither of these are reason to buy the book.

I liked the content of this book, but the authors style is pretty hard to come to terms with! My problem with it is the number of footnotes and parenthetical comments. It disrupts the flow of what is often an interesting discussion. It's a bit like having a very irritating companion constantly tapping you on the shoulder to interrupt you with his/her comments while you are trying to read. In the end I found the footnotes etc. so distracting that I simply ignored them - and I enjoyed the book a whole lot more. Some sensitive editing would make this book a much better read!

After seeing the rave reviews, I was planning on using this book in one of my courses. So I went out and bought a copy.

The book performs a disservice to the field of mathematics, and it should be removed from the shelves. It takes beautiful concepts, layers them under long, convoluted sentences which obscure the majesty of the subject, and then poses as a scholarly work via the use of ludicrous, insincere footnotes. As I waded through the muck, I kept asking myself, "has culture really declined this far that people have no conscience?" I'm trying to teach my students the beauty of truth, and here an author, his editors, and the publisher are working against me. I might be outnumbered, but this book will not be used in my classroom.

Who are the people writing the rave reviews? Do they have a financial stake in how well this book does? They must, as the only reason to try and sell this book would be money.

Clearly, Wallace has to be to your taste if you're going to enjoy this book, but let's not put words in his mouth. Marketing genius? Please. The only people who have even heard of this thing are geeks like us who've read the book. I had to order it from a large book store - it was never stocked in the first place.

Wallace is having fun, with his syntax, his grammar, his explanations, his idea of his audience. He assumes you aren't some mathematics scholar either, rather someone interested in picking up a few facts and understandings here and there so the old brain doesn't go numb with one's field.

As a writer, and someone who proudly declares that he never took a single math or science class in college, I found this book fascinating. No, I didn't necessarily take the time to reason out all the integrals and functions and limits (it's been 10 years since high-school calc), and there's a good chance Wallace could have been clearer and more to the point, but where's the fun in that? I certainly didn't enjoy math class as much as I enjoyed this book. And those footnotes aren't a claim to academia. It's just a good way to present information. Why should academic papers be the only forums for using it?

And why is everyone so deathly afraid/disdainful of "pomo"? It's fun philosophy to play around with - just like formalism and its predecessors. Thinking in different ways helps sharpen you brain for whatever endeavors you might be passionate about.

It's a great piece of literary candy. Nothing more.

Sorry if this book is an affront to some "Harvard" scholars and "PhD physicists" (or those that pretend to be the above) but for people in the real word, alas I am a lowly engineer, this book is a lot of FUN TO READ. It could even encourage some readers to want to learn more about the topic. I don't understand why some math and science professionals are always insulted when non-science writers, especially one as talented as David Foster Wallace, try their hand at writing on math and science. Wallace doesn't pretend to be an "expert" but he knows how to keep us interested and, yes, sometimes inspire us. He provides a detailed bibiliography for those who want to learn more. Best popular math book I've read since Paul Hoffman's, The Man Who Loved Only Numbers and David Ruelle's, Chance and Chaos.

Wallace should enroll in a writing class, or read other works of science writing, such as Charles Siefe's "Zero: the biography of a dangerous idea," which covers much of the same ground. This book does contain a lot of information, but you need a clothespin on your nose to wade through page after page of bad (insecure, tendentious, immature) writing. Why did the publisher even print this pathetic work of supposed "pop" science? I plan to ask Amazon to let me return it.

I think the first thing to be said of this book (or booklet, as Wallace recurrently refers to it) is that it's rather a lark to read. This will surprise no reader familiar with Wallace's literary and critical works. But, unlike his previous works, this one deals with extremely (towards the end) technical mathematics which the author is obliged to gloss over.-Quite a contrast to, say, Infinite Jest.

I was, by turns, frustrated with this lack of rigour, and appreciative of it. I can't put it better than Wallace does in a footnote on pp.220-221, "Rhetoricwise, let's concede one more time that if we were after technical rigor rather than general appreciation, all these sort of connections would be fully traced out/discussed, though of course then this whole booklet would be much longer and harder and the readerly-background-and-patience bar set a great deal higher. So, it's all a continuous series of tradeoffs." - Informed readers take note of his use of the term "continuous series" here!

Thus, Wallace does the best that I think any writer could in walking the tightrope between over-the-top technical mare's nests which only a few members of the faculty at Mathematics departments (and a few autodidacts) could grasp, and what he derides as the "Pop" accounts of such things as the development of Set Theory.-So, nobody, including Wallace, and myself, is going to be completely satisfied. While not a complete technical purist, I do wish he'd chosen to be more technical in some parts and less so in others. As a former student who has always wished his "formal" training in Mathematics went further that first year college Calculus (though I later worked my way through more advanced textbooks on my own), I was genuinely interested in the technical illuminations this book might provide. On the other hand, as an appreciator of fine writing, I know the two do not go hand in glove.

So, in the end, I should say that this book is as good a "tradeoff" as you're going to find. I was pleased to see that Wallace's wit and style haven't suffered from the subject matter. He rather resembles, in this respect, another writer who is more often quoted herein than any other for, as Wallace terms it alliteratively, his "pellucid prose": to wit, Bertrand Russell, a mathematician of first order, whose renegade life and pixie wit served him well throughout his (as Wallace puts it, wryly, in the penultimate footnote of the "booklet") long, distinguished life. Let's hope Wallace's life and output are equally as long and energetic.

A fascinating, irreverently funny, and accurate (as far as I can tell) tour of humankind's dealings with infinity, with more (and welcome) attention to the history of analysis and its transfinite travails than most other books nominally aimed at the general reader. Tough chewing as a first course (see below for more digestible introductions), but a wonderful second course for the whetted appetite. I'd give it 5.29 stars if an editor had made it read less like a (very good) third draft of an exuberant series of lectures, full of self-directed notes on how to better arrange the material, clunky phrases (e.g., "a nice opening-type quotation"), and idiosyncratic abbreviations. Keep a dictionary handy, unless gems like "apodictic," "horripilatively," and "deracinate" are already part of your word hoard.

Okay, 4.84 stars if you have something beyond basic calculus under your belt (foundations, point-set topology, functional analysis, etc.), 4.41 stars if you can think back (not necessarily remembering much) on introductory calculus without discomfort, 4 stars if you're not undebauched by basic function and set-theoretic notation at the level of a serious high school algebra course, and 3.61 stars otherwise if you're interested in the topic and are willing to skip the gnarly parts.

My candidate for the best general-audience introduction to the mathematics of infinity (both content and style) is Robert and Ellen Kaplan's marvelous "The Art of the Infinite: The Pleasures of Mathematics." See also Leo Zippin's "Uses of Infinity," Rudy Rucker's "Infinity and the Mind," and Eli Maor's "To Infinity and Beyond" for other excellent introductions. Shaughan Lavine's "Understanding the Infinite" and Joseph Dauben's "Georg Cantor: His Mathematics and Philosophy of the Infinite" are, like Wallace's book, more suited to professionals and experienced amateurs (as is, I believe, Edward Huntington's "The Continuum and Other Types of Serial Order," which I'm still waiting for).

Once I believed that the possibilities life offered were, indeed, infinite. I was rushing from jobsite to jobsite, bearing a large zippered portfolio under one bespoke elbow, puffing away on a well-seasoned briar, hollering authoritative instructions into a cell phone. One terrible day, all of that disappeared, and I plunged into a hellish world, utterly circumscribed by pain and senseless violence. I won't go into details, but I was blinded--a blind architect! My soul howled to the heavens, but the cold heavens were deaf to my howling soul. It was then that I framed the following simple-minded question: what, exactly, is infinity? Does it have a smell, or a characteristic taste? Can you get change for a infinity at the laundromat? How long mankind has placed that little squiggly-looking symbol under his thinking cap and sloshed it around in search of an answer! I sit at my lonely drafting table, groping for clues and for the sour lemon drops that I keep in a metal tin. Outside, I hear the hollers of the nuns at the local novitiate, St. Isidore's (patron of the Long Division Workbook). How long have I, personally, been in search of infinity? Ever since I went to hear "Einstein On The Beach" with my wife. She let out with one of her customary shrieks, and then plopped over, insensate. Well, her problems were over--but I had another five or six hours to go. My fingers flitted hopelessly over the braille score the men at Avery Fisher had provided me, and soon trembled with despair: had Glass no mercy? I staggered out of the theater past row after row of snoozing Philip Glass enthusiasts. Well, this is sort of how I felt after an actor friend of mine came over to read aloud to me from EVERYTHING AND MORE, David Foster Wallace's new book, which, as the title seems to promise, is about infinity and some other stuff. The actor spoke in what he described as a "Lincolnesque Baritone" (never mind that Lincoln was a tenor) and recited the opening sentence, but long before he was done I'd "slipped away," in the manner of a southern gentleman, into peaceful unconsciousness. I don't know if Wallace has moved on to the next literary level or whatnot but it seems as if after writing one book about a hyperaddictive kind of infinity he certainly seems to have found an ingenious way of simulating infinity itself in this book. Though this could be a nomenclatural problem and what we're really talking about is interminability. Anyway, now all he needs is to get the addictive part down. My actor friend, incidentally, had to be carried out of our apartment after his recital, though I think this might have had something to do with his need to "slake his thirst," as he put it, after having "performed," as he put it. Let me repeat myself: as much as it might seem otherwise, there is nothing debilitating about this small, lethal book!

A Review of David Foster Wallace's "Everything and More: A Compact History of {infinity}"

Is this book merely an instance of the bland leading the blind? It may be more perilous than that, since readers with a genuine but uncultivated interest in the subjects which the book purports to address---roughly, the concept of 'infinity' in mathematics---may be more than merely mislead by Wallace's rambling, irreverent romp through soundbytes from the
undergraduate math curriculum: they may be soured on the subjects themselves.

The first---and cardinal---error committed by Wallace is his presentational style. His mistake is one that could only be committed by one who either lacked comprehension of the math behind his pop-sci summaries, or else was so contemptuous of those results that a sincere attempt to communicate the underlying ideas seemed superflous. Bluntly put, the first thing any prospective initiate into the world of mathematical thought must do is to free himself from the need to accomodate one's thinking, reasoning---and indeed, presentational style---to the comfortable glibness which is prized in everyday discourse (and apparently, in certain long-winded works of fiction). Wallace probably belives that by adhering to a populist style, he will attract more readers to his subject. This may be true, but in so doing, he has marred the beauty of that subject so hopelessly beyond recognition that sincere readers will find little of value in his presentation.

The book is not only not recommended, it is recommended to be avoided.

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?)