HERE IS WHY THIS BOOK IS AWESOME:



This book addresses three related enthusiasms: for mathematics itself, for math history (the lives of the mathematicians & the historical chain of deduction that gave us the math of today) and for DFW's high school math teacher (who sounds totally amazing). A book about any one of these might be more straightforward but DFW conflates the three in a breezy, entertaining mess. The operating concept is the history of infinity as a topic that has driven mathematician

HERE IS WHY THIS BOOK IS AWESOME:This book addresses three related enthusiasms: for mathematics itself, for math history (the lives of the mathematicians & the historical chain of deduction that gave us the math of today) and for DFW's high school math teacher (who sounds totally amazing). A book about any one of these might be more straightforward but DFW conflates the three in a breezy, entertaining mess. The operating concept is the history of infinity as a topic that has driven mathematicians nuts. The designated hero of the story is Gregory Cantor, but you hardly even see him until the last chapter. The rest is foreshadowing & background material & lots and lots (lots!) of math.Lovers of DFW's prose couldn't ever find a purer source of it. I was constantly laughing at footnotes, loving the intertwine of math and history, enjoyed all the ways he bent the conventions of mathematical writing to the weird shape of his brain. If you like DFW but have been putting this one off, this really is not the one to put off. His stated goal is to make a bunch of boring math more interesting and to walk you through the hard parts. I am probably his ideal reader: an interested and smart yet lazy & unconcerned person who hasn't thought about infinity lately.My measure of a good book is how much it makes me think, and this book gets five starts for reminding me that Math is a planet and not just a multi-tool. And for succeeding in highlighting that the paradoxical nature of infinity is hiding right behind all the math-tricks I learned in high school, had anyone ever pointed them out to me or had I ever bothered to look. (I recall the opposite: we were encouraged not to go there.) The nature of the infinitely large and the infinitely small has felt, at least for a few days, like a metaphor for all sorts of other failures of logic and rationality. Likewise, the concept of a discrete set vs. a continuum is ably and interestingly highlighted here. The many ways in which it seems all of geometry and all of arithmetic are non-identical conjoined twins, even though that distinction divides math history into two warring camps, is suitably made deep. My appetite for understanding is bolstered. Infinity is fun!I have to admit my main discouragement in following the math presented here is that I can't seem to summon the sense of dread and confusion that comes from, for instance, asserting that 9.999... repeating forever is equal to 10. Maybe because I didn't have DFW's high school math teacher, I find I'm blasé about infinity in a way that I gather would appall most of the mathematicians who have grappled with the concepts. In a sense, I just don't care. And so many different ways of talking about the problems of infinity and discontinuity, from Zeno up to Cantor, as presented by DFW, really do feel like a long series of restatements of the obvious: that infinity is a paradox math can't ever straighten out, but if you don't worry too hard it's actually present everywhere and quite handy.A sad truth this book drives home, once again, is that high school Math is too often taught -- was taught to me, even in "Honors" math courses -- as Computation: come, kids, and learn about these nifty, cryptic, useful symbolic systems we found over here on this bookshelf! Do some drills, get some practice using them to solve certain kinds of problems, and just maybe (via the dreaded Word Problems) develop some intuition about which of these solutions might apply to which of your upcoming future questions.Wheras Math, as understood by mathematicians (such as DFW's amazing-sounding HS math teacher) is more like another planet -- an actual landscape, a real thing that exists and can be perceived, initially by our intuitions (i.e. that two grapes and two oranges are similar in the sense that there are two of them, and therefore "twoness" exists and can be known, as can the nesses of other integers) and then later by deducing from just those truths plus our intuitions, just as astrophysicists can know the likely orbits of habitable planets in far-off galaxies. There is this incredible detail to the mathematical landscape, and the people who discovered it were real explorers. This version of Math relates to mere Computation in about the same way that the study of physics relates to auto shop. But efforts to base grade school mathematical education in intuition of mathematical truths instead of computation drills (see: New Math) are constantly met with deep suspicion by all the parents and administrators who themselves only learned Computation and don't get the difference. So DFW lucked out there.(One thesis of Neal Stephenson's introduction is that this was a direct result of DFW growing up in a midwest college town, overpopulated with humble degreed braniacs who did things like teach high school math. Whereas I -- in defense of my own quite likable Honors Math teacher -- grew up in Silicon Valley, a society fairly fixated on Computation for Computation's sake.)Which in the end means that, to me, Cantor's diagonal proof about the rational number set & subsequent branding of the real number set as a higher order of infinity seems like much ado about nothing, just another rephrasing of the fact that the latter is continuous and the former is not, which means that the former is composed of numbers and the latter of spaces containing numbers, which really doesn't seem so "hard" to me, but i'm totally willing to accept that I'm just missing something. Perhaps this is the inevitable result of an education in Computation of math instead of Comprehension of it: I'm too quick to discount the divine & take the rest for granted.HERE IS WHY THIS BOOK SUCKS:I had a big objection to Infinite Jest based on one mathematical footnote DFW gave which convinced me his grasp of mathematics was not all he thought it was. I must look up and revisit that, because this book really thoroougly convinces me that he knew way more about Math than I ever will. Reading it, I have not just been entertained by a whole bunch of chaotic, burbling DFW-prose; I have also come to believe that I learned something.However, there are quite a few Real Mathematicians who would dispute that. This book was not well-reviewed by mathematicians, in two senses First, it seems not enough of them were asked to review the manuscript for errors before publication. Second, upon publication, many of them found the math to be full of holes. Here is probably the most charitable review in this vein; Here is one that really slides the knife in. I will not get into them. Suffice it to say that I have two warring concepts of DFW: one is True Genius, the other is Bullshitter In Genius Clothing. Reading the book, I was lured back to the Genius side. But I felt a necessity to check the facts, and when I did -- just like with Infinite Jest -- the odor of Bullshit again became detectable.Mathematicians, of course, are just the sort of fun-free jerks who would be anal enough to poke holes in a lyrical work of math fantasy that the rest of us are trying to enjoy. How you feel about that is a really important question. Please take a moment to ponder it; it is pertinent across the entire Popular Science section of your local bookstore.The math-reviewers don't hesitate to label DFW a "fiction writer" although his best work IMHO is journalism. But yes, he writes to entertain. This book is entertaining. And Popular Science, taken as a genre -- with Popular Math, its more recent sub-genre -- strives to entertain. That's how it gets Popular. Publishers put these books out to sell them, and the idea of DFW writing a treatise on the history of infinity had to sound good in the boardroom. He wrote something -- apparently something a bit more erudite and symbol-encrusted than they were hoping -- but they printed it anyway. It seemed entertaining enough. Print it! Sell it!And that's fine for fiction, but this book purports to relay mathematical and historical fact. In such a book, facts should be checked and then double-checked -- that is, if the book is really striving to educate. It would not have been hard AT ALL. But, if you believe science is a decorative art and history is "true stories", it's not much of a stretch to consider Mathematics a flexible world of witchcraft akin to that found in Harry Potter books.Can you tell how much that offends me? It really does.This book, brilliant as it is, comes across as a first draft, despite at least one mention of a previous, even more chaotic draft, and despite what undoubtedly must have been a fair amount of research. Then again, he's faulted by some for not researching better; for not having read more of the available research on Cantor, for instance -- recall that Gregory Cantor is the purported star of this book, and DFW screws up certain facts about his life. Meanwhile, an extremely mathy-looking organizational scheme is invented on the fly for the sole purpose of making the book seem more organized than it is.In a word: sloppy. DFW was a writer who's so talented at rhetoric, forming excellent sentences and entertaining voices, and also with a certain talent for bedazzling us with concepts from math, philosophy and tennis, that he could just ramble on about anything he thought was really interesting and sell the first draft to a major publisher. He was absolutely brilliant at sounding brilliant. But I keep on catching him trying to sound erudite without checking his facts, and it keeps eroding my faith in him.