Everything and More: A Compact History of Infinity

The style (and the superfluous use of acronyms) is somewhat irritating and gives the impression that the author just wants to show off with his academic use of latin abbreviations et similia, just to impress poor educated readers. With his apodictic judgements of other authors it is clear that he wants to put himself on a different and superior level: it's a sort of captatio benevolentiae I learned to distrust from school time, because often put in practice by "shallow" authors/professors. Said this, what about the mathematical errors the book[let] is riddled with? It's a shame. I've lost time and money on nothing.

This book is well written in a conversational tone that makes you feel like you're sitting down, talking with the author. The level of detail was just right -- enough to appreciate the complexities of the problems with enough proofs to make you understand without going overboard. (And, where appropriate, just sketches without formality)I also really like how the author traced the history of math through the greeks and into modern math, showing deep connections between Pythagoras, Plato, and Aristotle, and how they influenced (and continue to influence) math today. Many topics from school came back and seemed much more alive as the metaphysical impact was explained.If you survived college calculus and still retain some basic understanding of it, then you probably won't struggle to get through this book. If you stopped after high school math then you'll struggle.I'm a computer scientist by trade, and I found many interesting connections between computability, decidability, complexity theory, recursion, induction, countable vs. uncountable, etc. It was a great way to further my education in my spare time.The only thing that drove me nuts is the author's chapter/section writing style. Why can't he just use normal chapters like the rest of the world? ...And a table of contents. If he had been a little more conventional then it would have been perfect.

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.

This book is not for everyone. I have a math degree from MIT and although I was definitely not the greatest math student in the world I felt like I was probably above average in terms of what DFW expected his audience's math education to include. I had no idea how he was going to write a non-textbook style book on this topic.He almost succeeds in writing a popular book on this branch of math but it doesn't actually succeed in that I think most people will leave this book, if they even get through it at all, still confused about much of this topic and not really understanding a lot of his proofs or the full significance of many of the ideas. That being said, he still does a really good job. I think his goal is basically unachievable because math requires you to read like 1 line of information, then think for a while, and probably write some stuff down to make sure it makes sense, and then read another line. This is a tall order for people reading a popular book and I think these ideas can only be absorbed at a normal reading pace, which is what people expect of a popular book, if you can think of really clever examples that make each unit of information obvious so that the reader doesn't need to stop to think, so that the reader just understands and absorbs the information as they're understanding the words. That's not what happens here. What's impressive is that DFW describes the whole history of ideas, includes the proofs, and fits the parts of the story together so that they lead to the bigger ideas.I'd recommend this book to people who enjoy DFW's writing style, know high school level math, are wiling to put thought into the ideas that he goes through or are willing to just accept his assertions of various ideas being true. I do not recommend this book to people who want something easy to read and don't have the time or the patience to invest in being pretty active about understanding some complicated ideas. I think the ideal audience for this book is people who would describe themselves as loving both DFW and math, or someone who already knows all of these ideas really well and just wants an amusing little recap.

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.