Everything and More – A Compact History of Infinity (Great Discoveries (Hardcover)) Hardcover – Illustrated, 28 Nov. 2003

One minor caveat to start with: Wallace's liberal use of acronyms takes a little getting used to, but it's well worth that little extra effort.There are many popular accounts of infinity, some very sound (eg Vilenkin), some attractive but containing serious errors (eg Maor), and some lame (which remain nameless). But Wallace has the knack of delivering ideas with stunning simplicity; and I found the book hard to put down, in much the same way that, as a schoolboy, I found Sawyer's 'Prelude to Mathematics' quite addictive. His style is chatty without being in the least patronising: indeed he occasionally resorts to schoolboy humour, perhaps rather smutty, but never offensive; and I found myself breaking into spontaneous laughter at times.Mathematically the book is as ambitious as it could be without going into too much abstract symbolism, and any such book is bound to attract some criticism from specialists. Thus he talks intelligently about Zermelo, well-ordering, the Axiom of Choice, the Continuum Hypothesis,etc, and I applaud his achievement.

Yes, I have to agree that the use of acronyms and abbreviations can be a little irritating but you do get used to the style and it is definitely worth persevering. This is not an easy book, and I found it tough going at times even with some University-level maths behind me. The subject matter is facinating and the author is clearly a very smart cookie. I made it through and learned a great deal, but certainly not all that the book has to offer. Finishing with some sense of comprehension is a very rewarding feeling, but I think I will have to read it again after brushing up on my real analysis.I find it difficult to see how someone without much maths could follow the book. 4 stars to compensate for the previous reviewer, who by her own admission read less that a sixth of the book.

DFW (as he would no doubt abbreviate himself) tells an interesting story of the struggle with transfinite numbers from ancient Greece to the 20th century. Although intended for a general audience, I think that, without quite a lot of maths behind you, this book would be pretty hard going. As someone who was familiar with most of the concepts, I found the presentation often seemed willfully obtuse (especially when he claimed to be making it extra-simple).The book is peppered with the usual Wallace-isms of abbreivations, footnote, interludes and interpolations. The abbreviations were often unhelpful; the footnotes often very interesting. In some places his style makes the book very entertaining and in others infuriating.Ultimately, I found this book an enjoyable read but mostly from the historical perspective. The technical content is variable and the really interesting stuff at the end is (perhaps necessarily) only given a very cursory discussion. I wouldn't recommend it for the layman, and it might annoy the expert, but I think there is fun to be had for those with a bit of background in the subject and a mind open to a pretty unique mode of presentation.

I was so looking forward to settling down with this book. The positives are fairly straightforward. DFW is a fantastic writer, and wears his immense intellect very lightly. The negatives however, make the book a sad failure. There are a number of basic errors (badly edited ?) and at times Wallace wanders off the reservation in ways that undermine the overall narrative.I have heard it suggested that this was a "spoof" book, in which case perhaps it succeeds. However, I bought the book on the basis that it was a serious attempt to tackle a serious subject, and apart from some lovely little gems (almost all in the first quarter of the book), was left somewhat dismayed.If there was a 2 and a half star, I would probably have gone there instead of the 2, but there we have it.

Enjoyment of this book very much depends on whether you enjoy Wallace's writing style, it's wilful use of abbreviations and use of back-references without page numbers mean full comprehension is only really achievable on a second reading. However, Wallace's enthusiasm for the subject matter and ability to make a highly abstract topic entertaining mean that, for the interested layman, this book is an excellent way to gain an overview of development of set theory and whets the appetite for taking on a more in-depth investigation.

Practically unreadable. Foster Wallace's obsessive use of acronyms turns a fascinating subject into a confusing and boring narrative. After DBP for the Divine Brotherhood of Pythagoras, I could read no more.