A review by aleffert
Everything and More: A Compact History of Infinity by David Foster Wallace

3.0

This book has a serious Law of the Excluded Middle problem. Not just technically - he cites LEM (these things always end up abbreviated in typical DFW style) in totally unnecessary cases - but in that the book is neither A nor not A. David Foster Wallace thinks that the development of the mathematical understanding of infinity is deeply interesting and this book is him telling you about it. He's right. It is deeply interesting. The problem is how he decides to tell you about it. And in some ways he is stuck with the usual dilemma of pop science books: the intersection to technical detail, mathematical accessibility, and technical accessibility. He pursues this as a largely mathematical development, running through many of the relevant core developments from Pythagoras to Gödel. Deliberately skipping some interesting side stories about the personalities involved. This is fine, there are plenty of biographies of the mathematicians involved, though I'm sure their not usually told with DFW's gift for gusto. The problem is that he runs through the math, skimming the details, missing some rigor, and even getting stuff wrong, but without adding in much of the bravura writing on which his deserved reputation stands. I suspect that much of the book would have been incomprehensible to someone without a solid math background, at which point there is very little new here though he does put things in a nice progression.