I want to note for the HN crowd that the book is in the "just technical enough to inform yet not scare off the layman, but not technical enough for the practitioner" nonfiction subgenre. Critically, there are a number of finer details that DFW gets wrong; if you're mathematically inclined and intend to read this, I suggest pairing it with a printed copy of Prabhakar Ragde's errata document hosted by the DFW fansite The Howling Fantods ([1]).
I'm surprised by the mathematician's critiques of this book. I have a PhD in math and I read this book about 10 years ago now. I loved it. I'm sure there are some inaccuracies, but he gets the overall story correct. There's enough math in the book to be engaging for someone mathematically trained. There's also a lot more history than if you read a math book that just has proofs. And the book is entertaining in the way that DFW's books usually are. As a former mathematician I highly recommend.
I agree. The inaccuracies listed are like, once every few pages the author makes a statement like "P implies Q" without mentioning some minor condition, like, "only if you assume the axiom of choice". Yes, this is annoying for mathematicians, but there's just a fundamental compromise that has to be made. If you spell out every single detail then you will create a book that is not engaging enough to read straight through.
I think you will really enjoy this book if, like me, you:
1. Enjoy David Foster Wallace's literary style
2. Have a good mathematical understanding of set theory
Unfortunately, the intersection of these two conditions might make for a very small target audience!
That’s why you don’t have to explicitly add it as a qualifier at every instance in which it’s implied in your work of non fiction for a general audience.
I think if you aren't deeply concerned with the axiom of choice in your work about infinity for a general audience, then the entire affair is rather farcical. Most of the "weird" stuff about infinity derives from the axiom, after all. A book about infinity, for the lay person in particular, must be in large part a book about the axiom of choice.
Michael Harris is a great mathematician (number theory, let's go!!), but that review to me is pretty rambling and doesn't point out many inaccuracies in DFW's book, but takes issue with DFW's approach and style or writing. I did just skim the review and am a DFW fanboy, but Harris seems to have issues with books about infinity and math for lay people, which is fine, that's driving his opinions here.
I'd imagine there will also be a gap between what mathematician's think of novelists writing and what novelists think of real math. So there's that too.
I'm not aware of any, but maybe somebody else is. A more general question is are there any other DFW-ish math-ish writings to be found? Against The Day (Pynchon) is not really math-ish, but it does have a good bit of math (more than GR at least), and a DFW fan would probably like it. Stella Maris (McCarthy) is perhaps neither DFW-ish nor math-ish, but it is Serious Fiction centered on a mathematician and is probably the best work of fiction to feature Alexander Grothendieck. I have heard that Solenoid (Cartarescu) has some math in it, though I fear it's still sitting on my shelf. Every Arc Bends Its Radian (due in a couple months from Sergio De La Pava) has a math-ish title but I doubt it will actually contain much math.
Michael Harris -- a mathematician who wrote a review of the DFW Infinity book -- has a book called "Mathematics Without Apologies", which I liked, though it's non-fiction. There is also "Birth of a Theorem" by Fields medalist Cedric Villani which is an interesting read -- not fiction, but it is experimental in many respects and I would say worth a read.
