While I loved the first few chapters of the book, and they were mind-opening, I found the explanation of the proof unsatisfactory. As I recall, it was mentioned in the preface that the book will give a complete outline of the actual proof. I did not find this to be the case, the outline seemed to jump quite a bit from one thought to another leaving me with more questions about the proofs than answers. I still do not understand the proofs (though I now nearly understand an analogous result in computer science via Jeff Ulmann's book).