I didn't know what to make of this book review. The book review points out a lot of ways in which this book is a mess (poorly copy-edited, unclear motion from one author to another, terminology used without definition, etc.). Then at the end, it says:
What gives? This seems like a conclusion ripped from an entirely different review. If it's that this book is really the only choice right now, then you could say that. but this sentence here looks like it comes at the end of a rave review.
44 Conjectures of Stephen Wolfram Disproved
I confess to being a bit rusty on this subject, but isn't it the rationals that are a field? Or at the very least, you don't need to go to the reals to get a field, although they are a field...