this whole piece is rather confusing and muddled. first the subtitle says that godel didn't prove what you think he did. however, in the text below, the reviewer seems to agree that most people do not even know who godel is. no big deal. what i find unconvincing is the idea that his result is no big deal. 1) attacks by "mainstream" mathematicians against logicians and foundations of math folks are neither new nor opaque (after all, why entertain/encourage someone who questions your very programme!). 2) godel's result is indeed a metamathematical result. the fact that this permits a run of the mill mathematician to continue his work does little however to diminish the result, including for mathematics. but it is the much broader impact/implication of the result that makes it important. 3) pointing to a few misinterpretations/misuses of godel's incompleteness theorem does not help the argument either.
my opinion: skip the review, and perhaps the book, and read either hofstadter or penrose, or if in a lighter mood, the somewhat interesting "uncle petros and goldbach's conjecture":
http://www.maa.org/reviews/petros.html
for an interesting fictional take on godel's impact!
--ravi
