Years ago, I studied logic and recursion theory with Professor Gerald Sacks. The name of the class is somewhat misleading: essentially, we spent all semester on Gödel’s incompleteness theorem.
The class wasn’t easy, but Professor Sacks made one of the most profound discoveries in mathematical logic seem quite accessible. The finer details of the proof of Gödel’s incompleteness theorem are probably beyond me at this point, but I left with a fairly clear understanding of how to go about it. (That and reverential awe for Gödel himself.)
So when Rebecca Goldstein’s Incompleteness: The Proof and Paradox of Kurt Gödel came out, I lapped it up eagerly. Her prose was elegant, and her description of Gödel’s personal philosophical beliefs (he was a true Platonist) were enlightening. But the book was remarkably obtuse on its actual topic — incompleteness and Gödel’s theorem — even for one familiar with the subject to some degree.
The American Scientist had a review of Goldstein’s book that summed up my feelings better than I could ever have.
In sum, Goldstein does not understand mathematical logic and set theory, the subjects of Gödel’s mathematical work. Her book would have benefited if she had just left them out and not pretended to explain them.