Well Godel wasn't "one of the most brilliant mathematicians" of the 20th century. He solved one of Hilberts problems and made some contributions to the Continuum Hypothesis but there are far, far, far more important mathematicians. What is also neglected in this book is that by 1949, Einstein had long ceased to make contributions to physics, was well past his prime, considered an irrelevancy and probably a bit embarrassing to the people who remembered his heyday.
Yourgrau has taken the musings of two geniuses who were frankly has beens and blown it out of proportion. It is an experimental FACT that Godel's solution in no way describes our universe and even if it did, it doesn't have the features Yourgrau ascribes to it. Again one suspects he doesn't really understand what he is talking about.