How deep does Pickover's book go? I read in the reviews that each topic is limited to one page only, so I presume the real mathematics would not be covered. In other words, after reading this, will I understand the topics or would just understand things about them?
IIRC there are a few things that are simple enough to actually explain in a page, but yes, one page per...artifact? Very little real mathematics, you will just understand things about them. It is, however, the best written of these pop-math type books that I've come across. If you are comfortable with undergraduate-level mathematics, the Princeton Guide is a much better book for getting an idea about a specific topic. Pickover's book is more for getting a feel for what topics are out there. They were written for two very different audiences and I like them both for different reasons.
I also see a Physics book by the same author, but have the same question there too: http://www.amazon.com/Archimedes-Hawking-Science-Great-Behin...