Since I'm somewhat of a fan of books that cover the history of science and math, I had to buy this one when I saw it. In the preface, the author notes that since he is neither a mathematician nor a historian he is the perfect one to write this book. It turns out that both his math and his history and leave much to be desired.
Regarding mathematical proofs, Beckmann made a concious decision to ply the middle ground between mere hand-waving and totally rigorous proofs. The end result is a scattering of proofs that are neither easy enough to simply read and understand, nor detailed enough to follow to completion.
Petr Beckmann's treatment of history gives the impression that the world has been populated by only two classes of inhabitants: the evil and barbaric (Romans, Christians, Soviets) or the enlightened (Greeks, Chinese, English). His loathing for the Romans is particularly intense, and distracting to the extreme, especially since he takes random swipes at them throughout the entire first half of the book.
There are interesting tidbits scattered throughout the book, but most of these can be gleaned from other history of math books. Much of the book is also dated, such as his treatment of the four-color problem, which was proven recently. This can be forgiven, since the book is over twenty years old, but it does reduce its value as a read even lower than its minimal initial level.