The Biography of a Dangerous Idea
By Charles Seife
Penguin Books, 2000
Zero is, as it says, a history of the number zero, from the ancient Babylonians to modern-day physics. This book was very well received, and is a New York Times Notable Book and winner of the PEN/Martha Albrand Award. So take the rest of this review, in which I explain why this book is crap, with a grain of salt.
Readers are split in their reviews; many find this to be an interesting and worthwhile gallop through history, mathematics, and physics. They have a point. Seife covers a lot of ground, and keeps the reader engaged with interesting bits of history and putting otherwise boring bits of science in the proper context to make them relevant. Many others find this to be a confusing mix of pop history/science, pseudo-religious bullshit, and all-too-brief explanations of confusing ideas. They also have a point.
Unfortunately, Seife does not have a very high opinion of history, blithely presenting as fact stories of Archimedes running naked down the street shouting "Eureka!", Zeno of Elea's tortuous ear-biting death, and the inane idea that many ancient Egyptians were unable to count to five. Given that this text is presented primarily as a history, this sort of thing is not okay.
Even more unfortunately, Seife wrote this book, apparently, as the result of a religious epiphany, in which he realized that zero and infinity are inextricably linked to each other and to all human religion. He makes the argument that zero was a dangerous idea that was suppressed as a threat to the Christian/Islamic/Judaic concept of God (he may have a point), and that zero is eternally the key to all the mysteries of the universe (he sounds a bit nuts).
The final bit of misfortune is simply that despite Seife being well educated and well read in the areas of math and physics, he decided to dash through them in short form, with an unrelenting insistence of tying every idea from relativity to string theory to zero. The result is that you can follow him well enough if you have read about these concepts previously, but will be annoyed at what he is leaving out. Or you won't really follow him, in which case this whole thing is a waste of time.
But let me finish off with a few good points. Seife's explanation of projective geometry was the most accessible I have yet read. And while I hesitate to recommend this book as a serious work on non-fiction, it does give you a lot of good jumping-off points for further reading. Just don't be surprised if you find your favorite anecdote turns out to be only maybe-true.