The Nothing That Is: A Natural History of Zero.

Robert Kaplan. The Nothing That Is: A Natural History of Zero. Oxford, England: Oxford University Press, 1999.

In a rare book that is part detective story, part biography, part history, and interesting throughout, author Robert Kaplan traces the origins of zero in The Nothing That is: A Natural History of Zero. Kaplan, who has taught mathematics, philosophy, Greek, German, Sanskrit, and Inspired Guessing, brings a rich and varied background to what is perhaps mankind's greatest discovery. Or is it mankind's greatest invention? This is only one of the mysteries that Kaplan investigates in this book as he takes us through the portal of zero to a journey filled with memorable characters and improbable events.

Odd, isn't it, that the Greeks for all their mathematical genius, did not have a symbol for zero -- or did they? Go further East, where, more than a thousand years ago, Indian mathematicians made a very crucial leap in thought and calculation. By treating the zero like any other number, instead of a unique symbol, they opened the doors to strange, if not magical, new computation and a better understanding of how mathematics works. Doom-sayers would label this knowledge "dangerous Saracen magic" and the work of the Devil himself, but businessmen know a good thing when they see it and this handy little tool soon made business boom, helping to usher in the Renaissance. Not long after that, the zero became the linchpin to almost every revolution in every science. The rest, as they say, is history.

For Kaplan, the story of zero reveals truths about the nature not only of mathematics but of human thought itself. The story also shows how mathematics develops in a process of "recursive abstraction": once we create a symbol to represent an idea, that symbol gives rise to operations that in turn lead to new ideas. The beauty of mathematics is that even though we invent it, we seem to be discovering something that already exists.

This joy of discovery can be found throughout Kaplan's book as he ranges from Archimedes to Dostoevsky, making intriguing connections between mathematical ideas from every age and every culture. And you don't have to be a math whiz to follow what Kaplan is saying. In a section titled "A Note to the Reader" he says "If you have had high-school algebra and geometry nothing in what lies ahead should trouble you, even if it looks unfamiliar at first."

The only quibble I have with the book is that Kaplan put the bibliography and notes on the world-wide web (he gives the web address in the book). This is a disservice to those without computers and to those who may not want to use their computers while reading their books.