No one needs to be informed that we have been through a calculating revolution in the past few decades, with a computer seeming to be on everyone's desk and in everyone's pocket. This particular calculating revolution, though, has been just one in a series, starting with notching tally marks on a bone around 35,000 years ago. Just as we take computers for granted now, so also we take for granted 0, 1, 2, and all the rest, but those are inventions as much as computers are, and they were a revolution in their time. It is a revolution that can be credited to a mathematician who is more famous for popularizing (he didn't invent) a series of numbers that bears his name, Fibonacci, but he now gets credit for introducing Arabic numbers to Europe in _The Man of Numbers: Fibonacci's Arithmetic Revolution_ (Walker & Company) by Keith Devlin, a mathematician who is well known as "The Math Guy" on NPR. Fibonacci didn't invent Arabic numbers, of course, and they are so much better a calculating system than the Roman numerals that preceded them that they would have been adopted eventually, but Fibonacci made it happen. Devlin's fascinating account shows how he did it, and how he didn't get credit for it, and how we now know him to be one of the most influential mathematicians who ever lived.
Although Devlin's book is supposed to be about its title character, it isn't a biography. Unless some librarian discovers a long-lost manuscript someday, Fibonacci will never have a biography. We know a little about him and his influences, all of which Devlin tells us, but details like his place and date of birth and death, family life, or what he looked like just don't exist. Fibonacci's father, a merchant, took him to north Africa when the boy was fifteen. There, he learned the Arabic numbers and spent a decade in training from mathematicians. After he returned to Pisa, he published his masterwork in 1202, _Liber abbaci_, "Book of Calculation," a 600-page introduction to a better way of working with numbers. The book was not addressed to mathematicians, but to merchants. Fibonacci showed how what he called the "Indian figures" could be used to write any number, the ease with which they could perform the four basic calculator functions, how fractions could be used, how square and cube roots could be taken, and more. Quickly a merchant who insisted on using Roman numerals and counting boards was surpassed in efficiency by those who mastered the new system. The book was an instant success, so that Fibonacci issued different versions of it, and also others got into the act. In the next century, maybe a thousand or more similar manuscripts were written in Italian vernacular on the same themes. Textual analysis of these works all show that they were clearly beholden to Fibonacci's original.
In a final chapter, Devlin writes about the Fibonacci Numbers; if you know Fibonacci's name, it ought to be for the Arabic numbers you see every day, but probably it is due to a little problem he put into _Liber abbaci_, about rabbits who breed through generations, and how to count the number of pairs in each generation. It is the series 1, 1, 2, 3, 5, 8, 13, and so on, each number being the sum of the pair preceding it. It has remarkable mathematical properties, and the numbers show up in nature with surprising frequency. Fibonacci, however, didn't originate the series, and his name was attached to it only in the 1870s. They are interesting in their own right, but they aren't really Fibonacci's. Appreciating Fibonacci for his real achievement is the aim of this book, and Devlin presents a convincing argument to show that Fibonacci did nothing less than start the modern arithmetic revolution.