The 25th International Congress of Mathematicians took place in Madrid, Spain, during the summer of 2006. Several special events and specially designed exhibitions ran in parallel to the main events of the congress. In particular, the National Library of Spain organized an exhibition called "The Life of Numbers". The book under review, under the same title as the mentioned exhibition, was designed as a sort of catalogue of the pieces featured in the National Library for the exhibit. But this is not a plain catalogue by any means. Much to the contrary, the book stands on its own as a wonderful volume on the history and evolution of numbers. And what a beautiful book this is!
The book is composed of four different articles, written by Antonio J. Durán, Georges Ifrah and Alberto Manguel. These are: (1) Done on paper: the dual nature of numbers and the page; (2) Numbers are for counting (I and II), and (3) The way people learned how to count and calculate. The essays are written in a 'novelesque' or poetic sort of way. Each tells a story about numbers and about us, humans: stories about how numbers came to be and why; in what form they first appeared and how they evolved; how the need of expressing numbers in "print" (on a piece of paper, papyrus or a rock) helped in the development of mathematics. One of the most interesting features of the book is the vast amount of illustrations (by Sean Mackaoui, Natalia Pintado and Javier Pagola), photographs and diagrams included, which make every page exciting in its own right. In fact, the artistic design of the entire book is fantastic, from cover to cover, and it is obvious that an uncountable number of hours have gone into making this book as visually appealing and imaginative as it is. As the authors express in the preface, the book is meant to be read but also simply to be browsed. One only needs to open the volume at a random page, and the attention of the reader will get immediately drawn to one of the many interesting photographs of an old painting, a page of an ancient codex or the intricate structure of some extinct number system inscribed in stone.
My only complaint about the book, which is really minor, is that I have a feeling that something got lost in the translation from Spanish to English. Some sentences may seem a little odd, mainly because they are constructed in the way a Spanish sentence would be written, and then translated almost directly into English. Translation issues aside, the book is simply wonderful and deserves to be read and browsed. I will keep my copy on my coffee table for a long time.
Álvaro Lozano-Robledo is H. C. Wang Assistant Professor at Cornell University.