Borges and Mathematics.

Reaburn, Robyn

Borges and Mathematics

Guillermo Martinez

translated by Andrea G. Labinger

Purdue University Press

2003, 140 pp., soft cover

ISBN 978-1-55753-632-7

[ILLUSTRATION OMITTED]

This book consists of a series of essays by Guillermo Martinez, the novelist and short story writer, who is possibly best known for his book that combined mathematics and crime, The Oxford Murders. In this book he introduces us to the mathematical aspects of the works of the Argentinian writer Luis Borges (1899-1986). As Martinez is also Argentinian, and has a PhD in mathematical logic, he is uniquely qualified to undergo this task.

The book begins with two lectures given by Martinez on aspects of mathematics in Borges' work, including infinity, fractions, Pascal's sphere (whose centre is everywhere and circumference nowhere), while considering the nature and structure of the short story. These two lectures are followed by a series of essays on artificial intelligence, Fermat's theorem, Euclid, and Hilbert. He also includes a discussion on the works of Oliver Sacks (The Man Who Mistook His Wife for a Hat), Gergory Chaitin (The Limits of Mathematics), and Hans Enzensberger (The Number Devil). In each of these essays the reader is challenged to consider the nature of mathematics and to look at familiar concepts in a new way.

At the beginning of this book, Martinez states that, "I realize that among my readers there might be people who know a great deal about mathematics, but I'm going to address those who only know how to count to ten" (pp. 1-2). This is not achieved, however. For example, in a discussion about the solving of Fermat's theorem we read, "Two young mathematicians... noticed that certain intensely studied mathematical objects of that time, known as modular forms, gave rise to elliptical curves" (p. 76). The reader does not find out what "modular forms" and "elliptical curves" are. Other mathematical terms are explained, however, for example the idea of the set of all sets that are not elements of themselves (p. 18).

This is not a book for school students. It is a book for lovers of literature, those who are interested in the philosophy of mathematics, and for those who are interested in having their views of mathematics expanded and challenged. Whereas reading of the book would be enhanced if the reader had knowledge of Borges' work, it is not necessary, as Martinez describes the elements of his work that apply to what he is discussing. This book takes careful reading, but is well worth the effort.

Robyn Reaburn

University of Tasmania