Numbers are fascinating. The fascination begins in childhood, when we first learn to count. It continues as we learn arithmetic, algebra, geometry, and so on. Eventually, we learn that numbers not only help us to measure the world, but also to understand it and, to some extent, to control it. In The Adventure of Numbers, Gilles Godefroy follows the thread of our expanding understanding of numbers to lead us through the history of mathematics. His goal is to share the joy of discovering and understanding this great adventure of the mind.

The development of mathematics has been punctuated by a need to reconsider what we mean by “numbers”. It is often at these times that a major shift takes place, such as when the Pythagoreans discovered irrational numbers or when imaginary numbers were needed to solve the cubic. Each jump takes place in a context, where mathematics itself is forced to ponder fundamental questions, many of which led to famous controversies.

Godefroy's adventure starts in Mesopotamia, in the very early days of mathematics, and leads to the present day. The adventure is not over, though. There are still questions and controversies that are important today. They deal with consistency or complexity or with what constitutes a proof. There will be more questions tomorrow.

Gilles Godefroy is a member of the Institut de Mathématiques de Jussieu and Directeur de Recherches at the C.N.R.S.

Readership

Undergraduates, graduate students, and researchers interested in the history of mathematics.