The Adventure of Numbers
Numbers are fascinating. The fascination begins in childhood, when we first learn to count, and continues as we learn arithmetic, algebra, geometry, and so on. Eventually, we find 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 unfolds a great adventure of the mind by examining our expanding understanding of numbers throughout history. The development of mathematics has been punctuated by a need to reconsider what we mean by ``numbers'. It is often during these times that major shifts occur, for example 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 the very early days of mathematics in Mesopotamia and leads to the present day. The adventure does not end there. Important questions and controversies remain today that deal with consistency and complexity or with what constitutes a proof. And the future will hold even more questions. The author, Gilles Godefroy, is a member of the Institut de Mathematiques de Jussieu and Directeur de Recherches at the C.N.R.S. The book is suitable for independent study and supplementary reading and is recommended for undergraduates, graduate students, and researchers interested in the history of mathematics.