**Mathematical World**

Volume: 21;
2004;
194 pp;

MSC: Primary 01; 11;

**Electronic ISBN: 978-1-4704-2480-0
Product Code: MAWRLD/21.E**

List Price: $34.00

AMS Member Price: $27.20

MAA Member Price: $30.60

#### Supplemental Materials

# The Adventure of Numbers

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*Gilles Godefroy*

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
Mathématiques 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.

#### Reviews & Endorsements

It is very welcome that the original French version, published some 8 years ago, has been translated into English thus making the book open to a broader readership, experts as well as non experts. It presents a fascinating tour around the land of numbers: from the very beginnings of counting up to nonstandard and surreal number, from the solution of algebraic equations up to Goedel's incompleteness theorem and Robinson-Matyasevic's theorem on Hilbert's 10th problem. ...[F]or mathematicians including already first year undergraduate students the book will be very appealing and stimulating.

-- G. Kowol, Monatsheft fur Mathematik

*The Adventure of
Numbers* is a delightful panoramic story that traces the origin of the
concept of number from pre-history, through antiquity, the Middle Ages, the
Renaissance, and down to modern times. As such, it is a book that discusses a
lot of history; however, it is not so much a book about the history of
mathematics, but rather more of a mathematical narrative that uses history to
enliven its discussion of the evolution of mathematical concepts.
...inspirational reading about the unity and evolution of mathematical thought.

-- MAA Reviews

#### Table of Contents

# Table of Contents

## The Adventure of Numbers

- Cover Cover11
- Title iii4
- Copyright iv5
- Contents v6
- Preface vii8
- Chapter 1. Hands, Sticks, and Stones 114
- Chapter 2. By the Waters of Babylon 1124
- Chapter 3. Let None But Geometers Enter Here 2538
- Chapter 4. Algebra and Algorithms 4154
- Chapter 5. A New World 4962
- Chapter 6. "Eppur, Si Muove!" 6174
- Chapter 7. The Century of Revolutions 7588
- Chapter 8. "From the Paradise That Cantor Has Created for Us" … 95108
- Chapter 9. The Present Perplexity 115128
- Chapter 10. And Now? 141154
- Appendix 1. Number Bases 165178
- Appendix 2. The Fibonacci Sequence 169182
- Appendix 3. Polynomials 173186
- Appendix 4. Quaternions 179192
- Appendix 5. Axioms of Set Theory and Arithmetic 183196
- Glossary 191204
- Bibliography 193206
- Back Cover Back Cover1209