eBook ISBN:  9781470424800 
Product Code:  MAWRLD/21.E 
List Price:  $45.00 
MAA Member Price:  $40.50 
AMS Member Price:  $36.00 
eBook ISBN:  9781470424800 
Product Code:  MAWRLD/21.E 
List Price:  $45.00 
MAA Member Price:  $40.50 
AMS Member Price:  $36.00 

Book DetailsMathematical WorldVolume: 21; 2004; 194 ppMSC: Primary 01; 11
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.
ReadershipUndergraduates, graduate students, and researchers interested in the history of mathematics.

Table of Contents

Chapters

Chapter 1. Hands, sticks, and stones

Chapter 2. By the waters of Babylon

Chapter 3. Let none but geometers enter here

Chapter 4. Algebra and algorithms

Chapter 5. A new world

Chapter 6. “Eppur, si muove!”

Chapter 7. The century of revolutions

Chapter 8. “From the paradise that Cantor has created for us”...

Chapter 9. The present perplexity

Chapter 10. And now?

11. Appenidx 1. Number bases

12. Appenidx 2. The Fibonacci sequence

13. Appenidx 3. Polynomials

14. Appenidx 4. Quaternions

15. Appenidx 5. Axioms of set theory and arithmetic


Additional Material

Reviews

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 RobinsonMatyasevic'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 prehistory, 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


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

Chapters

Chapter 1. Hands, sticks, and stones

Chapter 2. By the waters of Babylon

Chapter 3. Let none but geometers enter here

Chapter 4. Algebra and algorithms

Chapter 5. A new world

Chapter 6. “Eppur, si muove!”

Chapter 7. The century of revolutions

Chapter 8. “From the paradise that Cantor has created for us”...

Chapter 9. The present perplexity

Chapter 10. And now?

11. Appenidx 1. Number bases

12. Appenidx 2. The Fibonacci sequence

13. Appenidx 3. Polynomials

14. Appenidx 4. Quaternions

15. Appenidx 5. Axioms of set theory and arithmetic

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 RobinsonMatyasevic'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 prehistory, 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