This book explores one of humanity's most profound intellectual journeys — the creation of numbers themselves. Moving beyond a simple chronological history of mathematics, this book examines the ideas and cultural contexts that gave rise to new kinds of numbers, from the earliest counting systems to ideas of infinitely small and infinitely large numbers. On the way, it looks at how revolutionary kinds of numbers became accepted and indeed essential.
Drawing on sources from mathematics, archaeology, linguistics, and psychology, the author traces how different civilizations — including ancient Greece, China, and the Arab world — shaped the evolution of numerical thought. Readers are guided to original texts (many newly translated and linked to online versions) to see how ideas of numbers were understood in their own time and how they continue to develop.
An extensively revised and expanded version of the author's earlier The Emergence of Number (1987), this edition reflects profound changes in the perception of number concepts in the last 150 years. It offers two new chapters on infinite numbers and infinitesimals, along with broader cross-cultural perspectives. Rich in historical insight yet accessible to modern readers, this book illuminates how human creativity and abstraction transformed counting into the vast landscape of modern mathematics.
Contents:
- Preface
- Acknowledgments
- About the Author
- List of Figures
- Prologue
- The Natural Numbers:
- Complex Numbers:
- Real Numbers:
- Measuring
- The Totality of Real Numbers
- Numbers and Infinity:
- Infinite Numbers
- Infinitely Small and Infinitely Large Numbers
- Epilogue
- Bibliography
- Index
Readership: Mathematicians, historians of mathematics, and historians of science in academia; Undergraduate and graduate students studying the history or philosophy of mathematics; Researchers and educators seeking original source material on number concepts; General readers interested in the intellectual and cultural evolution of numbers; Course use: Supplementary reading for courses in the history of mathematics, number theory, and philosophy of mathematics.