- Title Pages
- Dedication
- Introduction
- Definitions
- Note on the Illustrations
- Part 1 Numerals: Significant Manuscripts and Initiators
- Chapter 1 Curious Beginnings
- Chapter 2 Certain Ancient Number Systems
- Chapter 3 Silk and Royal Roads
- Chapter 4 The Indian Gift
- Chapter 5 Arrival in Europe
- Chapter 6 The Arab Gift
- Chapter 7 <i>Liber Abbaci</i>
- Chapter 8 Refuting Origins
- Part 2 Algebra
- Chapter 9 Sans Symbols
- Chapter 10 Diophantus’s <i>Arithmetica</i>
- Chapter 11 The Great Art
- Chapter 12 Symbol Infancy
- Chapter 13 The Timid Symbol
- Chapter 14 Hierarchies of Dignity
- Chapter 15 Vowels and Consonants
- Chapter 16 The Explosion
- Chapter 17 A Catalogue of Symbols
- Chapter 18 The Symbol Master
- Chapter 19 The Last of the Magicians
- Part 3 The Power of Symbols
- Chapter 20 Rendezvous in the Mind
- Chapter 21 The Good Symbol
- Chapter 22 Invisible Gorillas
- Chapter 23 Mental Pictures
- Chapter 24 Conclusion
- Appendix A Leibniz’s Notation
- Appendix B Newton’s Fluxion of <i>x<sup>n</sup></i>
- Appendix C Experiment
- Appendix D Visualizing Complex Numbers
- Appendix E Quaternions
- Acknowledgments
- Index

# Symbol Infancy

# Symbol Infancy

- Chapter:
- (p.116) Chapter 12 Symbol Infancy
- Source:
- Enlightening Symbols
- Author(s):
### Joseph Mazur

- Publisher:
- Princeton University Press

This chapter discusses the evolution of symbolic algebra that began in the first half of the sixteenth century. Algebra was not always called algebra. In the mid-fifteenth century some Italian and Latin writers called it *Regula rei e census*. The twentieth-century mathematician and science fiction author Eric Temple Bell allegedly remarked that in the mid-seventeenth century, mathematicians were able to introduce negative and rational exponents because symbolic manipulation liberated their thinking from the wilderness of words. The chapter considers the contributions of the Arab algebraist al-Qalasādi, who used letters of the Arabic alphabet to denote arithmetic operations and whose notation was clearly an attempt at symbolizing algebra through abbreviations, a first approximation to what we would consider true symbols. It also examines how Italy cultivated the seeds of algebra, citing in particular Gerolamo Cardano's *Ars Magna*.

*Keywords:*
symbolic algebra, algebra, arithmetic, exponents, al-Qalasādi, Arabic alphabet, notation, symbols, Gerolamo Cardano, Ars Magna

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- Title Pages
- Dedication
- Introduction
- Definitions
- Note on the Illustrations
- Part 1 Numerals: Significant Manuscripts and Initiators
- Chapter 1 Curious Beginnings
- Chapter 2 Certain Ancient Number Systems
- Chapter 3 Silk and Royal Roads
- Chapter 4 The Indian Gift
- Chapter 5 Arrival in Europe
- Chapter 6 The Arab Gift
- Chapter 7 <i>Liber Abbaci</i>
- Chapter 8 Refuting Origins
- Part 2 Algebra
- Chapter 9 Sans Symbols
- Chapter 10 Diophantus’s <i>Arithmetica</i>
- Chapter 11 The Great Art
- Chapter 12 Symbol Infancy
- Chapter 13 The Timid Symbol
- Chapter 14 Hierarchies of Dignity
- Chapter 15 Vowels and Consonants
- Chapter 16 The Explosion
- Chapter 17 A Catalogue of Symbols
- Chapter 18 The Symbol Master
- Chapter 19 The Last of the Magicians
- Part 3 The Power of Symbols
- Chapter 20 Rendezvous in the Mind
- Chapter 21 The Good Symbol
- Chapter 22 Invisible Gorillas
- Chapter 23 Mental Pictures
- Chapter 24 Conclusion
- Appendix A Leibniz’s Notation
- Appendix B Newton’s Fluxion of <i>x<sup>n</sup></i>
- Appendix C Experiment
- Appendix D Visualizing Complex Numbers
- Appendix E Quaternions
- Acknowledgments
- Index