- 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

# The Last of the Magicians

# The Last of the Magicians

- Chapter:
- (p.169) Chapter 19 The Last of the Magicians
- Source:
- Enlightening Symbols
- Author(s):
### Joseph Mazur

- Publisher:
- Princeton University Press

This chapter discusses Isaac Newton's contributions to algebra and mathematics, and particularly in terms of using symbols. It first examines Newton's idea of unknown variables as quantities flowing along a curve. Fluents, as he called them (from the Latin *fluxus*, which means “fluid”), were very close to the things that we now call dependent variables, our *x*'s, but limited by their dependence on time. Newton thought of curves as “flows of points” that represented quantities. According to Newton, the fundamental task of calculus was to find the fluxions of given fluents and the fluents of given fluxions. The chapter also considers Newton's work on infinitesimals and how his invention of calculus advanced a wide range of fields such as architecture, astronomy, chemistry, optics, and thermodynamics. It also describes some of the major developments that occurred in the fifty years following Newton's death.

*Keywords:*
calculus, Isaac Newton, algebra, mathematics, symbols, fluents, dependent variables, curves, fluxions, infinitesimals

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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