Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers

Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers

by Joseph Mazur


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While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols weren't available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know today? In Enlightening Symbols, popular math writer Joseph Mazur explains the fascinating history behind the development of our mathematical notation system. He shows how symbols were used initially, how one symbol replaced another over time, and how written math was conveyed before and after symbols became widely adopted.

Traversing mathematical history and the foundations of numerals in different cultures, Mazur looks at how historians have disagreed over the origins of the numerical system for the past two centuries. He follows the transfigurations of algebra from a rhetorical style to a symbolic one, demonstrating that most algebra before the sixteenth century was written in prose or in verse employing the written names of numerals. Mazur also investigates the subconscious and psychological effects that mathematical symbols have had on mathematical thought, moods, meaning, communication, and comprehension. He considers how these symbols influence us (through similarity, association, identity, resemblance, and repeated imagery), how they lead to new ideas by subconscious associations, how they make connections between experience and the unknown, and how they contribute to the communication of basic mathematics.

From words to abbreviations to symbols, this book shows how math evolved to the familiar forms we use today.

Product Details

ISBN-13: 9780691173375
Publisher: Princeton University Press
Publication date: 12/06/2016
Edition description: Reprint
Pages: 312
Sales rank: 806,828
Product dimensions: 6.00(w) x 9.20(h) x 0.80(d)

About the Author

Joseph Mazur is the author of Euclid in the Rainforest (Plume), which was a finalist for the PEN/Martha Albrand Award, Zeno's Paradox (Plume), What's Luck Got to Do with It? (Princeton), and Fluke (Basic).

Table of Contents

Introduction ix

Definitions xxi

Note on the Illustrations xxiii

Part 1 Numerals 1

1. Curious Beginnings 3

2. Certain Ancient Number Systems 10

3. Silk and Royal Roads 26

4. The Indian Gift 35

5. Arrival in Europe 51

6. The Arab Gift 60

7. Liber Abbaci 64

8. Refuting Origins 73

Part 2 Algebra 81

9. Sans Symbols 85

10. Diophantus's Arithmetica 93

11. The Great Art 109

12. Symbol Infancy 116

13. The Timid Symbol 127

14. Hierarchies of Dignity 133

15. Vowels and Consonants 141

16. The Explosion 150

17. A Catalogue of Symbols 160

18. The Symbol Master 165

19. The Last of the Magicians 169

Part 3 The Power of Symbols 177

20. Rendezvous in the Mind 179

21. The Good Symbol 189

22. Invisible Gorillas 192

23. Mental Pictures 210

24. Conclusion 216

Appendix A Leibniz’s Notation 221

Appendix B Newton’s Fluxion of xn 223

Appendix C Experiment 224

Appendix D Visualizing Complex Numbers 228

Appendix E Quaternions 230

Acknowledgments 233

Notes 235

Index 269

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Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers 4 out of 5 based on 0 ratings. 1 reviews.
Anonymous More than 1 year ago
This is a great account of the development of mathematical symbols and the associated history of mathematics. The content is first rate, but in a text about mathematical symbols, why are so many replaced with little squares? I would think that knowing the nature of the subject matter, the publishers of the electronic edition would have taken more care to preserve the symbols used. The section on the use of Hebrew letter as numbers ends up looking like some strange game of hopskotch. 5 stars for content, minus one star for typography.