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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"This book provides an insightful synthesis of the historical and mental revolutions that created humanity's most useful symbols—mathematical expressions."—Stanislas Dehaene, author of Reading in the Brain

"Mathematical symbols are much more than squiggles on paper—they serve as potent sources of insight into a wonderfully complex language. In this book, Joseph Mazur takes us on a fascinating journey into the origins of these symbols. You cannot ask for a better guide."—Mario Livio, astrophysicist and author of Brilliant Blunders

"Joseph Mazur teaches us that the history of mathematical notation is the history of human civilization."—Kenneth A. Ribet, University of California, Berkeley

"In this thoughtful, entertaining, and carefully researched book, Mazur lays out the development of the mathematical notations and symbols that we take for granted. He offers a fascinating look at the history of the conventions of writing mathematical ideas, and shows how important our choice of conventions has been for the growth of mathematical knowledge."—Emily R. Grosholz, author of Representation and Productive Ambiguity in Mathematics and the Sciences

"Worldwide, mathematicians speak a common symbolic language. Mazur traces how symbols developed and gradually took hold, uniting arithmetic, algebra, and geometry to give us metaphors as powerful as those of poems. A fascinating history!"—Philip Holmes, coauthor of Celestial Encounters

"A curiosity cabinet of mathematical gems, curated by Joseph Mazur's cosmopolitan good taste."—Siobhan Roberts, author of Wind Wizard

"Enlightening Symbols explains the origins of symbols used in mathematics. But this fun book is so much more than this. Filled with interesting stories, captivating material, and delightful observations, it offers readers a better understanding of the nature of mathematics and a wonderful overview of mathematical history."—Dominic Klyve, Central Washington University

"An enjoyable and informative tour of mathematics history, Enlightening Symbols describes how our modern system of notation led to the abstraction we work with today. This is an important and interesting story."—Anna Pierrehumbert, Trinity School

Product Details

ISBN-13: 9780691154633
Publisher: Princeton University Press
Publication date: 03/23/2014
Pages: 312
Sales rank: 1,294,243
Product dimensions: 6.40(w) x 9.20(h) x 1.10(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.