Joseph Mazur
Princeton University Press | 2014 | 312 páginas | rar - pdf (from html) | 4,15 Mb
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.
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
