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