Contents

Chapters in this book

1. Frontmatter i
2. Contents v
3. Acknowledgments vii
4. INTRODUCTION. Turning on the Light 1
5. Section I. The Light of Ambiguity
6. Introduction 23
7. Chapter 1. Ambiguity in Mathematics 25
8. Chapter 2. The Contradictory in Mathematics 80
9. Chapter 3. Paradoxes and Mathematics: Infinity and the Real Numbers 110
10. Chapter 4. More Paradoxes of Infinity: Geometry, Cardinality, and Beyond 146
11. Section II. The Light as Idea
12. Introduction 191
13. Chapter 5. The Idea as an Organizing Principle 193
14. Chapter 6. Ideas, Logic, and Paradox 253
15. Chapter 7. Great Ideas 284
16. Section III. The Light and the Eye of the Beholder
17. Introduction 325
18. Chapter 8. The Truth of Mathematics 327
19. Chapter 9. Conclusion: Is Mathematics Algorithmic or Creative? 368
20. Notes 389
21. Bibliography 399
22. Index 407