19. The Smile of Mona Lisa

Chapters in this book

1. Frontmatter i
2. Contents v
3. Preface vii
4. 1. Scientific Thinking 1
5. 2. What Is Mathematics? 5
6. 3. The Erlangen Program 11
7. 4. Mathematics and Ideologies 17
8. 5. The Unity of Mathematics 23
9. 6. A Glimpse into Algebraic Geometry and Arithmetic 29
10. 7. A Trip to Nancy with Alexander Grothendieck 34
11. 8. Structures 41
12. 9. The Computer and the Brain 46
13. 10. Mathematical Texts 52
14. 11.Honors 57
15. 12. Infinity: The Smoke Screen of the Gods 63
16. 13.Foundations 68
17. 14. Structures and Concept Creation 73
18. 15. Turing’s Apple 78
19. 16. Mathematical Invention: Psychology and Aesthetics 85
20. 17. The Circle Theorem and an Infinite- Dimensional Labyrinth 91
21. 18.Mistake! 97
22. 19. The Smile of Mona Lisa 103
23. 20. Tinkering and the Construction of Mathematical Theories 108
24. 21. The Strategy of Mathematical Invention 113
25. 22. Mathematical Physics and Emergent Behavior 119
26. 23. The Beauty of Mathematics 127
27. Notes 131
28. Index 157