فهرست مطالب
Title page
Preface
1. Scientific Thinking
2. What Is Mathematics?
3. The Erlangen Program
4. Mathematics and Ideologies
5. The Unity of Mathematics
6. A Glimpse into Algebraic Geometry and Arithmetic
7. A Trip to Nancy with Alexander Grothendieck
8. Structures
9. The Computer and the Brain
10. Mathematical Texts
Il. Honors
12. Infinity: The Smoke Screen of the Gods
13. Foundations
14. Structures and Concept Creation
15. Turing\'s Apple
16. Mathematical Invention: Psychology and Aesthetics
17. The Circle Theorem and an Infinite-Dimensional Labyrinth
18. Mistake!
19. The Smile of Mona Lisa
20. Tinkering and the Construction of Mathematical Theories
21. The Strategy of Mathematical Invention
22. Mathematical Physics and Emergent Behavior
23. The Beauty of Mathematics
Notes
Index
Preface
1. Scientific Thinking
2. What Is Mathematics?
3. The Erlangen Program
4. Mathematics and Ideologies
5. The Unity of Mathematics
6. A Glimpse into Algebraic Geometry and Arithmetic
7. A Trip to Nancy with Alexander Grothendieck
8. Structures
9. The Computer and the Brain
10. Mathematical Texts
Il. Honors
12. Infinity: The Smoke Screen of the Gods
13. Foundations
14. Structures and Concept Creation
15. Turing\'s Apple
16. Mathematical Invention: Psychology and Aesthetics
17. The Circle Theorem and an Infinite-Dimensional Labyrinth
18. Mistake!
19. The Smile of Mona Lisa
20. Tinkering and the Construction of Mathematical Theories
21. The Strategy of Mathematical Invention
22. Mathematical Physics and Emergent Behavior
23. The Beauty of Mathematics
Notes
Index
