Kapitel in diesem Buch

1. Frontmatter i
2. Contents vii
3. Foreword xi
4. Introduction xv
5. Mathematics Alive
6. The Role of the Untrue in Mathematics 1
7. Desperately Seeking Mathematical Proof 13
8. An Enduring Error 18
9. What Is Experimental Mathematics 32
10. What Is Information-Based Complexity 37
11. What Is Financial Mathematics 43
12. If Mathematics Is a Language, How Do You Swear in It 47
13. Mathematicians and the Practice of Mathematics
14. Birds and Frogs 57
15. Mathematics Is Not a Game But . . . 79
16. Massively Collaborative Mathematics 89
17. Bridging the Two Cultures: Paul Valéry 94
18. A Hidden Praise of Mathematics 99
19. Mathematics and Its Applications
20. Mathematics and the Internet: A Source of Enormous Confusion and Great Potential 109
21. The Higher Arithmetic: How to Count to a Zillion without Falling Off the End of the Number Line 134
22. Knowing When to Stop: How to Gamble If You Must—The Mathematics of Optimal Stopping 145
23. Homology: An Idea Whose Time Has Come 158
24. Mathematics Education
25. Adolescent Learning and Secondary Mathematics 163
26. Accommodations of Learning Disabilities in Mathematics Courses 175
27. Audience, Style and Criticism 194
28. Aesthetics as a Liberating Force in Mathematics Education 206
29. Mathematics Textbooks and Their Potential Role in Supporting Misconceptions 236
30. Exploring Curvature with Paper Models 247
31. Intuitive vs Analytical Thinking: Four Perspectives 260
32. History and Philosophy of Mathematics
33. Why Did Lagrange “Prove” the Parallel Postulate 283
34. Kronecker’s Algorithmic Mathematics 303
35. Indiscrete Variations on Gian-Carlo Rota’s Themes 311
36. Circle Packing: A Personal Reminiscence 330
37. Applying Inconsistent Mathematics 346
38. Why Do We Believe Theorems 358
39. Mathematics in the Media
40. Mathematicians Solve 45-Year-Old Kervaire Invariant Puzzle 373
41. Darwin: The Reluctant Mathematician 377
42. Loves Me, Loves Me Not (Do the Math) 380
43. The Mysterious Equilibrium of Zombies and Other Things Mathematicians See at the Movies 383
44. Strength in Numbers: On Mathematics and Musical Rhythm 387
45. Math-hattan 391
46. Contributors 395
47. Acknowledgments 403
48. Credits 405