Mathematics & Common Sense: A Case of Creative Tension

Contents......Page 6
Preface......Page 8
Acknowledgments......Page 12
Letters to Christina: Answers to Frequently Asked Questions......Page 18
Letters to Christina: Second Round......Page 32
1. What Is Mathematics?......Page 48
2. Mathematics and Common Sense: Relations and Contrasts......Page 56
3. How Common Sense Impacts Mathematical Reasoning: Some Very Simple Problems......Page 68
4. Where Is Mathematical Knowledge Lodged, and Where Does It Come From?......Page 76
5. What Is Mathematical Intuition?......Page 84
6. Are People Hard Wired to Do Mathematics?......Page 94
7. Why Counting Is Impossible......Page 98
8. Quantification in Today\'s World......Page 108
9. When Should One Add Two Numbers?......Page 114
10. Category Dilemmas......Page 118
11. Deductive Mathematics......Page 122
12. Mathematics Brings Forth Entities Whose Existence Is Counterintuitive......Page 128
13. \"In Principle We Can…\": Mathematical Existentialism......Page 138
14. Mathematical Proof and Its Discontents......Page 142
15. The Logic of Mathematics Can Spawn Monsters......Page 146
16. Rules and Their Exceptions......Page 150
17. If Mathematics Says \"No\" Does It Really Mean It?......Page 154
18. Inconsistencies and Their Virtues......Page 164
19. On Ambiguity in Mathematics......Page 172
20. Mathematical Evidence: Why Do I Believe a Theorem?......Page 176
21. Simplicity, Complexity, Beauty......Page 188
22. The Decline and Resurgence of the Visual in Mathematics......Page 194
23. When Is a Problem Solved?......Page 210
24. What Is Meant by the Word \"Random\"?......Page 226
25. The Paradox of \"Hitting It Big\"......Page 232
26. Probability and Common Sense: A Second Look......Page 238
27. Astrology as Early Applied Mathematics......Page 242
28. Mumbo Math......Page 248
29. Math Mixes It Up with Baseball......Page 254
30. Mickey Flies the Stealth: Mathematics, War, and Entertainment......Page 258
31. The Media and Mathematics Look at Each Other......Page 266
32. Platonism vs. Social Constructivism......Page 278
33. Mathematics at the Razor\'s Edge......Page 284