ریاضیات و عقل سلیم: موردی از تنش خلاقانه

From the Preface: "This book is addressed to all who are curious about the nature of mathematics and its role in society. It is neither a text book nor a specialists' book. It consists of a number of loosely linked essays that may be read independently and for which I have tried to provide a leitmotif by throwing light on the relationship between mathematics and common sense. In these essays I hope to foster a critical attitude towards both the existence of common sense in mathematics and the ambiguous role that it can play." 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 Mathematics has long suffered in the public eye through portrayals of mathematicians as socially inept geniuses devoted to an arcane discipline. This work demonstrates how mathematics surrounds, imbues, and maintains our everyday lives. It takes the reader through a point-by-point explanation of many frequently asked questions about mathematics. Philip J. Davis. Includes Bibliographical References.