Mathematics & Common Sense: A Case of Creative Tension

ISBN-13: 9781568812700 / Angielski / Twarda / 2006 / 288 str.

Philip J. Davis

Opis

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."

Spis treści

1. What Is Mathematics? 2. Mathematics and Common Sense: Relations and Contrasts. 3. How Common Sense Impacts Mathematical Reasoning: Some Very Simple Problems. 4. Where Is Mathematical Knowledge Lodged, and Where Does It Come From? 5. What Is Mathematical Intuition? 6. Are People Hard Wired to Do Mathematics? 7. Why Counting Is Impossible. 8. Quantification in Today’s World. 9. When Should One Add Two Numbers? 10. Category Dilemma. 11. Deductive Mathematics 12. Mathematics Brings Forth Entities Whose Existence Is Counterintuitive. 13. "In Principle We Can…". Mathematical Existentialism. 14. Mathematical Proof and Its Discontents. 15. The Logic of Mathematics Can Spawn Monsters . 16. Rules and Their Exceptions. 17. If Mathematics Says "No" Does It Really Mean It?.18. Inconsistencies and Their Virtues. 19. On Ambiguity in Mathematics. 20. Mathematical Evidence: Why Do I Believe a Theorem?.21. Simplicity, Complexity, Beauty. 22. The Decline and Resurgence of the Visual in Mathematics. 23. When Is a Problem Solved?.24. What Is Meant by the Word "Random"? 25. The Paradox of "Hitting It Big". 26. Probability and Common Sense: A Second Look. 27. Astrology as Early Applied Mathematics. 28. Mumbo Math. 29. Math Mixes It Up with Baseball. 30. Mickey Flies the Stealth: Mathematics, War, and Entertainment. 31. The Media and Mathematics Look at Each Other. 32. Platonism vs. Social Constructivism. 33. Mathematics at the Razor’s Edge

O autorze

Davis\, Philip J.