Mathematics & Common Sense: A Case of Creative Tension

by Davis; Philip J.

• ISBN13: 9781568812700
• ISBN10: 1568812701
• Format: Hardcover
• Copyright: 2006-11-30
• Publisher: A. K. Peters

Summary

Mathematics has long suffered in the public eye through portrayals of mathematicians as socially inept geniuses devoted to an arcane discipline. In this book Philip J. Davis addresses this image through a question-and-answer dialogue that lays to rest many of the misnomers and misunderstandings of mathematical study. Davis demonstrates how mathematics surrounds, imbues, and maintains our everyday lives: the digitization and automation of processes like pumping gas, withdrawing cash, and buying groceries are all fueled by mathematics. He takes the reader through a point-by-point explanation of many frequently asked questions about mathematics, gently introducing this "Handmaiden of Science" and telling you everything you've ever wanted to know about her.

Author Biography

Philip J. Davis was born in Lawrence, MA in 1923. He received both his BS and PhD in pure mathematics from Harvard University. He served as Chief for Numerical Analysis of the National Bureau of Standards in Washington, D.C. for five years, and since 1963 has been teaching at Brown University in Providence, RI, where he is now Professor Emeritus. Davis is co-author of The Mathematical Experience and Descartes' Dream, as well as several technical books.

Table of Contents

Preface	vii
Acknowledgments	xi
Letters to Christina: Answers to Frequently Asked Questions	xvii
Letters to Christina: Second Round	xxxi
1 What Is Mathematics?	1
2 Mathematics and Common Sense: Relations and Contrasts	9
3 How Common Sense Impacts Mathematical Reasoning: Some Very Simple Problems	21
4 Where Is Mathematical Knowledge Lodged, and Where Does It Come From?	29
5 What Is Mathematical Intuition?	37
6 Are People Hard Wired to Do Mathematics?	47
7 Why Counting Is Impossible	51
8 Quantification in Today's World	61
9 When Should One Add Two Numbers?	67
10 Category Dilemmas	71
11 Deductive Mathematics	75
12 Mathematics Brings Forth Entities Whose Existence Is Counterintuitive	81
13 "In Principle We Can...": Mathematical Existentialism	91
14 Mathematical Proof and Its Discontents	95
15 The Logic of Mathematics Can Spawn Monsters	99
16 Rules and Their Exceptions	103
17 If Mathematics Says "No" Does It Really Mean It?	107
18 Inconsistencies and Their Virtues	117
19 On Ambiguity in Mathematics	125
20 Mathematical Evidence: Why Do I Believe a Theorem?	129
21 Simplicity, Complexity, Beauty	141
22 The Decline and Resurgence of the Visual in Mathematics	147
23 When Is a Problem Solved?	163
24 What Is Meant by the Word "Random"?	179
25 The Paradox of "Hitting It Big"	185
26 Probability and Common Sense: A Second Look	191
27 Astrology as Early Applied Mathematics	195
28 Mumbo Math	201
29 Math Mixes It Up with Baseball	207
30 Mickey Flies the Stealth: Mathematics, War, and Entertainment	211
31 The Media and Mathematics Look at Each Other	219
32 Platonism vs. Social Constructivism	231
33 Mathematics at the Razor's Edge	237