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."
Table of Contents
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
Davis\, Philip J.
" “There is hardly an aspect of human existence to which mathematics cannot contribute understanding - though that is not to say that the value of human life can be reduced to a set of equations. ... In bringing some of these crucial issues to a wider audience, Davis has made a valuable contribution to the public understanding of the importance of the subject.” -John Ball, New Scientist, November 2006
Davis is one of a very small group of mathematicians who are interested and able to step outside the community and take a hard look at what mathematics really 'is'. Its uses, misuses, customs, relations with the so-called 'real' world, psychology and deep nature are all grist for his voracious mill."" -David Mumford, Brown University, November 2006
is risky to trust common sense-especially when dealing with mathematics. Convincingly Phil Davis demonstrates this, first by answering a few harmless-sounding 'frequently asked questions' about his discipline and then by skillfully seducing the reader into the curious kernel of the most fascinating of all sciences: Mathematics (sometimes written with a capital M, sometimes with a lowercase m; sometimes pure, sometimes applied; sometimes familiar, sometimes strange, even to experts)."" -Rudolf Taschner, November 2006
on a long experience in mathematics as a researcher, teacher and popularizer, Davis reflects upon the subject from many points of view: not only its development and instruction, but also its overly modest status in society in general."" -Ivor Grattan-Guinness, November 2006
""The individual essays are well-written, often including amusing epigraphs and detailed bibliographies ... [and] quite interesting to read... Often I found that [Davis] articulated quite well opinions that I never knew I had."" -Darren Glass, MAA Reviews, April 2007
""The author provides many creative discussions and examples, varying from simple to more abstract structures of mathematics ... the book can be recommended to all who are interested in mathematics and its nature, beauty, and role in modern society and science."" -EMS, September 2007
""... this book was fun to read, and I recommend at least a perusal to undergraduate math students, graduate students in mathematics, and working mathematicians. Teachers of undergraduate math students should consider assigning certain essays as readings for their students. It gives a healthy view of our subject. "" -The Mathematical Intelligencer , May 2008"