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 dilemmas -- 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.