How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create MathematicsPrinceton University Press, 02/05/2010 - 415 من الصفحات To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. |
المحتوى
INTRODUCTION | 1 |
CHAPTER 1 | 25 |
CHAPTER 2 | 66 |
The Contradictory in Mathematics | 80 |
CHAPTER 3 | 110 |
CHAPTER 4 | 136 |
CHAPTER 5 | 193 |
CHAPTER 9 | 200 |
Ideas Logic and Paradox | 253 |
CHAPTER 7 | 284 |
CHAPTER 8 | 327 |
Is Mathematics Algorithmic | 368 |
Notes | 389 |
407 | |