How mathematicians think using ambiguity, contradiction, and paradox to create mathematics
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...
Uloženo v:
| Hlavní autor: | |
|---|---|
| Médium: | E-kniha Kniha |
| Jazyk: | angličtina |
| Vydáno: |
Princeton, N.J. ; Woodstock
Princeton University Press
2010
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| Vydání: | 1 |
| Témata: | |
| ISBN: | 0691127387, 9780691145990, 9780691127385, 0691145997, 1400833957, 9781400833955 |
| On-line přístup: | Získat plný text |
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- How mathematicians think: using ambiguity, contradiction, and paradox to create mathematics -- Contents -- Acknowledgments -- Introduction: Turning on the Light -- Section I: The Light of Ambiguity -- Chapter 1: Ambiguity in Mathematics -- Chapter 2: The Contradictory in Mathematics -- Chapter 3: Paradoxes and Mathematics: Infinity and the Real Numbers -- Chapter 4: More Paradoxes of Infinity: Geometry, Cardinality, and Beyond -- Section II: The Light as Idea -- Chapter 5: The Idea as an Organizing Principle -- Chapter 6: Ideas, Logic, and Paradox -- Chapter 7: Great Ideas -- Section III: The Light and the Eye of the Beholder -- Chapter 8: The Truth of Mathematics -- Chapter 9: Conclusion: Is Mathematics Algorithmic or Creative? -- Notes -- Bibliography -- Index.
- Front Matter Table of Contents Acknowledgments INTRODUCTION CHAPTER 1: Ambiguity in Mathematics CHAPTER 2: The Contradictory in Mathematics CHAPTER 3: Paradoxes and Mathematics: CHAPTER 4: More Paradoxes of Infinity: CHAPTER 5: The Idea as an Organizing Principle CHAPTER 6: Ideas, Logic, and Paradox CHAPTER 7: Great Ideas CHAPTER 8: The Truth of Mathematics CHAPTER 9: Conclusion: Notes Bibliography Index
- Cover -- Title -- Copyright -- Contents -- Acknowledgments -- INTRODUCTION: Turning on the Light -- SECTION I: THE LIGHT OF AMBIGUITY -- CHAPTER 1 Ambiguity in Mathematics -- CHAPTER 2 The Contradictory in Mathematics -- CHAPTER 3 Paradoxes and Mathematics: Infinity and the Real Numbers -- CHAPTER 4 More Paradoxes of Infinity: Geometry, Cardinality, and Beyond -- SECTION II: THE LIGHT AS IDEA -- CHAPTER 5 The Idea as an Organizing Principle -- CHAPTER 6 Ideas, Logic, and Paradox -- CHAPTER 7 Great Ideas -- SECTION III: THE LIGHT AND THE EYE OF THE BEHOLDER -- CHAPTER 8 The Truth of Mathematics -- CHAPTER 9 Conclusion: Is Mathematics Algorithmic or Creative? -- Notes -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z
- Section I. The Light of Ambiguity --
- INTRODUCTION. Turning on the Light
- Chapter 5. The Idea as an Organizing Principle
- Chapter 3. Paradoxes and Mathematics: Infinity and the Real Numbers
- Chapter 1. Ambiguity in Mathematics
- Chapter 6. Ideas, Logic, and Paradox
- Index
- -
- Chapter 2. The Contradictory in Mathematics
- Chapter 7. Great Ideas
- Chapter 8. The Truth of Mathematics
- /
- Section III. The Light and the Eye of the Beholder --
- Chapter 9. Conclusion: Is Mathematics Algorithmic or Creative?
- Section II. The Light as Idea --
- Contents
- Chapter 4. More Paradoxes of Infinity: Geometry, Cardinality, and Beyond
- Acknowledgments
- Introduction
- Frontmatter --
- Notes
- Bibliography