How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create MathematicsTo 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. |
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... 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 ...
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How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to ... William Byers No preview available - 2007 |