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How mathematicians think : Using ambiguity, contradiction, and paradox to create mathematics.

Author: William Byers
Publisher: Woodstock : Princeton University Press, 2010.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
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,  Read more...
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Document Type: Book
All Authors / Contributors: William Byers
ISBN: 9780691145990 0691145997 9780691127385 0691127387
OCLC Number: 769234189
Awards: Winner of Library Journal Best Reference Source Award 2007
Commended for Choice Magazine Outstanding Reference/Academic Book Award 2007
Runner-up for Choice Magazine Outstanding Reference/Academic Book Award 2007
Description: 415 s
Contents: Acknowledgments vii INTRODUCTION: Turning on the Light 1 SECTION I: THE LIGHT OF AMBIGUITY 21 CHAPTER 1: Ambiguity in Mathematics 25 CHAPTER 2: The Contradictory in Mathematics 80 CHAPTER 3: Paradoxes and Mathematics: Infinity and the Real Numbers 110 CHAPTER 4: More Paradoxes of Infinity: Geometry, Cardinality, and Beyond 146 SECTION II: THE LIGHT AS IDEA 189 CHAPTER 5: The Idea as an Organizing Principle 193 CHAPTER 6: Ideas, Logic, and Paradox 253 CHAPTER 7: Great Ideas 284 SECTION III: THE LIGHT AND THE EYE OF THE BEHOLDER 323 CHAPTER 8: The Truth of Mathematics 327 CHAPTER 9: Conclusion: Is Mathematics Algorithmic or Creative? 368 Notes 389 Bibliography 399 Index 407

Abstract:

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  Read more...

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Winner of the 2007 Best Sci-Tech Books in Mathematics, Library Journal One of Choice's Outstanding Academic Titles for 2007 "Ambitious, accessible and provocative...[In] How Mathematicians Think, Read more...

 
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