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, in...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ [u.a.]
Princeton Univ. Press
2007
|
| Schlagworte: | |
| Online-Zugang: | Table of contents only Publisher description Inhaltsverzeichnis |
| Zusammenfassung: | "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."--BOOK JACKET. |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | VII, 415 S. Ill., graph. Darst. |
| ISBN: | 9780691127385 0691127387 |
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Datensatz im Suchindex
| _version_ | 1804136525650198528 |
|---|---|
| adam_text | * 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
contents
Chapter 9
Conclusion: Is Mathematics Algorithmic
or Creative? 368
Notes 389
Bibliography 399
Index 407
VI
|
| adam_txt |
* 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
contents
Chapter 9
Conclusion: Is Mathematics Algorithmic
or Creative? 368
Notes 389
Bibliography 399
Index 407
VI |
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| discipline | Mathematik Philosophie |
| discipline_str_mv | Mathematik Philosophie |
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| spelling | Byers, William Verfasser aut How mathematicians think using ambiguity, contradiction, and paradox to create mathematics William Byers Princeton, NJ [u.a.] Princeton Univ. Press 2007 VII, 415 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index "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."--BOOK JACKET. Cognition numérique Mathématiciens - Psychologie Mathématiques - Philosophie Mathematik Philosophie Psychologie Mathematicians Psychology Mathematics Psychological aspects Mathematics Philosophy Mathematik (DE-588)4037944-9 gnd rswk-swf Kreatives Denken (DE-588)4165549-7 gnd rswk-swf Paradoxon (DE-588)4044593-8 gnd rswk-swf Ambiguität (DE-588)4138525-1 gnd rswk-swf Mathematik (DE-588)4037944-9 s Kreatives Denken (DE-588)4165549-7 s DE-604 Ambiguität (DE-588)4138525-1 s Paradoxon (DE-588)4044593-8 s b DE-604 http://www.loc.gov/catdir/toc/ecip073/2006033160.html Table of contents only http://www.loc.gov/catdir/enhancements/fy0704/2006033160-d.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015655301&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Byers, William How mathematicians think using ambiguity, contradiction, and paradox to create mathematics Cognition numérique Mathématiciens - Psychologie Mathématiques - Philosophie Mathematik Philosophie Psychologie Mathematicians Psychology Mathematics Psychological aspects Mathematics Philosophy Mathematik (DE-588)4037944-9 gnd Kreatives Denken (DE-588)4165549-7 gnd Paradoxon (DE-588)4044593-8 gnd Ambiguität (DE-588)4138525-1 gnd |
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| title | How mathematicians think using ambiguity, contradiction, and paradox to create mathematics |
| title_auth | How mathematicians think using ambiguity, contradiction, and paradox to create mathematics |
| title_exact_search | How mathematicians think using ambiguity, contradiction, and paradox to create mathematics |
| title_exact_search_txtP | How mathematicians think using ambiguity, contradiction, and paradox to create mathematics |
| title_full | How mathematicians think using ambiguity, contradiction, and paradox to create mathematics William Byers |
| title_fullStr | How mathematicians think using ambiguity, contradiction, and paradox to create mathematics William Byers |
| title_full_unstemmed | How mathematicians think using ambiguity, contradiction, and paradox to create mathematics William Byers |
| title_short | How mathematicians think |
| title_sort | how mathematicians think using ambiguity contradiction and paradox to create mathematics |
| title_sub | using ambiguity, contradiction, and paradox to create mathematics |
| topic | Cognition numérique Mathématiciens - Psychologie Mathématiques - Philosophie Mathematik Philosophie Psychologie Mathematicians Psychology Mathematics Psychological aspects Mathematics Philosophy Mathematik (DE-588)4037944-9 gnd Kreatives Denken (DE-588)4165549-7 gnd Paradoxon (DE-588)4044593-8 gnd Ambiguität (DE-588)4138525-1 gnd |
| topic_facet | Cognition numérique Mathématiciens - Psychologie Mathématiques - Philosophie Mathematik Philosophie Psychologie Mathematicians Psychology Mathematics Psychological aspects Mathematics Philosophy Kreatives Denken Paradoxon Ambiguität |
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