How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, N.J.
Princeton University Press
2010
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| Schlagworte: | |
| Online-Zugang: | Volltext Volltext |
| Beschreibung: | Main description: 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. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself |
| Beschreibung: | 1 Online-Ressource (424 S.) |
| ISBN: | 9781400833955 |
| DOI: | 10.1515/9781400833955 |
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| spelling | Byers, William Verfasser aut How Mathematicians Think Using Ambiguity, Contradiction, and Paradox to Create Mathematics Princeton, N.J. Princeton University Press 2010 1 Online-Ressource (424 S.) txt rdacontent c rdamedia cr rdacarrier Main description: 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. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself Ambiguität (DE-588)4138525-1 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Paradoxon (DE-588)4044593-8 gnd rswk-swf Kreatives Denken (DE-588)4165549-7 gnd rswk-swf Mathematik (DE-588)4037944-9 s Kreatives Denken (DE-588)4165549-7 s 1\p DE-604 Ambiguität (DE-588)4138525-1 s 2\p DE-604 Paradoxon (DE-588)4044593-8 s 3\p DE-604 https://doi.org/10.1515/9781400833955 Verlag Volltext http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400833955&searchTitles=true Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Byers, William How Mathematicians Think Using Ambiguity, Contradiction, and Paradox to Create Mathematics Ambiguität (DE-588)4138525-1 gnd Mathematik (DE-588)4037944-9 gnd Paradoxon (DE-588)4044593-8 gnd Kreatives Denken (DE-588)4165549-7 gnd |
| subject_GND | (DE-588)4138525-1 (DE-588)4037944-9 (DE-588)4044593-8 (DE-588)4165549-7 |
| 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_full | How Mathematicians Think Using Ambiguity, Contradiction, and Paradox to Create Mathematics |
| title_fullStr | How Mathematicians Think Using Ambiguity, Contradiction, and Paradox to Create Mathematics |
| title_full_unstemmed | How Mathematicians Think Using Ambiguity, Contradiction, and Paradox to Create Mathematics |
| 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 | Ambiguität (DE-588)4138525-1 gnd Mathematik (DE-588)4037944-9 gnd Paradoxon (DE-588)4044593-8 gnd Kreatives Denken (DE-588)4165549-7 gnd |
| topic_facet | Ambiguität Mathematik Paradoxon Kreatives Denken |
| url | https://doi.org/10.1515/9781400833955 http://www.degruyter.com/search?f_0=isbnissn&q_0=9781400833955&searchTitles=true |
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