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: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton :
Princeton University Press,
©2007.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| 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."--Jacket |
| Beschreibung: | 1 online resource (vii, 415 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 399-405) and index. |
| ISBN: | 9781400833955 1400833957 9786612531453 6612531452 128253145X 9781282531451 |
Internformat
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| 245 | 1 | 0 | |a How mathematicians think : |b using ambiguity, contradiction, and paradox to create mathematics / |c William Byers. |
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| 504 | |a Includes bibliographical references (pages 399-405) and index. | ||
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| 588 | 0 | |a Print version record. | |
| 505 | 0 | 0 | |t Acknowledgments -- |t Introduction : Turning on the light -- |t Section 1 : The light of ambiguity |g ch. 1 -- |t Ambiguity in mathematics |g ch. 2 -- |t The contradictory in mathematics |g ch. 3 -- |t Paradoxes and mathematics : infinity and the real numbers |g ch. 4 -- |t More paradoxes of infinity : geometry, cardinality, and beyond -- |t Section 2 : The light as idea |g ch. 5. The -- |t idea as an organizing principle |g ch. 6 -- |t Ideas, logic, and paradox |g ch. 7 -- |t Great ideas -- |t Section 3 : The light and the eye of the beholder |g ch. 8. The -- |t truth of mathematics |g ch. 9 -- |t Conclusion : is mathematics algorithmic or creative? -- |t Notes -- |t Bibliography -- |t Index. |
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| contents | Acknowledgments -- Introduction : Turning on the light -- Section 1 : The light of ambiguity Ambiguity in mathematics The contradictory in mathematics Paradoxes and mathematics : infinity and the real numbers More paradoxes of infinity : geometry, cardinality, and beyond -- Section 2 : The light as idea idea as an organizing principle Ideas, logic, and paradox Great ideas -- Section 3 : The light and the eye of the beholder truth of mathematics Conclusion : is mathematics algorithmic or creative? -- Notes -- Bibliography -- Index. |
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| dewey-ones | 510 - Mathematics |
| dewey-raw | 510.92 |
| dewey-search | 510.92 |
| dewey-sort | 3510.92 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| indexdate | 2024-11-27T13:17:10Z |
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| publisher | Princeton University Press, |
| record_format | marc |
| spelling | Byers, William, 1943- How mathematicians think : using ambiguity, contradiction, and paradox to create mathematics / William Byers. Princeton : Princeton University Press, ©2007. 1 online resource (vii, 415 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier polychrome. rdacc http://rdaregistry.info/termList/RDAColourContent/1003 text file rdaft http://rdaregistry.info/termList/fileType/1002 Includes bibliographical references (pages 399-405) 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."--Jacket Print version record. Acknowledgments -- Introduction : Turning on the light -- Section 1 : The light of ambiguity ch. 1 -- Ambiguity in mathematics ch. 2 -- The contradictory in mathematics ch. 3 -- Paradoxes and mathematics : infinity and the real numbers ch. 4 -- More paradoxes of infinity : geometry, cardinality, and beyond -- Section 2 : The light as idea ch. 5. The -- idea as an organizing principle ch. 6 -- Ideas, logic, and paradox ch. 7 -- Great ideas -- Section 3 : The light and the eye of the beholder ch. 8. The -- truth of mathematics ch. 9 -- Conclusion : is mathematics algorithmic or creative? -- Notes -- Bibliography -- Index. English. Mathematicians Psychology. Mathematics Psychological aspects. Mathematics Philosophy. http://id.loc.gov/authorities/subjects/sh85082153 Mathématiciens Psychologie. Cognition numérique. Mathématiques Philosophie. Mathématiques Aspect psychologique. MATHEMATICS History & Philosophy. bisacsh Mathematicians Psychology fast Mathematics Philosophy fast Mathematics Psychological aspects fast Print version: Byers, William, 1943- How mathematicians think. Princeton : Princeton University Press, ©2007 9780691145990 (DLC) 2006033160 (OCoLC)73502041 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=313432 Volltext |
| spellingShingle | Byers, William, 1943- How mathematicians think : using ambiguity, contradiction, and paradox to create mathematics / Acknowledgments -- Introduction : Turning on the light -- Section 1 : The light of ambiguity Ambiguity in mathematics The contradictory in mathematics Paradoxes and mathematics : infinity and the real numbers More paradoxes of infinity : geometry, cardinality, and beyond -- Section 2 : The light as idea idea as an organizing principle Ideas, logic, and paradox Great ideas -- Section 3 : The light and the eye of the beholder truth of mathematics Conclusion : is mathematics algorithmic or creative? -- Notes -- Bibliography -- Index. Mathematicians Psychology. Mathematics Psychological aspects. Mathematics Philosophy. http://id.loc.gov/authorities/subjects/sh85082153 Mathématiciens Psychologie. Cognition numérique. Mathématiques Philosophie. Mathématiques Aspect psychologique. MATHEMATICS History & Philosophy. bisacsh Mathematicians Psychology fast Mathematics Philosophy fast Mathematics Psychological aspects fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85082153 |
| title | How mathematicians think : using ambiguity, contradiction, and paradox to create mathematics / |
| title_alt | Acknowledgments -- Introduction : Turning on the light -- Section 1 : The light of ambiguity Ambiguity in mathematics The contradictory in mathematics Paradoxes and mathematics : infinity and the real numbers More paradoxes of infinity : geometry, cardinality, and beyond -- Section 2 : The light as idea idea as an organizing principle Ideas, logic, and paradox Great ideas -- Section 3 : The light and the eye of the beholder truth of mathematics Conclusion : is mathematics algorithmic or creative? -- Notes -- Bibliography -- Index. |
| 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 / 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 | Mathematicians Psychology. Mathematics Psychological aspects. Mathematics Philosophy. http://id.loc.gov/authorities/subjects/sh85082153 Mathématiciens Psychologie. Cognition numérique. Mathématiques Philosophie. Mathématiques Aspect psychologique. MATHEMATICS History & Philosophy. bisacsh Mathematicians Psychology fast Mathematics Philosophy fast Mathematics Psychological aspects fast |
| topic_facet | Mathematicians Psychology. Mathematics Psychological aspects. Mathematics Philosophy. Mathématiciens Psychologie. Cognition numérique. Mathématiques Philosophie. Mathématiques Aspect psychologique. MATHEMATICS History & Philosophy. Mathematicians Psychology Mathematics Philosophy Mathematics Psychological aspects |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=313432 |
| work_keys_str_mv | AT byerswilliam howmathematiciansthinkusingambiguitycontradictionandparadoxtocreatemathematics |