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...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, NJ [u.a.]
Princeton Univ. Press
2007
|
| Subjects: | |
| Online Access: | Table of contents only Publisher description Inhaltsverzeichnis |
| 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, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results."--BOOK JACKET. |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | VII, 415 S. Ill., graph. Darst. |
| ISBN: | 9780691127385 0691127387 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV022447354 | ||
| 003 | DE-604 | ||
| 005 | 20130823 | ||
| 007 | t | ||
| 008 | 070531s2007 xxuad|| |||| 00||| eng d | ||
| 010 | |a 2006033160 | ||
| 020 | |a 9780691127385 |9 978-0-691-12738-5 | ||
| 020 | |a 0691127387 |c acidfree paper |9 0-691-12738-7 | ||
| 035 | |a (OCoLC)73502041 | ||
| 035 | |a (DE-599)BVBBV022447354 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-12 |a DE-703 |a DE-19 |a DE-83 |a DE-188 |a DE-11 | ||
| 050 | 0 | |a BF456.N7 | |
| 082 | 0 | |a 510.92 | |
| 084 | |a CC 2600 |0 (DE-625)17610: |2 rvk | ||
| 084 | |a SG 700 |0 (DE-625)143071: |2 rvk | ||
| 100 | 1 | |a Byers, William |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a How mathematicians think |b using ambiguity, contradiction, and paradox to create mathematics |c William Byers |
| 264 | 1 | |a Princeton, NJ [u.a.] |b Princeton Univ. Press |c 2007 | |
| 300 | |a VII, 415 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 520 | 1 | |a "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. | |
| 650 | 4 | |a Cognition numérique | |
| 650 | 4 | |a Mathématiciens - Psychologie | |
| 650 | 4 | |a Mathématiques - Philosophie | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Philosophie | |
| 650 | 4 | |a Psychologie | |
| 650 | 4 | |a Mathematicians |x Psychology | |
| 650 | 4 | |a Mathematics |x Psychological aspects | |
| 650 | 4 | |a Mathematics |x Philosophy | |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kreatives Denken |0 (DE-588)4165549-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Paradoxon |0 (DE-588)4044593-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Ambiguität |0 (DE-588)4138525-1 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 0 | 1 | |a Kreatives Denken |0 (DE-588)4165549-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 689 | 1 | 0 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 1 | 1 | |a Ambiguität |0 (DE-588)4138525-1 |D s |
| 689 | 1 | |5 DE-604 | |
| 689 | 2 | 0 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 2 | 1 | |a Paradoxon |0 (DE-588)4044593-8 |D s |
| 689 | 2 | |C b |5 DE-604 | |
| 856 | 4 | |u http://www.loc.gov/catdir/toc/ecip073/2006033160.html |3 Table of contents only | |
| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0704/2006033160-d.html |3 Publisher description | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u 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 |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-015655301 | ||
Record in the Search Index
| _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 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Byers, William |
| author_facet | Byers, William |
| author_role | aut |
| author_sort | Byers, William |
| author_variant | w b wb |
| building | Verbundindex |
| bvnumber | BV022447354 |
| callnumber-first | B - Philosophy, Psychology, Religion |
| callnumber-label | BF456 |
| callnumber-raw | BF456.N7 |
| callnumber-search | BF456.N7 |
| callnumber-sort | BF 3456 N7 |
| callnumber-subject | BF - Psychology |
| classification_rvk | CC 2600 SG 700 |
| ctrlnum | (OCoLC)73502041 (DE-599)BVBBV022447354 |
| dewey-full | 510.92 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510.92 |
| dewey-search | 510.92 |
| dewey-sort | 3510.92 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Philosophie |
| discipline_str_mv | Mathematik Philosophie |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>03134nam a2200661 c 4500</leader><controlfield tag="001">BV022447354</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20130823 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">070531s2007 xxuad|| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2006033160</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780691127385</subfield><subfield code="9">978-0-691-12738-5</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0691127387</subfield><subfield code="c">acidfree paper</subfield><subfield code="9">0-691-12738-7</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)73502041</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV022447354</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-703</subfield><subfield code="a">DE-19</subfield><subfield code="a">DE-83</subfield><subfield code="a">DE-188</subfield><subfield code="a">DE-11</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">BF456.N7</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510.92</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">CC 2600</subfield><subfield code="0">(DE-625)17610:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SG 700</subfield><subfield code="0">(DE-625)143071:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Byers, William</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">How mathematicians think</subfield><subfield code="b">using ambiguity, contradiction, and paradox to create mathematics</subfield><subfield code="c">William Byers</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Princeton, NJ [u.a.]</subfield><subfield code="b">Princeton Univ. Press</subfield><subfield code="c">2007</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VII, 415 S.</subfield><subfield code="b">Ill., graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index</subfield></datafield><datafield tag="520" ind1="1" ind2=" "><subfield code="a">"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.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Cognition numérique</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathématiciens - Psychologie</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathématiques - Philosophie</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Philosophie</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Psychologie</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematicians</subfield><subfield code="x">Psychology</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield><subfield code="x">Psychological aspects</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield><subfield code="x">Philosophy</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kreatives Denken</subfield><subfield code="0">(DE-588)4165549-7</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Paradoxon</subfield><subfield code="0">(DE-588)4044593-8</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Ambiguität</subfield><subfield code="0">(DE-588)4138525-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Kreatives Denken</subfield><subfield code="0">(DE-588)4165549-7</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="1" ind2="0"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2="1"><subfield code="a">Ambiguität</subfield><subfield code="0">(DE-588)4138525-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="1" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="689" ind1="2" ind2="0"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2="1"><subfield code="a">Paradoxon</subfield><subfield code="0">(DE-588)4044593-8</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="2" ind2=" "><subfield code="C">b</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="u">http://www.loc.gov/catdir/toc/ecip073/2006033160.html</subfield><subfield code="3">Table of contents only</subfield></datafield><datafield tag="856" ind1="4" ind2=" "><subfield code="u">http://www.loc.gov/catdir/enhancements/fy0704/2006033160-d.html</subfield><subfield code="3">Publisher description</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">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</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-015655301</subfield></datafield></record></collection> |
| id | DE-604.BV022447354 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:35:02Z |
| indexdate | 2024-07-09T20:57:47Z |
| institution | BVB |
| isbn | 9780691127385 0691127387 |
| language | English |
| lccn | 2006033160 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015655301 |
| oclc_num | 73502041 |
| open_access_boolean | |
| owner | DE-12 DE-703 DE-19 DE-BY-UBM DE-83 DE-188 DE-11 |
| owner_facet | DE-12 DE-703 DE-19 DE-BY-UBM DE-83 DE-188 DE-11 |
| physical | VII, 415 S. Ill., graph. Darst. |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Princeton Univ. Press |
| record_format | marc |
| 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 |
| subject_GND | (DE-588)4037944-9 (DE-588)4165549-7 (DE-588)4044593-8 (DE-588)4138525-1 |
| 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 |
| url | http://www.loc.gov/catdir/toc/ecip073/2006033160.html http://www.loc.gov/catdir/enhancements/fy0704/2006033160-d.html 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 |
| work_keys_str_mv | AT byerswilliam howmathematiciansthinkusingambiguitycontradictionandparadoxtocreatemathematics |