LEADER 04437nam 2200685 450 001 9910465246403321 005 20211005170157.0 010 $a9781400833955$belectronic book 010 $a1-282-53145-X 010 $a1-4008-3395-7 010 $a0-691-12738-7 024 7 $a10.1515/9781400833955 035 $a(CKB)2560000000324435 035 $a(SSID)ssj0000361285 035 $a(PQKBManifestationID)11305314 035 $a(PQKBTitleCode)TC0000361285 035 $a(PQKBWorkID)10353109 035 $a(PQKB)10024595 035 $a(MiAaPQ)EBC485784 035 $a(DE-B1597)446394 035 $a(OCoLC)979779657 035 $a(DE-B1597)9781400833955 035 $a(Au-PeEL)EBL485784 035 $a(CaPaEBR)ebr10376732 035 $a(CaONFJC)MIL253145 035 $a(OCoLC)609856422 035 $a(EXLCZ)992560000000324435 100 $a20061004h20072007 uy 0 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aHow mathematicians think $eusing ambiguity, contradiction, and paradox to create mathematics /$fWilliam Byers 205 $aCourse Book 210 1$aPrinceton, NJ :$cPrinceton University Press,$d2007. 210 4$dİ2007 215 $a1 online resource (vii, 415 pages) $cillustration 300 $aBibliographic Level Mode of Issuance: Monograph 311 1 $a0-691-15091-5 311 08$aPrint version: 9780691145990 0-691-14599-7 320 $aIncludes bibliographical references (pages 399-405) and index. 327 $tFrontmatter --$tContents --$tAcknowledgments --$tINTRODUCTION. Turning on the Light --$tSection I. The Light of Ambiguity --$tIntroduction --$tChapter 1. Ambiguity in Mathematics --$tChapter 2. The Contradictory in Mathematics --$tChapter 3. Paradoxes and Mathematics: Infinity and the Real Numbers --$tChapter 4. More Paradoxes of Infinity: Geometry, Cardinality, and Beyond --$tSection II. The Light as Idea --$tIntroduction --$tChapter 5. The Idea as an Organizing Principle --$tChapter 6. Ideas, Logic, and Paradox --$tChapter 7. Great Ideas --$tSection III. The Light and the Eye of the Beholder --$tIntroduction --$tChapter 8. The Truth of Mathematics --$tChapter 9. Conclusion: Is Mathematics Algorithmic or Creative? --$tNotes --$tBibliography --$tIndex 330 $aTo 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. 606 $aMathematicians$xPsychology 606 $aMathematics$xPsychological aspects 606 $aMathematics$xPhilosophy 608 $aElectronic books. 615 0$aMathematicians$xPsychology. 615 0$aMathematics$xPsychological aspects. 615 0$aMathematics$xPhilosophy. 676 $a510 700 $aByers$b William$f1943-$0944438 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910465246403321 996 $aHow mathematicians think$92475405 997 $aUNINA