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1、thearchitectureofmodernmathematicsTheArchitectureofModernMathematicsEssaysinHistoryandPhilosophyEditedbyJ.FERREIRÓSandJ.J.GRAY13GreatClarendonStreet,Oxfordox26dpOxfordUniversityPressisadepartmentoftheUniversityofOxford.ItfurtherstheUniversity’sobjective
2、ofexcellenceinresearch,scholarship,andeducationbypublishingworldwideinOxfordNewYorkAucklandCapeTownDaresSalaamHongKongKarachiKualaLumpurMadridMelbourneMexicoCityNairobiNewDelhiShanghaiTaipeiTorontoWithofficesinArgentinaAustriaBrazilChileCzechRepublicFran
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4、xfordUniversityPress,2006ThemoralrightsoftheauthorshavebeenassertedDatabaserightOxfordUniversityPress(maker)Firstpublished2006Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,withoutth
5、epriorpermissioninwritingofOxfordUniversityPress,orasexpresslypermittedbylaw,orundertermsagreedwiththeappropriatereprographicsrightsorganization.EnquiriesconcerningreproductionoutsidethescopeoftheaboveshouldbesenttotheRightsDepartment,OxfordUniversityPr
6、ess,attheaddressaboveYoumustnotcirculatethisbookinanyotherbindingorcoverandyoumustimposethesameconditiononanyacquirerBritishLibraryCataloguinginPublicationDataDataavailableLibraryofCongressCataloginginPublicationDataDataavailableTypesetbyNewgenImagingSy
7、stems(P)Ltd.,Chennai,IndiaPrintedinGreatBritainonacid-freepaperbyBiddlesLtd.,King’sLynn,NorfolkISBN0–19–856793–6978–0–19–856793–613579108642ContentsAcknowledgementsviiListofContributorsixIntroduction1J.FerreirósandJ.J.GrayREINTERPRETATIONSINTHEHISTORYAN
8、DPHILOSOPHYOFFOUNDATIONS45FregeandtheRoleofHistoricalElucidation:MethodologyandtheFoundationsofMathematics47MichaelBeaneyRiemann’sHabilitationsvortragattheCrossroadsofMathematics,Physics,andPhilosophy67JoséFerreirósTheRiemannianB