the art of the infinite - the pleasures of math

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TheTowerofMathematicsistheTowerofBabelinverted:itsvoicesgrowmorecoherentasitrises.TheimageofitisbasedonPieterBrueghel’s“LittleTowerofBabel”(1554).

 RobertKaplanandEllenKaplanIllustrationsbyEllenKaplan2003OxfordNewYorkAuckland

2、BangkokBuenosAiresCapeTownChennaiDaresSalaamDelhiHongKongIstanbulKarachiKolkataKualaLumpurMadridMelbourneMexicoCityMumbaiNairobiSãoPauloShanghaiTaipeiTokyoTorontoCopyright©2003byRobertKaplanandEllenKaplanPublishedbyOxfordUniversityPress,Inc.198MadisonAvenue,NewYork,NewYork10016www.oup-usa.

3、orgOxfordisaregisteredtrademarkofOxfordUniversityPressAllrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recording,orotherwise,withoutthepriorpermissionofOxfordUniversityPress.LibraryofCon

4、gressCataloging-in-PublicationDataisavailableISBN-0-19-514743-XAlsobyRobertKaplanTheNothingThatIs:ANaturalHistoryofZero135798642PrintedintheUnitedStatesofAmericaonacid-freepaperForMichael,Jane,andFelixThispageintentionallyleftblank

 




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 Wehavebeenunusuallyfortunateinourreaders,whofromfourdiffer-entperspectivesbroughtourbookintofocus.JeanJones,BarryMazur,JohnStillwell,andJimTantonputaquantityoftimeandqualityofthough

7、tintotheircomments,whichmadetheobscuretransparentandthecrookedstraight.Weareverygrateful.Thecommunityofmathematiciansismoregenerousthanmost.Ourthankstoallwhohavehelped,withspecialthankstoAndrewRanickiandPaddyPatterson.Noonecouldaskforbetterpeopletoworkwiththan