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“Mazur” — // — : — page  — # Enlightening Symbols “Mazur” — // — : — page  — # Also by Joseph Mazur EuclidintheRainforest:DiscoveringUniversalTruth inLogicandMath(2006) Zeno’sParadox:UnravelingtheAncientMystery behindtheScienceofSpaceandTime(2007) What’sLuckGottoDowithIt?TheHistory,Mathematics, andPsychologyoftheGambler’sIllusion(2010) Edited Number:TheLanguageofScience(2007) “Mazur” — // — : — page  — # Enlightening Symbols A Short History of Mathematical Notation and Its Hidden Powers Joseph Mazur PrincetonUniversityPress PrincetonandOxford “Mazur” — // — : — page  — # Copyright©byJosephMazur Requestsforpermissiontoreproducematerialfromthisworkshouldbesentto Permissions,PrincetonUniversityPress PublishedbyPrincetonUniversityPress,WilliamStreet, Princeton,NewJersey IntheUnitedKingdom:PrincetonUniversityPress,OxfordStreet, Woodstock,OxfordshireOXTW press.princeton.edu AllRightsReserved LibraryofCongressCataloging-in-PublicationData Mazur,Joseph. Enlighteningsymbols:ashorthistoryofmathematicalnotationanditshidden powers/JosephMazur. pagescm Includesbibliographicalreferencesandindex. ISBN----(hardcover:alk.paper).Mathematical notation—History.I.Title. QA.M .(cid:156)—dc  BritishLibraryCataloging-in-PublicationDataisavailable ThisbookhasbeencomposedinMinionandCandida Printedonacid-freepaper.“ PrintedintheUnitedStatesofAmerica           “Mazur” — // — : — page v — # To my big brother, Barry, who taught me from 0 “Mazur” — // — : — page vi — # “Mazur” — // — : — page vii — # Contents Introduction ix Definitions xxi NoteontheIllustrations xxiii Part 1 Numerals 1 . CuriousBeginnings  . CertainAncientNumberSystems  . SilkandRoyalRoads  . TheIndianGift  . ArrivalinEurope  . TheArabGift  . LiberAbbaci  . RefutingOrigins  Part 2 Algebra 81 . SansSymbols  . Diophantus’sArithmetica  . TheGreatArt  . SymbolInfancy  . TheTimidSymbol  . HierarchiesofDignity  Contents vii “Mazur” — // — : — page viii — # . VowelsandConsonants  . TheExplosion  . ACatalogueofSymbols  . TheSymbolMaster  . TheLastoftheMagicians  Part 3 The Power of Symbols 177 . RendezvousintheMind  . TheGoodSymbol  . InvisibleGorillas  . MentalPictures  . Conclusion  AppendixALeibniz’sNotation  AppendixBNewton’sFluxionofxn  AppendixCExperiment  AppendixDVisualizingComplexNumbers  AppendixEQuaternions  Acknowledgments  Notes  Index  viii Contents “Mazur” — // — : — page ix — # Introduction Amathematician,amusician,andapsychologistwalkedintoabar... Severalyearsago,beforeIhadanythoughtsofwritingabookonthehistoryof symbols,IhadaconversationwithafewcolleaguesattheCavaTuracciolo,alittle winebar inthe villageof Bellagioon LakeComo. Thepsychologist declaredthat symbolshadbeenaroundlongbeforehumanshadaverballanguage,andthatthey areattherootsofthemostbasicandprimitivethoughts.Themusicianpointedout thatmodernmusicalnotationismostlyattributedtooneBenedictinemonkGuido d’Arezzo,wholivedattheturnofthefirstmillennium,butthatamoreprimitive formofsymbolnotationgoesalmostasfarbackasPhoenicianwriting.I,themath- ematician,astonishedmyfriendsbyrevealingthat,otherthannumerals,mathemat- icalsymbols—evenalgebraicequations—arerelativelyrecentcreations,andthatal- most all mathematical expressions were rhetorical before the end of the fifteenth century. “What?!”thepsychologistsnapped.“Whataboutmultiplication?Youmeanto tellusthattherewasnosymbolfor‘times’?” “Notbeforethesixteenth...maybeevenseventeenthcentury.” “Andequality?Whatabout‘equals’?themusicianasked. “Notbefore...oh...thesixteenthcentury.” “ButsurelyEuclidmusthavehadasymbolforaddition,”saidthepsychologist. “WhataboutthePythagoreantheorem,thatthingaboutaddingthesquaresofthe sidesofarighttriangle?” Introduction ix

Description:
While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols werent available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know
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Enlightening Symbols: A Short History of Mathematical Notation and Its Hidden Powers PDF

311 Pages·2014·29.22 MB·English
by  Joseph Mazur
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“Mazur” — // — : — page  — # Enlightening Symbols “Mazur” — // — : — page  — # Also by Joseph Mazur EuclidintheRainforest:DiscoveringUniversalTruth inLogicandMath(2006) Zeno’sParadox:UnravelingtheAncientMystery behindtheScienceofSpaceandTime(2007) What’sLuckGottoDowithIt?TheHistory,Mathematics, andPsychologyoftheGambler’sIllusion(2010) Edited Number:TheLanguageofScience(2007) “Mazur” — // — : — page  — # Enlightening Symbols A Short History of Mathematical Notation and Its Hidden Powers Joseph Mazur PrincetonUniversityPress PrincetonandOxford “Mazur” — // — : — page  — # Copyright©byJosephMazur Requestsforpermissiontoreproducematerialfromthisworkshouldbesentto Permissions,PrincetonUniversityPress PublishedbyPrincetonUniversityPress,WilliamStreet, Princeton,NewJersey IntheUnitedKingdom:PrincetonUniversityPress,OxfordStreet, Woodstock,OxfordshireOXTW press.princeton.edu AllRightsReserved LibraryofCongressCataloging-in-PublicationData Mazur,Joseph. Enlighteningsymbols:ashorthistoryofmathematicalnotationanditshidden powers/JosephMazur. pagescm Includesbibliographicalreferencesandindex. ISBN----(hardcover:alk.paper).Mathematical notation—History.I.Title. QA.M .(cid:156)—dc  BritishLibraryCataloging-in-PublicationDataisavailable ThisbookhasbeencomposedinMinionandCandida Printedonacid-freepaper.“ PrintedintheUnitedStatesofAmerica           “Mazur” — // — : — page v — # To my big brother, Barry, who taught me from 0 “Mazur” — // — : — page vi — # “Mazur” — // — : — page vii — # Contents Introduction ix Definitions xxi NoteontheIllustrations xxiii Part 1 Numerals 1 . CuriousBeginnings  . CertainAncientNumberSystems  . SilkandRoyalRoads  . TheIndianGift  . ArrivalinEurope  . TheArabGift  . LiberAbbaci  . RefutingOrigins  Part 2 Algebra 81 . SansSymbols  . Diophantus’sArithmetica  . TheGreatArt  . SymbolInfancy  . TheTimidSymbol  . HierarchiesofDignity  Contents vii “Mazur” — // — : — page viii — # . VowelsandConsonants  . TheExplosion  . ACatalogueofSymbols  . TheSymbolMaster  . TheLastoftheMagicians  Part 3 The Power of Symbols 177 . RendezvousintheMind  . TheGoodSymbol  . InvisibleGorillas  . MentalPictures  . Conclusion  AppendixALeibniz’sNotation  AppendixBNewton’sFluxionofxn  AppendixCExperiment  AppendixDVisualizingComplexNumbers  AppendixEQuaternions  Acknowledgments  Notes  Index  viii Contents “Mazur” — // — : — page ix — # Introduction Amathematician,amusician,andapsychologistwalkedintoabar... Severalyearsago,beforeIhadanythoughtsofwritingabookonthehistoryof symbols,IhadaconversationwithafewcolleaguesattheCavaTuracciolo,alittle winebar inthe villageof Bellagioon LakeComo. Thepsychologist declaredthat symbolshadbeenaroundlongbeforehumanshadaverballanguage,andthatthey areattherootsofthemostbasicandprimitivethoughts.Themusicianpointedout thatmodernmusicalnotationismostlyattributedtooneBenedictinemonkGuido d’Arezzo,wholivedattheturnofthefirstmillennium,butthatamoreprimitive formofsymbolnotationgoesalmostasfarbackasPhoenicianwriting.I,themath- ematician,astonishedmyfriendsbyrevealingthat,otherthannumerals,mathemat- icalsymbols—evenalgebraicequations—arerelativelyrecentcreations,andthatal- most all mathematical expressions were rhetorical before the end of the fifteenth century. “What?!”thepsychologistsnapped.“Whataboutmultiplication?Youmeanto tellusthattherewasnosymbolfor‘times’?” “Notbeforethesixteenth...maybeevenseventeenthcentury.” “Andequality?Whatabout‘equals’?themusicianasked. “Notbefore...oh...thesixteenthcentury.” “ButsurelyEuclidmusthavehadasymbolforaddition,”saidthepsychologist. “WhataboutthePythagoreantheorem,thatthingaboutaddingthesquaresofthe sidesofarighttriangle?” Introduction ix

Description:
While all of us regularly use basic math symbols such as those for plus, minus, and equals, few of us know that many of these symbols werent available before the sixteenth century. What did mathematicians rely on for their work before then? And how did mathematical notations evolve into what we know
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