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1、TheNineChaptersontheMathematicalProceduresandLiuHui’sMathematicalTheoryGuoShuchunAbstractWhendiscussingancientmathematicaltheories,scholarsoftenlimitthem-selvestoGreekmathematicsand,especiallytoitsaxiomaticsystem,whichtheyuseasthestandardtoevaluatetraditionalma
2、thematicsinothercultures:whicheverfailedtoformanaxiomaticsystemisconsideredtobewithouttheory.Therefore,eventhosescholarswhohighlypraisetheachievementsinancientChinesemathe-maticsconsiderthat“thegreatestdeficiencyinoldChinesemathematicalthoughtwastheabsenceofthei
3、deaofrigorousproofs”andthatthereisnoformallogicinancientChinesemathematics;inparticularitdidnothavedeductivelogic.Theyfurthercontendthat,“intheflightfrompracticeintotherealmofpureintellect,Chinesemathematicsdidnotparticipate,”[5,p.151]1andconcludethatChinesemath
4、ematicshasnotheory.IthinkthatLiuHui’scommentary(263A.D.)totheNineChaptersontheMathe-maticalProcedures,hereafterNineChapters,completelyprovedtheformulasandsolutionsinNineChapters.It,mainlybasedondeductivelogics,elucidateddeepmathematicaltheories.EventhoughNineCh
5、aptersitselfdoesnotcontainmathe-maticalreasoningandproofs,whichisamajorflawinthepursuitofmathematicaltheoryinthehistoryofChinesemathematics,therearecertaincorrectabstractpro-ceduresthatpossessageneralapplicabilitywhichshouldbeconsideredasmathe-maticaltheoriesinC
6、hinesemathematics.SirGeoffreyLloyd,afterexplainingthedifferencebetweenLiuHui’sandEuclid’smathematics,said“Maiscelanesignifiepasuneabsenced’inter´etpourlavalidationdesrˆesultatsoupourlarecherched’une´systematisation”[3,pr´eface,p.xi].Basedonthe´NineChapters,thisa
7、rticlewilldiscussLiuHui’scontributiontothemathematicaltheoryinordertostimulatemorefruitfuldiscussions.GuoShuchunInstitutefortheHistoryofNaturalScience,ChineseAcademyofSciences,55ZhongGuanCunDongLu,ZhongGuanCun,Beijing100190,P.R.Chinae-mail:shuchunguo@gmail.com1
8、NeedhamcitedtheclaimthatChinesemathematicslacks“rigorousproofs,”fromhiscorrespon-dencewiththeJapanesehistorianofChinesemathematics,YoshioMikami[三上義夫].E.Knoblochetal.(eds.),S
