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1、ÉLIECARTANANDHISMATHEMATICALWORKSHIING-SHENCHERNANDCLAUDECHEVALLEYAfteralongillnessÉlieCartandiedonMay6,1951,inParis.Hisdeathcameatatimewhenhisreputationandtheinfluenceofhisideaswereinfullascent.Undoubtedlyoneofthegreatestmathe•maticiansofthiscentury,h
2、iscareerwascharacterizedbyarareharmonyofgeniusandmodesty.ÊlieCartanwasbornonApril9,1869inDolomieu(Isère),avillageinthesouthofFrance.Hisfatherwasablacksmith.Cartan'selementaryeducationwasmadepossiblebyoneofthestatestipendsforgiftedchildren.In1888heenter
3、edthe"ÉcoleNormaleSu•périeure,"wherehelearnedhighermathematicsfromsuchmastersasTannery,Picard,Darboux,andHermite.Hisresearchworkstartedwithhisfamousthesisoncontinuousgroups,asubjectsug•gestedtohimbyhisfellowstudentTresse,recentlyreturnedfromstudyingwit
4、hSophusLieinLeipzig.Cartan'sfirstteachingpositionwasatMontpellier,wherehewas"maîtredeconférences";hethenwentsuccessivelytoLyon,toNancy,andfinallyin1909toParis.HewasmadeaprofessorattheSorbonnein1912.Thereportonhisworkwhichwasthebasisforthispromotionwasw
5、rittenbyPoincaré;1thiswasoneofthecircumstancesinhiscareerofwhichheseemedtohavebeengenuinelyproud.HeremainedattheSorbonneuntilhisretirementin1940.Cartanwasanexcellentteacher;hislecturesweregratifyingintel•lectualexperiences,whichleftthestudentwithagener
6、allymistakenideathathehadgraspedalltherewasonthesubject.Itisthereforethemoresurprisingthatforalongtimehisideasdidnotexerttheinfluencetheysorichlydeservedtohaveonyoungmathematicians.ThiswasperhapspartlyduetoCartan'sextrememodesty.UnlikePoincaré,hedidnot
7、trytoavoidhavingstudentsworkunderhisdirection.However,hehadtoomuchofasenseofhumortoorganizearoundhimselfthekindofenthusiasticfanaticismwhichhelpstoformamathematicalschool.Ontheotherhand,thebulkofthemathematicalresearchwhichwasaccomplishedatthebeginning
8、ofthiscenturyinFrancecenteredaroundthetheoryofanalyticfunc•tions;thissubject,madeglamorousbytheachievementrepresented1ThisreportwasinpartpublishedinActaMath.vol.38(1921)pp.137-145.Itshouldbeofconsiderablehistoricinteresttohavenowacomple
