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1、BULLETIN(NewSeries)OFTHEAMERICANMATHEMATICALSOCIETYVolume37,Number1,Pages25{38S0273-0979(99)00801-0ArticleelectronicallypublishedonDecember21,1999THEPRESENTANDTHEFUTUREOFMATHEMATICALPHYSICSPROFESSORH.POINCAREWhatisthepresentstateofmathematicalphysics?Whatareitsproblems?Whatisitsfutur
2、e?Isitabouttochangeitsorientation?Willtheobjectandmethodsofthisscienceappearintenyearstoourimmediatesuccessorsinthesamelightastheyappeartous?Orarewetowitnessafar-reachingtransformation?Thesearethequestionsweareforcedtofaceto-dayattheoutsetofourinquiry.Itiseasytoask;diculttoanswer.Ifw
3、efelttemptedtohazardaprediction,weshouldeasilyresistthistemptationbystoppingtothinkofthenonsensethemosteminentscholarsofahundredyearsagowouldhavespokeninanswertothequestionofwhatthissciencewouldbeinthenineteenthcentury.Theywouldhavethoughtthemselvesboldintheirpredictions;andaftertheev
4、enthowtimidweshouldhavefoundthem!Donotexpectofmethereforeanykindofprophesy.Butif,likeallprudentphysicians,Irefusetogiveaprognosis,stillIcannotdenymyselfalittlediagnosis.Well,then,yes;therearesymptomsofaseriouscrisis,whichwouldseemtoindicatethatwemayexpectpresentlyatransformation.Howev
5、er,thereisnocauseforgreatanxiety.Weareassuredthatthepatientwillnotdie,andindeedwemayhopethatthiscrisiswillbesalutary,sincethehistoryofthepastwouldseemtoinsurethat.Infact,thiscrisisisnotthe rst,andinordertounderstandititiswelltorecallthosewhichhavegonebefore.Allowmeabriefhistoricalsket
6、ch.Mathematicalphysics,aswearewellaware,isano springofcelestialmechanics,whichgaveitbirthattheendoftheeighteenthcenturyatthemomentwhenithaditselfattaineditscompletedevelopment.Thechild,especiallyduringits rstyears,showedastrikingresemblancetoitsmother.Theastronomicaluniverseconsistsof
7、masses,undoubtedlyofgreatmagnitude,butseparatedbysuchimmensedistancesthattheyappeartousasmaterialpoints;thesepointsattracteachotherintheinverseratioofthesquaresoftheirdistances,andthisattractionistheonlyforcewhicha ectstheirmotion.Butifoursenseswerekeenenoughtoshowusallthedetailsofthe
8、bodie
