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1、ThreemathematicalcrisisAncientMathematicsMedievalMathematicsEarlyModernMathematicsModernMathematicsClassificationMathematicsThefirstmathematicalcrisisInancientGreece,Pythagorasputforwardthefamousproposition"Allisnumber.Allthenumberscanbemarkedasintegerorintegerratio.''11d=?PythagorasSolution
2、ofthefirstmathematicalcrisisInabout370BC,Pythagoras'stwostudentssolvedthefirstcrisisofmathematicsbyintroducingtheconceptofincommensurablequantities(不可约通量)ingeometryorirrationalnumber(无理数).ButthiscrisiswascompletelysolvedintheNineteenthCentury,relyingontheestablishmentofrealnumbertheory.Influ
3、enceofthefirstmathematicalcrisisInfluenceofthefirstmathematicalcrisisishuge,whichgreatlypromotedthedevelopmentofmathematicsandrelatedsciences.Firstofall,thefirstmathematicalcrisismadepeopleawareoftheexistenceoftheirrationalnumber(无理数),aftertheirrationalnumberwasborn,manymathematicians,formal
4、studyofirrationalnumbergavestrictdefinitionoftheirrationalnumberandproposedanewclassificationofrationalandirrationalnumbers,layingthefoundationforthedevelopmentofmathematicalanalysis.ThesecondmathematicalcrisisThesecondmathematicalcrisis'sgermination（萌芽）isinabout450BC,fromthehistoricalandlog
5、icalpointofview,thiscrisisisinevitable.IthappenedinseventeenthCentury,whenNewtonfoundedthecalculus.Itwastriggeredby''Bekele'srevolt''.Bekeleasked:"infinitesimal"(无穷小量)asaquantity,isitexactly0?Thefamousparadox------BekeleparadoxBekeleNewtonSolutionofthesecondmathematicalcrisisUntilthenineteen
6、thCentury,Cauchydetailedlyandsystematicallydevelopedofthelimittheory.Weistrassfoundedthelimittheory.Inaddition,thetheoryofrealnumbers,settheorywereestablished,thusfreeinginfinitesimal（无穷小量）frommetaphysical(形而上学的)fetters（束缚）.CauchyWeistrassInfluenceofthesecondmathematicalcrisisThesecondmathem
7、aticalcrisisbeganwithpeople‘sexplorationoftheinfinitequantity,whileBekeleparadoxisthedirectcauseofthiscrisis.Theprocessofsolvingthiscrisisledtotheglamour(辉煌)ofanalyticsintheeighteenthCentury,soitiscalled"theageofanalysis"(分析时代).Thethirdmathematical
