AfterthedeeofaGreekcivilization,thedevelopmentofmathematiteredatroughinEurope,whiletheaese,Indian,andArabiancivilizationstiopromotetheprogressofmathematitesemathematicsfocusedonpracticarithmetidalgorithmthinking.TheamathematicalcssiineChaptersohematicalArtsystematicallysummarizedthealgorithmsoffieldmeasurement,graintransportation,engineeringcalcution,aionsolvinginaa,fapleteaarithmeticsystem.esemathematissuccessivelymadeworld-leadingachievementsinfraoperation,positiveaivenumberoperation,remaiheorem,andhigh-orderequationsolution.IndianmathematisiedthemodernArabiumeralsystem(0-9),perfectedthedecimaltihod,andidthefoundatilobalunifiednumericalcalcution.ArabianmathematisiedandiedthemathematicachievementsofGreedia,anda,sortedoutalgebraictheories,andpreservedandspreadthemathematicalcssicsofacivilizationsduringthemedievalEuropeandarkages,beinganimportantbridgefortheianddevelopmentofmathematics.
TheRenaissahe16thturyusheredinthegoldenageofmodernmathematics.Withtheliberationofhumanthoughtandthedevelopmentofastronomy,physidnavigation,mathematicsfaewdevelopmentdemands.Ihtury,Descartesfoundedanalytietry,unifiedgeometryandalgebraforthefirsttime,andrealizedthetransformatieometricfigureresearchtoalgebraicequationresearch,openingupanewfieldofmathematialysis.Subsequently,onandLeibnizindepelyiedcalculus,whichsolvedtheathematicalproblemsofvariablemotion,instantaneousvelocity,andcurvedareacalcutionthatcouldnotbesolvedbycssicalmathematics.Thebirthofcalculusmarkedtheentryofmathematitotheeraofvariablemathematitheeraofstantmathematidgreatlyexpaheboundaryofmathematicalresearch.
The18thand19thturieswithesystematizationandrefiofmodernmathematics.MathematissuchasEuler,Lagrange,andLapceperfectedthetheoreticalsystemofcalculusaablisheddisciplinessuchasdifferentialequations,analyticmeicsmathematidprobabilitytheory.Atthesametime,heory,projectivegeometry,non-Euclideary,andgrouptheoryweresuccessivelyestablished,makingmathematicsbranchmorediversifiedaicalsystemmorous.Ie19thtury,theaxiomatizatioofmathematicsrose,andmathematissortedoutthelogicalfoundationofvariousmathematicalbranches,makingmodernmathematiapleteandstandardizedtheoreticalsystem.
Ihtury,mathematiteredtheeraofmodernmathematicswithrapidexplosion.Withtheprogressofquantummeics,retivity,puterteology,andinformationsce,mathematicalresearchexpaomoreabstradcutting-edgefields.Topology,funanalysis,abstractalgebra,differentialgeometry,mathematicallogidotheremergingdisciplinesdevelopedrapidly.Atthesametime,theinterseathematidotherdisciplinesbecameincreasinglyclose,andinterdisciplinarymathematicssuchasmathematicalphysics,mathematicalbiology,financialmathematic
s,andputationalmathematicsemergedinrgenumbers.Itury,drivenbybigdata,artificialintelligendaerospaceteology,mathematicsisdevelopingtowardshigherabstra,stroerse,andwiderapplication,beingthecorebasicdisciplinesuppallmodernsdteology.
2.CoreBranodernMathematicsSystem
Modernmathematicshasformedahugeandrigorousdiscipliemafterthousandsofyearsofdevelopment.Acctoresearchobjects,researchmethods,anddisciplinaryattributes,itbedividedintofourcorefields:puremathematics,appliedmathematiputationalmathematidinterdisciplinarymathematics.Eachfieldtainsmultiplesubdividedbranches,whichareindepeofeachotherandcloselyinterected,jointlystitutingthepletemathematicalsystem.
2.1PureMathematics
Puremathematics,alsoknownasbasicmathematics,focusesonabstractmathematicaltheoriesandlogicalrules,takingmathematicalstructure,quantityretionship,spatialform,andlogicalwsasresearchobjects,adirectlytargetspecificpracticapplicationsarios.Itisthetheoreticalfoundationofallmathematicaldisciplinesandthesourathematinovation.Themaincorebranchesofpuremathematicludeheory,algebra,geometry,analysis,andmathematicallogic.
heoryisoheoldestbranchesofpuremathematics,takingintegersandintegerpropertiesasthemainresearchobjects.Itsreseartentsincludeelementaryheory,analytiumbertheory,algebraiumbertheory,andadditiveheory.Elementaryheorystudiesbasitegerpropertiessucha