Характерен опит
Риман (3 снимки)
September17,1826,HewasborninBreselenz,asmalltownintheKingdomofHanover(nowGermany).HisfatherFriedrichBonnhardRiemannwasalocalLutheranpriest.Herankssecondamongsixchildren.Heisaquiet,sickandshyperson,wholikestobealoneallhislife.HiscolleagueDedekindisoneofthefewpeoplewhoknowhim.AccordingtoDadekin,inadditiontoRiemann'sreallybadphysicalcondition,heisalsoahypochondriasis.In1840,RiemannmovedtoHanovertolivewithhisgrandmotherandenteredmiddleschool.
In1842,afterthedeathofhisgrandmother,hemovedtoJohanneuminLüneburg.
In1846,RiemannenteredtheUniversityofGöttingentostudyphilosophyandtheology.Duringthistimehewenttolistentosomemathematicslectures,includingGauss'slectureonleastsquares.Aftergettingpermissionfromhisfather,heswitchedtomathematics.IwenttotheUniversityofBerlinfortwoyearsduringtheuniversity,andwasinfluencedbyC.G.J.JacobiandP.G.L.Dirichlet.
Inthespringof1847,RiemanntransferredtotheUniversityofBerlinandjoinedJacobi,DirichletandSteiner.HereturnedtoGöttingentwoyearslater.
In1851,hereceivedadoctoratedegreefromtheUniversityofGöttingen.
In1851,thenecessaryandsufficientconditionsforthederivabilityofcomplexvariablefunctions(ieCauchy-Riemannequation)weredemonstrated.WiththehelpofDirichlet'sprinciple,theRiemannmappingtheoremwasexpounded,whichbecamethebasisofthegeometrictheoryoffunctions.
In1853,theRiemannintegralwasdefinedandthecriteriafortheconvergenceoftrigonometricserieswerestudied.
In1854,hecarriedforwardGauss’sdifferentialgeometryresearchoncurvedsurfaces,proposedtousetheconceptofmanifoldstounderstandtheessenceofspace,andusethepositivedefinitequadraticunderstandingmetricdeterminedbythesquareofthedifferentialarclengthtoestablishLiTheconceptofMannspaceincludedEuclideangeometryandnon-Euclideangeometryintohissystem.
In1854,hemadehisdebutonthestageandgaveaspeechentitled"Theoryasthebasisofgeometry",whichcreatedRiemanniangeometryandprovidedamathematicalfoundationforEinstein'sgeneraltheoryofrelativity.
In1857,hewasawardedanon-staffprofessorattheUniversityofGöttingen
In1857,hepublishedaresearchpaperontheAbelianfunction,leadingtotheconceptofRiemannsurface,andcombiningAbelianintegralwithAbelianThetheoryofBellfunctionbroughttoanewturningpointandmadesystematicresearch.Amongthem,theRiemannsurfacehasbeenstudiedindepthfromtheperspectivesoftopology,analysis,andalgebraicgeometry.Hecreatedaseriesofconceptsthathadaprofoundimpactonthedevelopmentofalgebraictopology,andclarifiedtheRiemann-RochtheoremwhichwaslatersupplementedbyG.Roch.In1857,hewaspromotedtoasupernumeraryprofessorattheUniversityofGöttingen.In1859,hesucceededDirichletasaprofessor.Andpublishedthepaper"Onthenumberofprimenumberslessthanagivenvalue",andputforwardtheRiemannhypothesis.
През 1862 г. той се жени за Елизе Кох.
OnJuly20,1866,hediedoftuberculosisinSelascaduringhisthirdtriptoItalytorecuperate.
Основни вноски
In1859,thepaperonthedistributionofprimenumbers"Onthenumberofprimenumberslessthanagivenvalue"studiedtheRiemannzetafunctionandgaveAfterdiscussingtheintegralrepresentationofthezetafunctionandthefunctionalequationitsatisfies,hepointedoutthatthereisaprofoundconnectionbetweenthedistributionofprimenumbersandtheRiemannzetafunction.ThecoreofthisassociationistheintegralexpressionofJ(x).
In1854,Riemann'sspeechentitled"OntheHypothesisastheBasisofGeometry"publishedattheUniversityofGöttingenfoundedRiemanniangeometry.Riemannregardsthesurfaceitselfasanindependentgeometricentity,ratherthantreatingitasjustageometricentityinEuclideanspace.In1915,A.EinsteinusedRiemanniangeometryandtensoranalysistoolstocreateanewtheoryofgravity—generalrelativity.
Inaddition,hehasmadesignificantcontributionstopartialdifferentialequationsandtheirapplicationsinphysics.Itevenmadeimportantcontributionstophysicsitself,suchasheat,electromagneticnon-over-distanceinteraction,andshockwavetheory.
Riemann’sworkdirectlyaffectedthedevelopmentofmathematicsinthesecondhalfofthe19thcentury.Manyoutstandingmathematiciansre-examinedthetheoremsthatRiemannhadasserted.UndertheinfluenceofRiemann’sthought,manybranchesofmathematicsmadebrilliantachievements..
Riemannfirstputforwardnewideasandnewmethodsofusingcomplexvariablefunctiontheory,especiallyusingζfunctiontostudynumbertheory,whichopenedaneweraofanalyticnumbertheory,andhadaprofoundunderstandingofthedevelopmentofsingle-complexvariablefunctiontheory.Influence.Heisoneofthemostoriginalmathematiciansinthehistoryofmathematicsintheworld.Riemann'sworksarenotmany,buttheyareextremelyprofoundandrichinconceptcreationandimagination.
Името му се появява в риманова цетафункция, риманов интеграл, риманова лема, риманово многообразие, риманово пространство, теорема за картографиране на риман, проблем на риман-хилберт, уравнение на Коши-риман, матрица на риманова верига.
Върши работа
Riemann’sworksmainlyinclude:"BasicsoftheGeneralTheoryofFunctionsofSingleandComplexVariables","AssumptionsBasedonGeometry",and"UsingTrigonometricSeriestoRepresentFunctions"Possibility,"DifferentialEquationsinMathematicalPhysics"(co-authoredwithWeber),"EllipticFunctionTheory","Gravity,Electricity,andMagnetism","NumberofPrimeNumbersNotExceedingKnownNumbers",etc.
DaDejinpublishedthecompleteworksofRiemannin1876.TheRiemannstudentscollectedtheirlecturenotesandpublishedthemin1902asasupplementtothecompletecollection.
Хипотезата на Риман
OneoftheproblemsthatRiemannleftforposterityisthefamousХипотезата на Риман,whichwasproposedbyHilbertin1900.Theeighthquestionofthisquestionisnowlistedasoneofthesevenmajorproblemsofthemillennium.Whatitneedstosolveisthatthenon-trivialzeropointsoftheRiemannZetafunctionζ(s)arealllocatedonthestraightlineofthecomplexplaneRe(s)=1/2.Mathematicianscallthisstraightlinethecriticalline.Usingthisterminology,Riemann’sconjecturecanbeexpressedas:allnon-trivialzerosoftheRiemannζ(s)functionarelocatedonthecriticalline.
InSeptember2018,MichaelAtiyahdeclaredthatheprovedRiemann’sconjectureandwillbepresentedattheHeidelbergPrizeWinnersForumonSeptember24.OnSeptember24,MichaelAtiyahpostedapreprintofhisproofofRiemann'shypothesis(conjecture).
CharacterEvaluation
SirEddingtonsaid:"AgeometricscholarlikeRiemanncanalmostforeseemoreimportantfeaturesoftherealworld."
Гаус каза: "Риман... има креативен, активен и истински математически ум, с брилянтна и богата креативност."
ThehistorianofmodernmathematicsBellbelieves:"AsamathematicianThegreatnessofRiemannliesinthepowerfuluniversalityandunlimitedscopeofthemethodsandnewideasherevealedtopureandappliedmathematics."
TheGermanmathematicianKleinsaid:"RiemannhasWithextraordinaryintuitiveability,hisunderstandinggeniussurpassesallmathematiciansofthesamegeneration."