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Bernhard Riemann | | Britannica

SUBSCRIBESUBSCRIBESUBSCRIBEHomeHistory & SocietyScience & TechBiographiesAnimals & NatureGeography & TravelArts & CultureProConMoneyGames & QuizzesVideosOn This DayOne Good FactDictionaryNew ArticlesHistory & SocietyLifestyles & Social IssuesPhilosophy & ReligionPolitics, Law & GovernmentWorld HistoryScience & TechHealth & MedicineScienceTechnologyBiographiesBrowse BiographiesAnimals & NatureBirds, Reptiles & Other VertebratesEnvironmentFossils & Geologic TimeInsects & Other InvertebratesMammalsPlantsGeography & TravelGeography & TravelArts & CultureEntertainment & Pop CultureLiteratureSports & RecreationVisual ArtsImage GalleriesPodcastsSummariesTop QuestionsLists and StoriesBritannica KidsAsk the ChatbotGames & QuizzesHistory & SocietyScience & TechBiographiesAnimals & NatureGeography & TravelArts & CultureProConMoneyVideosBernhard RiemannIntroductionReferences & Edit HistoryQuick Facts & Related TopicsImagesBernhard Riemann summaryFaces of ScienceNumbers and MathematicsPhysics and Natural LawAll About Math QuizWhat is Ptolemy best known for?How did Ptolemy impact the world?What were Ptolemy’s achievements?What did Werner Heisenberg do during World War II?What is Werner Heisenberg best known for?ScienceMathematicsFacebookXhttps://www.britannica.com/biography/Bernhard-RiemannUniversity of California, Berkeley - Department of Mathematics - Biography of Georg Friedrich Bernhard RiemanThe Story of Mathematics - Biography of RiemannBernhard Riemann - Student Encyclopedia (Ages 11 and up)Jeremy John Gray Emeritus Professor, School of Mathematics and Statistics, Open University. Author of Plato's Ghost; Henri Poincaré: A Scientific Biography; Ideas of Space; and others.Britannica Editors Encyclopaedia Britannica's editors oversee subject areas in which they have extensive knowledge, whether from years of experience gained by working on that content or via study for an advanced degree....HistorygeometryAlbert Einsteinrelativitycomplex analysisnumber theoryAdrien-Marie LegendremathematicsUniversity of GöttingenHumboldt University of BerlinsuccessiontuberculosisItalyEnrico BettiRichard DedekindBritannica Quiz Physics and Natural LawGermanyKarl WeierstrassintellectualconceptualFelix KleinDavid HilbertCarl Gaussiconicpolynomialcurvecomplex variableRiemann surfacegenustopologygeometrymanifoldEuclidean spacedimensioninfiniteEugenio Beltraminon-Euclidean geometryalternativeEuclidean geometryspace-timegeneral relativityphysicselectromagnetismgravitationfunctionzeta functionprimeRiemann zeta functionvaluelineAugustin-Louis CauchyRiemann hypothesishypothesisHanoverItalyRiemann hypothesisRiemann surfaceRiemann zeta functioncomplex variabledefinite integralmanifoldrelativityspaceunified field theorySee all related contentSUBSCRIBE Riemann took a novel view of what it means for mathematical objects to exist. He sought general existence proofs, rather than “constructive proofs” that actually produce the objects. He believed that this approach led to conceptual clarity and prevented the mathematician from getting lost in the details, but even some experts disagreed with such nonconstructive proofs. Riemann also studied how functions compare with their trigonometric or Fourier seriesilluminatesdifferential equationsgroup theorypartial differential equationsJeremy John Gray

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