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Algebraic topology

From Wikiquote

Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces.

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AbelAnaxagorasArchimedesAristarchus of SamosAverroesArnoldBanachCantorCartanChernCohenDescartesDiophantusErdősEuclidEulerFourierGaussGödelGrassmannGrothendieckHamiltonHilbertHypatiaLagrangeLaplaceLeibnizMilnorNewtonvon NeumannNoetherPenrosePerelmanPoincaréPólyaPythagorasRiemannRussellSchwartzSerreTaoTarskiThalesTuringWeilWeylWilesWitten

Numbers

123360eπFibonacci numbersIrrational numberNegative numberNumberPrime numberQuaternionOctonion

Concepts

AbstractionAlgorithmsAxiomatic systemCompletenessDeductive reasoningDifferential equationDimensionEllipseElliptic curveExponential growthInfinityIntegrationGeodesicInductionProofPartial differential equationPrinciple of least actionPrisoner's dilemmaProbabilityRandomnessTheoremTopological spaceWave equation

Results

Euler's identityFermat's Last Theorem

Pure math

Abstract algebraAlgebraAnalysisAlgebraic geometry (Sheaf theory) • Algebraic topologyArithmeticCalculusCategory theoryCombinatoricsCommutative algebraComplex analysisDifferential calculusDifferential geometryDifferential topologyErgodic theoryFoundations of mathematicsFunctional analysisGame theoryGeometryGlobal analysisGraph theoryGroup theoryHarmonic analysisHomological algebraInvariant theoryLogicNon-Euclidean geometryNonstandard analysisNumber theoryNumerical analysisOperations researchRepresentation theoryRing theorySet theorySheaf theoryStatisticsSymplectic geometryTopology

Applied math

Computational fluid dynamicsEconometricsFluid mechanicsMathematical physicsScience

History of math

Ancient Greek mathematicsEuclid's ElementsHistory of algebraHistory of calculusHistory of logarithmsIndian mathematicsPrincipia Mathematica

Other

Mathematics and mysticismMathematics educationMathematics, from the points of view of the Mathematician and of the PhysicistPhilosophy of mathematicsUnification in science and mathematics