Set theory

branch of mathematics that studies sets, which are collections of objects

Set theory is the branch of mathematical logic that studies sets, which informally are collections of objects.

QuotesEdit

  • Does set theory, once we get beyond the integers, refer to an existing reality, or must it be regarded, as formalists would regard it, as an interesting formal game? ... A typical argument for the objective reality of set theory is that it is obtained by extrapolation from our intuitions of finite objects, and people see no reason why this has less validity. Moreover, set theory has been studied for a long time with no hint of a contradiction. It is suggested that this cannot be an accident, and thus set theory reflects an existing reality. In particular, the Continuum Hypothesis and related statements are true or false, and our task is to resolve them.
    • Paul Cohen: (2005). "Skolem and pessimism about proof in mathematics". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 363 (1835): 2407–2418. ISSN 1364-503X. DOI:10.1098/rsta.2005.1661. (quote from p. 2416)

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Mathematics
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Numbers

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Concepts

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Results

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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

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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