Definition
Abstraction in mathematics is the process of extracting the underlying structures, patterns or properties of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalizing it so that it has wider applications or matching among other abstract descriptions of equivalent phenomena. In other words, to be abstract is to remove context and application. Two of the most highly abstract areas of modern mathematics are category theory and model theory.
Related concepts
Abstract algebraAbstract algebraic logicAbstract detailAbstract logicAbstract model theoryAbstract nonsenseAbstract structureAbstract thinkingAffine geometryAlgebraAnalytic geometryAreaArithmeticAssimilation (psychology)AxiomAxiomatic systemBertrand RussellBolyaiCarl Friedrich GaussCartesian co-ordinatesCategory theoryConceptConjectureDescartesErlangen programEuclid's ElementsFelix KleinFinite geometryGeneralizationGeometryGroup (mathematics)Hippocrates of ChiosInvariant (mathematics)MacTutor History of Mathematics archiveMathematical maturityMathematical proofMathematical structureMathematicsModel theoryN-dimensional spaceNikolai LobachevskyNon-Euclidean geometryPhenomenaProjective geometryRiemannSymmetry
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