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Abstraction (mathematics)

Abstraction in [mathematics] is the process of extracting the underlying essence of a mathematical concept, removing any dependence on real world objects with which it might originally have been connected, and generalising it so that it has wider applications or matching among other abstract descriptions of equivalent [phenomena] .

Many areas of mathematics began with the study of real world problems, before the underlying rules and concepts were identified and defined as [abstract structure] s. For example, [geometry] has its origins in the calculation of distances and areas in the real world; [statistics] has its origins in the calculation of probabilities in [gambling] ; and [algebra] started with methods of solving problems in [arithmetic] .

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