Abstraction (mathematics)

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.^[1]^[2]^[3] In other words, to be abstract is to remove context and application.^[4] Two of the most highly abstract areas of modern mathematics are category theory and model theory.

^ Bertrand Russell, in The Principles of Mathematics Volume 1 (pg 219), refers to "the principle of abstraction".
^ Robert B. Ash. A Primer of Abstract Mathematics. Cambridge University Press, Jan 1, 1998
^ The New American Encyclopedic Dictionary. Edited by Edward Thomas Roe, Le Roy Hooker, Thomas W. Handford. Pg 34
^ Donaldson, Neil. Introduction to Group Theory. p. 1.

[1] Bertrand Russell, in The Principles of Mathematics Volume 1 (pg 219), refers to "the principle of abstraction".

[2] Robert B. Ash. A Primer of Abstract Mathematics. Cambridge University Press, Jan 1, 1998

[3] The New American Encyclopedic Dictionary. Edited by Edward Thomas Roe, Le Roy Hooker, Thomas W. Handford. Pg 34

[4] Donaldson, Neil. Introduction to Group Theory. p. 1.

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