Editing Abstraction (mathematics) (section)

{{Short description|Process of extracting the underlying essence of a mathematical concept}}

'''Abstraction''' in [[mathematics]] is the process of extracting the underlying [[Mathematical structure|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]].<ref>[[Bertrand Russell]], in ''The Principles of Mathematics'' Volume 1 (pg 219), refers to "the principle of abstraction".</ref><ref>Robert B. Ash. A Primer of Abstract Mathematics. Cambridge University Press, Jan 1, 1998</ref><ref>The New American Encyclopedic Dictionary. Edited by Edward Thomas Roe, Le Roy Hooker, Thomas W. Handford. Pg [https://books.google.com/books?id=KhQLAQAAMAAJ&pg=PA34 34]</ref> In other words, to be abstract is to remove context and application.<ref>{{Cite book |last=Donaldson |first=Neil |title=Introduction to Group Theory |page=1 |language=en}}</ref> Two of the most highly abstract areas of modern mathematics are [[category theory]] and [[model theory]].