Mathematician

===Pure mathematics===
{{main|Pure mathematics}}
[[Pure mathematics]] is [[mathematics]] that studies entirely abstract [[concept]]s. From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as ''speculative mathematics'',<ref>See for example titles of works by [[Thomas Simpson]] from the mid-18th century: ''Essays on Several Curious and Useful Subjects in Speculative and Mixed Mathematicks'', ''Miscellaneous Tracts on Some Curious and Very Interesting Subjects in Mechanics, Physical Astronomy and Speculative Mathematics''.{{Cite EB1911 |wstitle=Simpson, Thomas |volume=25 |page=135}}</ref> and at variance with the trend towards meeting the needs of [[navigation]], [[astronomy]], [[physics]], [[economics]], [[engineering]], and other applications.

Another insightful view put forth is that ''pure mathematics is not necessarily [[applied mathematics]]'': it is possible to study abstract entities with respect to their intrinsic nature, and not be concerned with how they manifest in the real world.<ref name="Magid">Andy Magid, Letter from the Editor, in ''Notices of the AMS'', November 2005, American Mathematical Society, p.1173. [https://www.ams.org/notices/200510/commentary.pdf] {{Webarchive|url=https://web.archive.org/web/20160303182222/http://www.ams.org/notices/200510/commentary.pdf|date=2016-03-03}}</ref> Even though the pure and applied viewpoints are distinct philosophical positions, in practice there is much overlap in the activity of pure and applied mathematicians.

To develop accurate models for describing the real world, many applied mathematicians draw on tools and techniques that are often considered to be "pure" mathematics. On the other hand, many pure mathematicians draw on natural and social phenomena as inspiration for their abstract research.