Mathematician

==Activities==
[[File:Noether.jpg|thumb|[[Emmy Noether]], mathematical theorist and teacher]]

===Applied mathematics===
{{main|Applied mathematics}}
Mathematicians involved with solving problems with applications in real life are called [[applied mathematician]]s. Applied mathematicians are mathematical scientists who, with their specialized knowledge and [[professional]] methodology, approach many of the imposing problems presented in related scientific fields. With professional focus on a wide variety of problems, theoretical systems, and localized constructs, applied mathematicians work regularly in the study and formulation of [[mathematical models]]. Mathematicians and applied mathematicians are considered to be two of the STEM (science, technology, engineering, and mathematics) careers.{{Citation needed|date=August 2015}}

The discipline of [[applied mathematics]] concerns itself with mathematical methods that are typically used in science, engineering, business, and industry; thus, "applied mathematics" is a [[mathematical science]] with specialized knowledge. The term "applied mathematics" also describes the [[professional]] specialty in which mathematicians work on problems, often concrete but sometimes abstract. As professionals focused on problem solving, ''applied mathematicians'' look into the ''formulation, study, and use of mathematical models'' in [[science]], [[engineering]], [[business]], and other areas of mathematical practice.

===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.

===Mathematics teaching===
Many professional mathematicians also engage in the teaching of mathematics. Duties may include:
* teaching university mathematics courses;
* supervising undergraduate and graduate research; and
* serving on academic committees.

===Consulting===
Many careers in mathematics outside of universities involve consulting. For instance, actuaries assemble and analyze data to estimate the probability and likely cost of the occurrence of an event such as death, sickness, injury, disability, or loss of property. Actuaries also address financial questions, including those involving the level of pension contributions required to produce a certain retirement income and the way in which a company should invest resources to maximize its return on investments in light of potential risk. Using their broad knowledge, actuaries help design and price insurance policies, pension plans, and other financial strategies in a manner which will help ensure that the plans are maintained on a sound financial basis.

As another example, mathematical finance will derive and extend the [[Mathematical model|mathematical]] or [[Numerical analysis|numerical]] models without necessarily establishing a link to financial theory, taking observed market prices as input. Mathematical consistency is required, not compatibility with economic theory. Thus, for example, while a financial economist might study the structural reasons why a company may have a certain [[share price]], a financial mathematician may take the share price as a given, and attempt to use [[stochastic calculus]] to obtain the corresponding value of [[Derivative (finance)|derivative]]s of the [[stock]] (''see: [[Valuation of options]]; [[Financial modeling#Quantitative finance|Financial modeling]]'').