Mathematician

{{short description|Person with an extensive knowledge of mathematics}}
{{pp|small=yes}}
{{More citations needed|date=April 2021}}{{Infobox Occupation
| name=Mathematician
|
official_names=
<!------------Details------------------->
| type= [[Academic]]
| activity_sector=
| image= [[image:Euclid.jpg|250px]]
| caption = [[Euclid]] (holding [[calipers]]), Greek mathematician, known as the "Father of Geometry"
| competencies=[[Mathematics]], [[analytical skill]]s and [[critical thinking]] skills
| formation= [[Doctoral degree]], occasionally [[master's degree]]
| employment_field= universities, <br/>private corporations, <br/>financial industry, <br/>government
| related_occupation= [[statistician]], [[actuary]]
}}

{{Math topics TOC}}

A '''mathematician''' is someone who uses an extensive knowledge of [[mathematics]] in their work, typically to solve [[mathematical problem]]s. Mathematicians are concerned with [[number]]s, [[data]], [[quantity]], [[mathematical structure|structure]], [[space]], [[Mathematical model|models]], and [[mathematics#Calculus and analysis|change]].

==History==
{{broader|History of mathematics}}

One of the earliest known mathematicians was [[Thales of Miletus]] ({{Circa|624|546 BC}}); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed.<ref>{{Harvnb|Boyer|1991|page=43}}.</ref> He is credited with the first use of deductive reasoning applied to [[geometry]], by deriving four corollaries to [[Thales's theorem]].

The number of known mathematicians grew when [[Pythagoras of Samos]] ({{Circa|582|507 BC}}) established the [[Pythagorean school]], whose doctrine it was that mathematics ruled the universe and whose motto was "All is number".<ref>{{Harvnb|Boyer|1991|page=49}}.</ref> It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins.

The first woman mathematician recorded by history was [[Hypatia]] of Alexandria ({{Circa|AD 350}} – 415). She succeeded her father as librarian at the Great Library and wrote many works on applied mathematics. Because of a political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells (some say roofing tiles).<ref>{{Cite web |title=Medieval Sourcebook: Socrates Scholasticus: The Murder of Hypatia (late 4th Cent.) from Ecclesiastical History, Bk VI: Chap. 15 |url=http://www.fordham.edu/halsall/source/hypatia.html |url-status=live |archive-url=https://web.archive.org/web/20140814182454/http://www.fordham.edu/halsall/source/hypatia.html |archive-date=2014-08-14 |access-date=2014-11-19 |website=[[Internet History Sourcebooks Project]]}}</ref>

Science and mathematics in the Islamic world during the Middle Ages followed various models and modes of funding varied based primarily on scholars. It was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas. Funding for translation of scientific texts in other languages was ongoing throughout the reign of certain caliphs,<ref>{{Harvnb|Abattouy|Renn|Weinig|2001}}.{{Page needed|date=August 2021}}</ref> and it turned out that certain scholars became experts in the works they translated, and in turn received further support for continuing to develop certain sciences. As these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences. An example of a translator and mathematician who benefited from this type of support was [[al-Khawarizmi]]. A notable feature of many scholars working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on [[optics]], [[Mathematics|maths]] and [[astronomy]] of [[Ibn al-Haytham]].

The [[Renaissance]] brought an increased emphasis on mathematics and science to Europe. During this period of transition from a mainly feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: [[Luca Pacioli]] (founder of [[accounting]]); [[Niccolò Fontana Tartaglia]] (notable engineer and bookkeeper); [[Gerolamo Cardano]] (earliest founder of probability and binomial expansion); [[Robert Recorde]] (physician) and [[François Viète]] (lawyer).

As time passed, many mathematicians gravitated towards universities. An emphasis on free thinking and experimentation had begun in Britain's oldest universities beginning in the seventeenth century at Oxford with the scientists [[Robert Hooke]] and [[Robert Boyle]], and at Cambridge where [[Isaac Newton]] was [[Lucasian Professor of Mathematics|Lucasian Professor of Mathematics & Physics]]. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the "regurgitation of knowledge" to "encourag[ing] productive thinking."<ref>Röhrs, "The Classical Idea of the University", ''Tradition and Reform of the University under an International Perspective'' p.20</ref> In 1810, Humboldt convinced the king of [[Prussia]], [[Frederick William III of Prussia|Fredrick William III]], to build a university in Berlin based on [[Friedrich Schleiermacher]]'s liberal ideas; the goal was to demonstrate the process of the discovery of knowledge and to teach students to "take account of fundamental laws of science in all their thinking." Thus, seminars and laboratories started to evolve.<ref>{{Harvnb|Rüegg|2004|pages=5–6}}.</ref>

British universities of this period adopted some approaches familiar to the Italian and German universities, but as they already enjoyed substantial freedoms and [[autonomy]] the changes there had begun with the [[Age of Enlightenment]], the same influences that inspired Humboldt. The Universities of [[University of Oxford|Oxford]] and [[University of Cambridge|Cambridge]] emphasized the importance of [[research]], arguably more authentically implementing Humboldt's idea of a university than even German universities, which were subject to state authority.<ref>{{Harvnb|Rüegg|2004|page=12}}.</ref> Overall, science (including mathematics) became the focus of universities in the 19th and 20th centuries. Students could conduct research in [[seminars]] or [[laboratories]] and began to produce doctoral theses with more scientific content.<ref>{{Harvnb|Rüegg|2004|page=13}}.</ref> According to Humboldt, the mission of the [[University of Berlin]] was to pursue scientific knowledge.<ref>{{Harvnb|Rüegg|2004|page=16}}.</ref> The German university system fostered professional, bureaucratically regulated scientific research performed in well-equipped laboratories, instead of the kind of research done by private and individual scholars in Great Britain and France.<ref>{{Harvnb|Rüegg|2004|pages=17–18}}.</ref> In fact, Rüegg asserts that the German system is responsible for the development of the modern research university because it focused on the idea of "freedom of scientific research, teaching and study."<ref>{{Harvnb|Rüegg|2004|page=31}}.</ref>

==Required education==
Mathematicians usually cover a breadth of topics within mathematics in their [[undergraduate education]], and then proceed to specialize in topics of their own choice at the [[graduate-level|graduate level]]. In some universities, a [[qualifying exam]] serves to test both the breadth and depth of a student's understanding of mathematics; the students who pass are permitted to work on a [[doctoral dissertation]].

==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]]'').

== Occupations ==
[[File:Occupations related to mathematics, WPA poster, ca. 1938.jpg|thumb|right|In 1938 in the United States, mathematicians were desired as teachers, calculating machine operators, mechanical engineers, accounting auditor bookkeepers, and actuary statisticians.]]
According to the [[Dictionary of Occupational Titles]] occupations in mathematics include the following.<ref>{{Cite web |title=020 OCCUPATIONS IN MATHEMATICS |url=http://occupationalinfo.org/defset1_3829.html |url-status=dead |archive-url=https://web.archive.org/web/20121102115159/http://occupationalinfo.org/defset1_3829.html |archive-date=2012-11-02 |access-date=2013-01-20 |website=Dictionary Of Occupational Titles}}</ref>

* Mathematician
* Operations-Research Analyst
* Mathematical Statistician
* Mathematical Technician
* [[Actuary]]
* Applied Statistician
* Weight Analyst

== Prizes in mathematics ==
There is no [[Nobel Prize]] in mathematics, though sometimes mathematicians have won the Nobel Prize in a different field, such as economics or physics. Prominent prizes in mathematics include the [[Abel Prize]], the [[Chern Medal]], the [[Fields Medal]], the [[Gauss Prize]], the [[Frederic Esser Nemmers Prize|Nemmers Prize]], the [[Balzan Prize]], the [[Crafoord Prize]], the [[Shaw Prize]], the [[Steele Prize]], the [[Wolf Prize]], the [[Schock Prize]], and the [[Nevanlinna Prize]].

The [[American Mathematical Society]], [[Association for Women in Mathematics]], and other mathematical societies offer several prizes aimed at increasing the representation of women and minorities in the future of mathematics.

==Mathematical autobiographies==
Several well known mathematicians have written autobiographies in part to explain to a general audience what it is about mathematics that has made them want to devote their lives to its study. These provide some of the best glimpses into what it means to be a mathematician. The following list contains some works that are not autobiographies, but rather essays on mathematics and mathematicians with strong autobiographical elements.

* ''The Book of My Life'' – [[Girolamo Cardano]]<ref>{{Citation |last=Cardano |first=Girolamo |title=The Book of My Life (De Vita Propria Liber) |year=2002 |publisher=The New York Review of Books |isbn=1-59017-016-4 |author-link=Girolamo Cardano}}</ref>
* ''[[A Mathematician's Apology]]'' - [[G.H. Hardy]]<ref>{{harvnb|Hardy|2012}}</ref>
* ''[[A Mathematician's Miscellany]]'' (republished as Littlewood's miscellany) - [[J. E. Littlewood]]<ref>{{Citation |last=Littlewood |first=J. E. |title=Littlewood's miscellany |url=https://archive.org/details/littlewoodsmisce0000litt |year=1990 |editor-last=Béla Bollobás |orig-year=Originally ''A Mathematician's Miscellany'' published in 1953 |publisher=Cambridge University Press |isbn=0-521-33702 X |author-link=J. E. Littlewood |url-access=registration}}</ref>
* ''I Am a Mathematician'' - [[Norbert Wiener]]<ref>{{Citation |last=Wiener |first=Norbert |title=I Am a Mathematician / The Later Life of a Prodigy |year=1956 |publisher=The M.I.T. Press |isbn=0-262-73007-3}}</ref>
* ''I Want to be a Mathematician'' - [[Paul R. Halmos]]
* ''Adventures of a Mathematician'' - [[Stanislaw Ulam]]<ref>{{Citation |last=Ulam |first=S. M. |title=Adventures of a Mathematician |url=https://archive.org/details/adventuresofmath0000ulam |year=1976 |publisher=Charles Scribner's Sons |isbn=0-684-14391-7 |url-access=registration}}</ref>
* ''Enigmas of Chance'' - [[Mark Kac]]<ref>{{Citation |last=Kac |first=Mark |title=Enigmas of Chance / An Autobiography |year=1987 |publisher=University of California Press |isbn=0-520-05986-7}}</ref>
* ''Random Curves'' - [[Neal Koblitz]]
* ''[[Edward Frenkel#Love and Math|Love and Math]]'' - [[Edward Frenkel]]
* ''Mathematics Without Apologies'' - [[Michael Harris (mathematician)|Michael Harris]]<ref>{{Citation |last=Harris |first=Michael |title=Mathematics without apologies / portrait of a problematic vocation |year=2015 |publisher=Princeton University Press |isbn=978-0-691-15423-7}}</ref>

== See also ==

{{Portal|Mathematics}}
* {{Annotated link|Lists of mathematicians}}
* {{Annotated link|List of films about mathematicians}}
* {{Annotated link|Human computer}}
* {{Annotated link|Mathematical joke}}
* {{Annotated link|A Mathematician's Apology|''A Mathematician's Apology''}}
* {{Annotated link|Men of Mathematics|''Men of Mathematics''}}
* {{Annotated link|Mental calculator}}
* {{Annotated link|Timeline of ancient Greek mathematicians}}

== Notes ==
{{Reflist|20em}}

==Bibliography==
{{Refbegin}}
* {{Cite journal |last1=Abattouy |first1=Mohammed |last2=Renn |first2=Jürgen |last3=Weinig |first3=Paul |year=2001 |title=Transmission as Transformation: The Translation Movements in the Medieval East and West in a Comparative Perspective |journal=Science in Context |volume=14 |issue=1–2 |pages=1–12 |doi=10.1017/S0269889701000011 |publisher=Cambridge University Press|s2cid=145190232 }}
* {{Cite book |last=Boyer |title=A History of Mathematics |year=1991}}
* {{Cite book |last=Dunham |first=William |author-link=William Dunham (mathematician) |title=The Mathematical Universe |publisher=John Wiley |year=1994}}
* {{Cite book |last=Halmos |first=Paul |title=I Want to Be a Mathematician |publisher=Springer-Verlag |year=1985}}
* {{Cite book |last=Hardy |first=G.H. |title=A Mathematician's Apology |publisher=Cambridge University Press |year=2012 |isbn=    978-1-107-60463-6 |author-link=G.H. Hardy |orig-year=1940 |oclc=942496876 |url=https://archive.org/details/mathematiciansap0000hard_u4z4/ |url-access=registration |edition=Reprinted with foreword}}
* {{Cite encyclopedia |last=Rüegg |first=Walter |title=Themes |encyclopedia=A History of the University in Europe |year=2004 |volume=3 |publisher=Cambridge University Press |isbn=978-0-521-36107-1 |editor-last=Rüegg |editor-first=Walter}}
{{Refend}}

==Further reading==
* {{Citation |last=Krantz |first=Steven G. |title=A Mathematician comes of age |year=2012 |publisher=[[The Mathematical Association of America]] |isbn=978-0-88385-578-2 |author-link=Steven G. Krantz}}

==External links==
{{Wikiquote|Mathematicians}}
{{Commons category|Mathematicians}}
* [https://web.archive.org/web/20070206151209/http://stats.bls.gov/oco/ocos043.htm Occupational Outlook: Mathematicians]. Information on the occupation of mathematician from the US Department of Labor.
* [https://web.archive.org/web/20070609220806/http://www.careercornerstone.org/math/math.htm Sloan Career Cornerstone Center: Careers in Mathematics]. Although US-centric, a useful resource for anyone interested in a career as a mathematician. Learn what mathematicians do on a daily basis, where they work, how much they earn, and more.
* [https://mathshistory.st-andrews.ac.uk The MacTutor History of Mathematics archive]. A comprehensive list of detailed biographies.
* [http://genealogy.math.ndsu.nodak.edu/ The Mathematics Genealogy Project]. Allows scholars to follow the succession of thesis advisors for most mathematicians, living or dead.
* {{MathWorld|urlname=UnsolvedProblems|title=Unsolved Problems}}
* [https://archive.today/20121214194422/http://valure.wiki.ccsd.edu/ Middle School Mathematician Project] Short biographies of select mathematicians assembled by middle school students.
* [http://www.mathmajor.org/careers Career Information for Students of Math and Aspiring Mathematicians]{{dead link|date=January 2018 |bot=InternetArchiveBot |fix-attempted=yes }} from [https://web.archive.org/web/20111003171929/http://mathmajor.org/ MathMajor]

{{Areas of mathematics}}
{{Authority control}}

[[Category:Mathematical science occupations|.]]
[[Category:Mathematicians| ]]