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{{short description|Person with an extensive knowledge of mathematics}}
{{Infobox Occupation
{{pp|small=yes}}
{{More citations needed|date=April 2021}}{{Infobox Occupation
| name=Mathematician | name=Mathematician
| |
official_names= official_names=
<!------------Details-------------------> <!------------Details------------------->
| type= ] | type= ]
| activity_sector= | activity_sector=
| image= ] | image= ]
| caption = ] | caption = ] (holding ]), Greek mathematician, known as the "Father of Geometry"
| competencies=Mathematics, ]s and ] skills | competencies=], ]s and ] skills
| formation= ], occasionally ] | formation= ], occasionally ]
| employment_field= universities, <br/> | employment_field= universities, <br/>private corporations, <br/>financial industry, <br/>government
private corporations, <br/>financial industry, <br/>government
| related_occupation= ], ] | related_occupation= ], ]
}} }}


{{Math topics TOC}}
A '''mathematician''' is a person with extensive ] of ] who uses this knowledge in their work, typically to solve ]s. Mathematics is concerned with ]s, ], ], ], ], ] and change.

A '''mathematician''' is someone who uses an extensive knowledge of ] in their work, typically to solve ]s. Mathematicians are concerned with ]s, ], ], ], ], ], and ].


==History== ==History==
{{Hatnote|This section is on the history of mathematicians. For a history of mathematics in general, see ]}} {{broader|History of mathematics}}
]


One of the earliest known mathematicians was ] (c. 624–c.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>{{Citation|last=Boyer|year=1991|title=A History of Mathematics|page= 43}}</ref> He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to ]. One of the earliest known mathematicians was ] ({{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 ], by deriving four corollaries to ].


The number of known mathematicians grew when ] (c. 582–c. 507 BC) established the ], whose doctrine it was that mathematics ruled the universe and whose motto was "All is number".<ref>{{Harv|Boyer|1991|loc="Ionia and the Pythagoreans" p. 49}}</ref> It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The number of known mathematicians grew when ] ({{Circa|582|507 BC}}) established the ], 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 ] of Alexandria (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></ref> The first woman mathematician recorded by history was ] 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=]}}</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>Abattouy, M., Renn, J. & Weinig, P., 2001. Transmission as Transformation: The Translation Movements in the Medieval East and West in a Comparative Perspective. Science in Context, 14(1-2), 1-12.</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 ]. A notable feature of many scholars working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on ], ] and ] of ]. 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 ]. A notable feature of many scholars working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on ], ] and ] of ].


The ] brought an increased emphasis on mathematics and science to Europe. Many well known mathematicians from this area had other occupations: ] was a monk; ] was an engineer and bookkeeper; and ] was a well-known physician. The ] 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: ] (founder of ]); ] (notable engineer and bookkeeper); ] (earliest founder of probability and binomial expansion); ] (physician) and ] (lawyer).


As time passed, many mathematicians gravitated towards universities. An emphasis on free thinking and experimentation had notably already begun in Britain's oldest universities beginning in the seventeenth century at Oxford with the fathers of British scientific methodology ] and ], and at Cambridge where ] was ]. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the “regurgitation of knowledge” to “encourag 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 to build a university in Berlin based on ]’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>Rüegg, "Themes", ''A History of the University in Europe, Vol. III'', p.5-6</ref> 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 ] with the scientists ] and ], and at ] where ] was ]. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the "regurgitation of knowledge" to "encourag 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, ] convinced the king of ], ], to build a university in Berlin based on ]'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 German universities, but as they already enjoyed substantial freedoms and ] the changes there had begun with the ], the same influences that inspired Humboldt. The Universities of ] and ] emphasized the importance of ], arguably more authentically implementing Humboldt’s idea of a university than even German universities, which were subject to state authority.<ref>Rüegg, "Themes", ''A History of the University in Europe, Vol. III'', p.12</ref> Overall, science (including mathematics) became the focus of universities in the 19th and 20th centuries. Students could conduct research in ] or ] and began to produce doctoral theses with more scientific content.<ref>Rüegg, "Themes", ''A History of the University in Europe, Vol. III'', p.13</ref> According to Humboldt, the mission of the ] was to pursue scientific knowledge.<ref>Rüegg, "Themes", ''A History of the University in Europe, Vol. III'', p.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>Rüegg, "Themes", ''A History of the University in Europe, Vol. III'', p.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>Rüegg, "Themes", ''A History of the University in Europe, Vol. III'', p.31</ref> British universities of this period adopted some approaches familiar to the Italian and German universities, but as they already enjoyed substantial freedoms and ] the changes there had begun with the ], the same influences that inspired Humboldt. The Universities of ] and ] emphasized the importance of ], 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 ] or ] and began to produce doctoral theses with more scientific content.<ref>{{Harvnb|Rüegg|2004|page=13}}.</ref> According to Humboldt, the mission of the ] 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>

===Notable mathematicians===
Some notable mathematicians include ], ], ], ], ], ], ], ], ], ], ], ], ], ], ], ], ], ], ], and ].

<gallery widths="170" heights="220" caption="" align="center">
Euklid-von-Alexandria_1.jpg|], fl. 300 BC
Domenico-Fetti Archimedes 1620.jpg|], c.  287 – 212 BC
File:2064 aryabhata-crp.jpg|], c. 476 -550 CE
Abu Abdullah Muhammad bin Musa al-Khwarizmi edit.png|], c. 780 – 850
Omar Khayyam Profile.jpg|], 1048 – 1131
Frans Hals - Portret van René Descartes.jpg|], 1596 – 1650
Pierre de Fermat.jpg|], 1601 – 1665
GodfreyKneller-IsaacNewton-1689.jpg|], 1642 – 1727
Gottfried Wilhelm von Leibniz.jpg|], 1646 – 1716
Leonhard Euler.jpg|], 1707 – 1783
Joseph-Louis_Lagrange.jpeg|], 1736 – 1813
Carl Friedrich Gauss.jpg|], 1777 – 1855
Niels Henrik Abel.jpg|], 1802 – 1829
Evariste galois.jpg|], 1811 – 1832
Georg_Friedrich_Bernhard_Riemann.jpeg|], 1826 – 1866
Felix_Klein.jpeg|], 1849 – 1925
JH Poincare.jpg|], 1854 – 1912
Hilbert.jpg|], 1862 – 1943
Noether.jpg|], 1882 – 1935
Hermann_Weyl_ETH-Bib_Portr_00890.jpg|], 1885 – 1955
Srinivasa_Ramanujan_-_OPC_-_1.jpg|], 1887 – 1920
</gallery>


==Required education== ==Required education==
Mathematicians usually cover a breadth of topics within mathematics in their ], and then proceed to specialize in topics of their own choice at the ]. In some universities, a ] 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 ]. Mathematicians usually cover a breadth of topics within mathematics in their ], and then proceed to specialize in topics of their own choice at the ]. In some universities, a ] 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 ].


==Activities== ==Activities==
], mathematical theorist and teacher]]

===Applied mathematics=== ===Applied mathematics===
{{main|Applied mathematics}} {{main|Applied mathematics}}
Mathematicians involved with solving problems with applications in real life are called ]s. Applied mathematicians are mathematical scientists who, with their specialized knowledge and ] 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 ]. Mathematicians and applied mathematicians are considered to be two of the STEM (science, technology, engineering, and mathematics) careers.<ref>{{cite web|title=Thinking About a STEM Career: Read This!|url=http://www.guidetoonlineschools.com/thelearningcurve/stem-careers-read-this|publisher=The Learning Curve|accessdate=10 May 2013}}</ref> Mathematicians involved with solving problems with applications in real life are called ]s. Applied mathematicians are mathematical scientists who, with their specialized knowledge and ] 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 ]. 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 ] concerns itself with mathematical methods that are typically used in science, engineering, business, and industry; thus, "applied mathematics" is a ] with specialized knowledge. The term "applied mathematics" also describes the ] 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 ], ], ], and other areas of mathematical practice. The discipline of ] concerns itself with mathematical methods that are typically used in science, engineering, business, and industry; thus, "applied mathematics" is a ] with specialized knowledge. The term "applied mathematics" also describes the ] 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 ], ], ], and other areas of mathematical practice.


===Abstract mathematics=== ===Pure mathematics===
{{main|Pure mathematics}} {{main|Pure mathematics}}
] is ] that studies entirely abstract ]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 ] 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''.</ref> and at variance with the trend towards meeting the needs of ], ], ], ], ], and so on. ] is ] that studies entirely abstract ]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 ] 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 ], ], ], ], ], and other applications.


Another insightful view put forth is that ''pure mathematics is not necessarily ]'': 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. </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. Another insightful view put forth is that ''pure mathematics is not necessarily ]'': 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. {{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. 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=== ===Mathematics teaching===
Many professional mathematicians also engage in the teaching of mathematics. Duties may include: Many professional mathematicians also engage in the teaching of mathematics. Duties may include:
* teaching university mathematics courses; * teaching university mathematics courses;
* supervising undergraduate and graduate research; and * supervising undergraduate and graduate research; and
* serving on academic committees. * serving on academic committees.
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== Occupations == == Occupations ==
]
According to the ] occupations in mathematics include the following.<ref>{{Cite web|url=http://occupationalinfo.org/defset1_3829.html |title=020 OCCUPATIONS IN MATHEMATICS |work=Dictionary Of Occupational Titles |accessdate=2013-01-20}}</ref>
According to the ] 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 * Mathematician
* Operations-Research Analyst * ] Analyst
* Mathematical Statistician * Mathematical Statistician
* Mathematical Technician * Mathematical Technician
* ] * ]
* Applied Statistician * Applied ]
* Weight Analyst * Weight Analyst


== Quotations about mathematicians == == Prizes in mathematics ==
There is no ] 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 ], the ], the ], the ], the ], the ], the ], the ], the ], the ], the ], and the ].
{{Wikiquote}}
The following are quotations about mathematicians, or by mathematicians.


The ], ], and other mathematical societies offer several prizes aimed at increasing the representation of women and minorities in the future of mathematics.
: ''A mathematician is a device for turning coffee into theorems.''
::—Attributed to both ]<ref>{{cite web|url=http://www-history.mcs.st-andrews.ac.uk/Biographies/Renyi.html |title=Biography of Alfréd Rényi |publisher=History.mcs.st-andrews.ac.uk |date= |accessdate=2012-08-17}}</ref> and ]


==Mathematical autobiographies==
: ''Die Mathematiker sind eine Art Franzosen; redet man mit ihnen, so übersetzen sie es in ihre Sprache, und dann ist es alsobald ganz etwas anderes.'' (Mathematicians are a sort of Frenchmen; if you talk to them, they translate it into their own language, and then it is immediately something quite different.)
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.
::—]<ref>''Maximen und Reflexionen, Sechste Abtheilung'' cited in {{citation|first=Robert Edouard|last=Moritz|title=On Mathematics / A Collection of Witty, Profound, Amusing Passages about Mathematics and Mathematicians|year=1958|origyear=1914|publisher=Dover|isbn=0-486-20489-8|page=123}}</ref>


* ''The Book of My Life'' – ]<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>
: ''Each generation has its few great mathematicians...and research harms no one.''
* '']'' - ]<ref>{{harvnb|Hardy|2012}}</ref>
::—] (1930- ), "Mathematics and Creativity"<ref>Alfred Adler, "Mathematics and Creativity," ''The New Yorker'', 1972, reprinted in Timothy Ferris, ed., ''The World Treasury of Physics, Astronomy, and Mathematics'', Back Bay Books, reprint, June 30, 1993, p, 435.</ref>
* '']'' (republished as Littlewood's miscellany) - ]<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'' - ]<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>
: ''In short, I never yet encountered the mere mathematician who could be trusted out of equal roots, or one who did not clandestinely hold it as a point of his faith that x squared + px was absolutely and unconditionally equal to q. Say to one of these gentlemen, by way of experiment, if you please, that you believe occasions may occur where x squared + px is not altogether equal to q, and, having made him understand what you mean, get out of his reach as speedily as convenient, for, beyond doubt, he will endeavor to knock you down.''
* ''I Want to be a Mathematician'' - ]
::—], ''The purloined letter''
* ''Adventures of a Mathematician'' - ]<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'' - ]<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>
: ''A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.''
* ''Random Curves'' - ]
::—], ''A Mathematician's Apology''
* '']'' - ]

* ''Mathematics Without Apologies'' - ]<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>
: ''Some of you may have met mathematicians and wondered how they got that way.''
::—]

: ''It is impossible to be a mathematician without being a poet in soul.''
::—]

: ''There are two ways to do great mathematics. The first is to be smarter than everybody else. The second way is to be stupider than everybody else—but persistent.''
::—]
: ''Mathematics is the queen of the sciences and arithmetic the queen of mathematics.''
::—]<ref>''Sartorius von Waltershausen: Gauss zum Gedachtniss. (Leipzig, 1856), p. 79'' cited in {{citation|first=Robert Edouard|last=Moritz|title=On Mathematics / A Collection of Witty, Profound, Amusing Passages about Mathematics and Mathematicians|year=1958|origyear=1914|publisher=Dover|isbn=0-486-20489-8|page=271}}</ref>

== Women in mathematics ==
{{See also|List of female mathematicians}}

While the majority of mathematicians are male, there have been some demographic changes since ]. For example in Europe, from 1992 onwards, several women have been laureates of the prestigious ]. Some prominent female mathematicians throughout History are ] (ca. 400 AD), ] (1815–1852), ] (1718–1799), ] (1882–1935), ] (1776–1831), ] (1850–1891), ] (1860–1940), ] (1905–1977), ] (1919–1985), ] (1906–1995), ] (1706–1749), ] (1900–1998), ] (1922–2004), ] (1925–2001) and ].

The ] is a professional society whose purpose is "to encourage women and girls to study and to have active careers in the mathematical sciences, and to promote equal opportunity and the equal treatment of women and girls in the mathematical sciences."
The ] and other mathematical societies offer several prizes aimed at increasing the representation of women and minorities in the future of mathematics.

== 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. Prominent prizes in mathematics include the ], the ], the ], the ], the ], the ], the ], the ], the ], the ], the ], and the ].


== See also == == See also ==


{{Portal|Mathematics}} {{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}}
* '']'' (book)
* {{Annotated link|Timeline of ancient Greek mathematicians}}
* ]


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


==References== ==Bibliography==
{{Refbegin}} {{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 }}
* '']'', by ]. Memoir, with foreword by ].
* {{Cite book |last=Boyer |title=A History of Mathematics |year=1991}}
** Reprint edition, ], 1992; ISBN 0-521-42706-1
* {{Cite book |last=Dunham |first=William |author-link=William Dunham (mathematician) |title=The Mathematical Universe |publisher=John Wiley |year=1994}}
** First edition, 1940
* ]. ''I Want to Be a Mathematician''. Springer-Verlag 1985. * {{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}}
* ]. ''The Mathematical Universe''. John Wiley 1994.
* {{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}} {{Refend}}

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


==External links== ==External links==
{{Wikiquote|Mathematicians}} {{Wikiquote|Mathematicians}}
{{Commons category|Mathematicians}} {{Commons category|Mathematicians}}
* . Information on the occupation of mathematician from the US Department of Labor. * . Information on the occupation of mathematician from the US Department of Labor.
* . 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. * . 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.
* . A comprehensive list of detailed biographies. * {{Webarchive|url=https://web.archive.org/web/20191114200642/https://mathshistory.st-andrews.ac.uk/ |date=2019-11-14 }}. A comprehensive list of detailed biographies.
* . Allows to follow the succession of thesis advisors for most mathematicians, living or dead. * {{Webarchive|url=https://web.archive.org/web/20090219095714/http://genealogy.math.ndsu.nodak.edu/ |date=2009-02-19 }}. Allows scholars to follow the succession of thesis advisors for most mathematicians, living or dead.
* {{MathWorld|urlname=UnsolvedProblems|title=Unsolved Problems}} * {{MathWorld|urlname=UnsolvedProblems|title=Unsolved Problems}}
* Short biographies of select mathematicians assembled by middle school students. * Short biographies of select mathematicians assembled by middle school students.
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Latest revision as of 21:55, 14 December 2024

Person with an extensive knowledge of mathematics

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Mathematician
Euclid (holding calipers), Greek mathematician, known as the "Father of Geometry"
Occupation
Occupation typeAcademic
Description
CompetenciesMathematics, analytical skills and critical thinking skills
Education requiredDoctoral degree, occasionally master's degree
Fields of
employment		universities,
private corporations,
financial industry,
government
Related jobsstatistician, actuary
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A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.

History

For broader coverage of this topic, see History of mathematics.

One of the earliest known mathematicians was Thales of Miletus (c. 624 – c. 546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. 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 (c. 582 – c. 507 BC) established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". 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 (c. 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).

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, 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, 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 & Physics. Moving into the 19th century, the objective of universities all across Europe evolved from teaching the "regurgitation of knowledge" to "encourag productive thinking." In 1810, Alexander von Humboldt convinced the king 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.

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 Oxford and 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. 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. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge. 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. 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."

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. 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

Emmy Noether, mathematical theorist and teacher

Applied mathematics

Main article: Applied mathematics

Mathematicians involved with solving problems with applications in real life are called applied mathematicians. 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.

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 article: Pure mathematics

Pure mathematics is mathematics that studies entirely abstract concepts. From the eighteenth century onwards, this was a recognized category of mathematical activity, sometimes characterized as speculative mathematics, 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. 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 or 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 derivatives of the stock (see: Valuation of options; Financial modeling).

Occupations

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.

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 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.

See also

Notes

  1. Boyer 1991, p. 43.
  2. Boyer 1991, p. 49.
  3. "Medieval Sourcebook: Socrates Scholasticus: The Murder of Hypatia (late 4th Cent.) from Ecclesiastical History, Bk VI: Chap. 15". Internet History Sourcebooks Project. Archived from the original on 2014-08-14. Retrieved 2014-11-19.
  4. Abattouy, Renn & Weinig 2001.
  5. Röhrs, "The Classical Idea of the University", Tradition and Reform of the University under an International Perspective p.20
  6. Rüegg 2004, pp. 5–6.
  7. Rüegg 2004, p. 12.
  8. Rüegg 2004, p. 13.
  9. Rüegg 2004, p. 16.
  10. Rüegg 2004, pp. 17–18.
  11. Rüegg 2004, p. 31.
  12. 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.Chisholm, Hugh, ed. (1911). "Simpson, Thomas" . Encyclopædia Britannica. Vol. 25 (11th ed.). Cambridge University Press. p. 135.
  13. Andy Magid, Letter from the Editor, in Notices of the AMS, November 2005, American Mathematical Society, p.1173. Archived 2016-03-03 at the Wayback Machine
  14. "020 OCCUPATIONS IN MATHEMATICS". Dictionary Of Occupational Titles. Archived from the original on 2012-11-02. Retrieved 2013-01-20.
  15. Cardano, Girolamo (2002), The Book of My Life (De Vita Propria Liber), The New York Review of Books, ISBN 1-59017-016-4
  16. Hardy 2012
  17. Littlewood, J. E. (1990) , Béla Bollobás (ed.), Littlewood's miscellany, Cambridge University Press, ISBN 0-521-33702 X
  18. Wiener, Norbert (1956), I Am a Mathematician / The Later Life of a Prodigy, The M.I.T. Press, ISBN 0-262-73007-3
  19. Ulam, S. M. (1976), Adventures of a Mathematician, Charles Scribner's Sons, ISBN 0-684-14391-7
  20. Kac, Mark (1987), Enigmas of Chance / An Autobiography, University of California Press, ISBN 0-520-05986-7
  21. Harris, Michael (2015), Mathematics without apologies / portrait of a problematic vocation, Princeton University Press, ISBN 978-0-691-15423-7

Bibliography

  • Abattouy, Mohammed; Renn, Jürgen; Weinig, Paul (2001). "Transmission as Transformation: The Translation Movements in the Medieval East and West in a Comparative Perspective". Science in Context. 14 (1–2). Cambridge University Press: 1–12. doi:10.1017/S0269889701000011. S2CID 145190232.
  • Boyer (1991). A History of Mathematics.
  • Dunham, William (1994). The Mathematical Universe. John Wiley.
  • Halmos, Paul (1985). I Want to Be a Mathematician. Springer-Verlag.
  • Hardy, G.H. (2012) . A Mathematician's Apology (Reprinted with foreword ed.). Cambridge University Press. ISBN 978-1-107-60463-6. OCLC 942496876.
  • Rüegg, Walter (2004). "Themes". In Rüegg, Walter (ed.). A History of the University in Europe. Vol. 3. Cambridge University Press. ISBN 978-0-521-36107-1.

Further reading

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