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Euclid (holding calipers), Greek mathematician, known as the "Father of Geometry"
Occupation type
Competencies Mathematics, analytical skills and critical thinking skills
Education required
Doctoral degree, occasionally master's degree
Fields of
private corporations,
financial industry,
Related jobs
statistician, actuary

A mathematician is someone who studies mathematics, either as a hobby or as a job. Many mathematicians are math professors at universities. Euclid, Ramanujan, Sir Isaac Newton are some of the most famous early mathematicians.

Mathematics is concerned with numbers, data, quantity, structure, space, models, and change.


Sofja Wassiljewna Kowalewskaja 1
Sofja Wassiljewna Kowalewskaja, the first woman to hold a professorship for mathematics.

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.

Abstract 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.


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.


According to the Dictionary of Occupational Titles occupations in mathematics include the following.

  • Mathematician
  • Operations-Research Analyst
  • Mathematical Statistician
  • Mathematical Technician
  • Actuary
  • Applied Statistician
  • Weight Analyst

Mathematical societies and foundations

Acronyms Name Headquarters Initiation
AAS Australian Academy of Science Australia 1954
Abertis Fundación Abertis Spain 1999
ACM Association for Computing Machinery Special Interest Group 1947
AMS American Mathematical Society United States 1888
ANCEFN Academia Nacional de Ciencias Exactas, Físicas y Naturales Argentina 1874
ANCYT Academia Nacional de Ciencia y Tecnología Peru
ANTS Algorithmic Number Theory Symposium Germany 1994
APS American Physical Society United States 1889
APSF Alfred Pritchard Sloan Foundation United States 1875
ASA American Statistical Association United States 1839
ASF Académie des Sciences France 1666
ASL Association for Symbolic Logic United States 1936
AWM Association for Women in Mathematics United States 1971
ASME American Society Of Mechanical Engineers United States 1880
AustMS Australian Mathematical Society Australia 1956
BMG Berliner Mathematischen Gesellschaft Germany 1901
BMS Belgian Mathematical Society Belgium 1921
CIMAT Centro de Investigación en Matemáticas, A.C. Mexico 1980
CMF Fundación Chern United States 2010
CMI Clay Mathematics Institute United States 1998
CMS Canadian Mathematical Society Canada 1945
CNCA Consejo Nacional de la Cultura y las Artes de Chile Chile 2003
CNRS Centre national de la recherche scientifique France 1939
CONICIT Consejo Nacional para Investigaciones Científicas y Tecnológicas San Jose Costa Rica 1972
CRM Centre de Recherches Mathematiques Canada 1968
CSIC Consejo Superior de Investigaciones Científicas Spain 1998
DMV Deutsche Mathematiker-Vereinigung Germany 1993
ECM European Congresses of Mathematics Poland 1992
ECCOMAS European Community on Computational Methods in Applied Sciences and Engineering Europe 1901
EMS European Mathematical Society Germany
EPFL École polytechnique fédérale de Lausanne Switzerland
ERC,CEI European Research Council Europe 2002
ESF Fundación Europea de la Ciencia Europe
ETHZ Eidgenossische Technische Hochschule-Zurich Switzerland
FBBVA Fundación BBVA Spain
FCFM Facultad de Ciencias Físicas y Matemáticas, Universidad de Chile Chile 1840
FCRI Fundació Catalana per a la Recerca i la Innovació Spain
FPA Fundación Príncipe de Asturias Spain 1980
FSK Fundación Sofía Kovalévskaia Mexico 1942
GAMNI Groupe pour l’Avancement des Méthodes Numériques de l’Ingénieur France 1992
GenCat Generalitat de Catalunya Spain
HAS Hungarian Academy of Sciences Hungary 1825
IAMP International Association of Mathematical Physics Europe 1976
ICA Institute Of Combinatorics And Its Applications Canada 1990
ICMAT Instituto de Ciencias Matemáticas Spain 2008
ICHM International Commission on the History of Mathematics United States 1971
ICIAM International Council for Industrial and Applied Mathematics United States 1987
ICM International Congress of Mathematicians
ICMI International Commission on Mathematical Instruction 1897
ICTCM International Conference on Technology in Collegiate Mathematics
ICTP Abdus Salam International Centre for Theoretical Physics Italy 1964
IEC Institvt d'Estvdis Catalans Spain 1907
IEEE-CS IEEE Computer Society United States 1946
IMA Institute of Mathematics and its Applications England 1964
IMAFF Instituto de Matemáticas y Física Fundamental Spain
IMT Institut de Mathématiques de Toulouse France 1887
IMU International Mathematical Union Germany 1920
INFORMS Institute for Operations Research and the Management Sciences United States
ISDE International Society of Difference Equations
Konex Fundación Konex Argentina 1980
KVA Swedish Royal Academies Sweden 1739
LMS London Mathematical Society England 1865
MAA Mathematical Association of America United States 1915
MEC Ministerio de Educación y Ciencia de Spain Spain
MFO Mathematisches Forschungsinstitut Oberwolfach Germany 1944
MICIT Ministerio de Ciencia y Tecnología San José Costa Rica
MOS Mathematical Optimization Society 1973
MSJ Mathematical Society of Japan Japan 1946
NAS National Academy of Sciences United States 1974
NFT Number Theory Foundation United States
NUST National University of Sciences and Technology Pakistan 1991
ÖMG Österreichische Mathematische Gesellschaft Austria 1903
PIMS Pacific Institute for the Mathematical Sciences Canada 1996
RAS Russian Academy of Sciences Russia 1724
RSC Royal Society of Canada Canada 1882
RSL Royal Society of London England 1660
RSME Real Sociedad Matemática Española Spain
RSS Royal Statistical Society England 1834
SASTRA Shanmugha Arts, Science, Technology & Research Academy India 1984
SCM Societat Catalana de Matemàtiques Spain 1998
SEMA Sociedad Española de Matemática Aplicada Spain 1991
SEP Secretaría de educación pública Mexico
SIAG SIAM Activity Group United States
SIAM Society for Industrial and Applied Mathematics United States 1951
SIMAI Società Italiana di Matematica Applicata e Industriale Italy 1989
SMAI Lisez maintenant Société de mathématiques appliquées et industrielles France 1983
SMF Société Mathématique de France France 1872
SMM Sociedad Matemática Mexicana Mexico 1943
SPB Saint Petersburg Mathematical Society Russia 1890
UMALCA Unión Matemática de América Latina y el Caribe Latin America 1995
UMI Unione Matematica Italiana Italy 1922
WFNMC World Federation of National Mathematics Competitions 1984

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