Mathematician
Doctoral degree, occasionally master's degree | |
Fields of employment | universities, private corporations, financial industry, government |
---|---|
Related jobs | statistician, actuary |
Part of a series on | ||
Mathematics | ||
---|---|---|
|
||
Mathematics Portal | ||
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
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.[1] 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
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).[3]
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,
The
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[ing] productive thinking."[5] In 1810, 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.[6]
British universities of this period adopted some approaches familiar to the Italian and German universities, but as they already enjoyed substantial freedoms and
Required education
Mathematicians usually cover a breadth of topics within mathematics in their
Activities
Applied mathematics
Mathematicians involved with solving problems with applications in real life are called
The discipline of
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,[12] 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.[13] 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
According to the Dictionary of Occupational Titles occupations in mathematics include the following.[14]
- Mathematician
- Operations-Research Analyst
- Mathematical Statistician
- Mathematical Technician
- Actuary
- Applied Statistician
- Weight Analyst
Prizes in mathematics
There is no
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[15]
- G.H. Hardy[16]
- J. E. Littlewood[17]
- I Am a Mathematician - Norbert Wiener[18]
- I Want to be a Mathematician - Paul R. Halmos
- Adventures of a Mathematician - Stanislaw Ulam[19]
- Enigmas of Chance - Mark Kac[20]
- Random Curves - Neal Koblitz
- Love and Math - Edward Frenkel
- Mathematics Without Apologies - Michael Harris[21]
See also
- Lists of mathematicians
- List of films about mathematicians
- Human computer– Person performing mathematical calculations, before electronic computers became available
- Mathematical joke – Humor about mathematics or mathematicians
- A Mathematician's Apology – 1940 essay by British mathematician G. H. Hardy
- Men of Mathematics – Popular history book of mathematics by E.T. Bell
- Mental calculator – Person exceptionally skilled at mathematical mental calculations
- Timeline of ancient Greek mathematicians
Notes
- ^ Boyer 1991, p. 43.
- ^ Boyer 1991, p. 49.
- ^ "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.
- ^ Abattouy, Renn & Weinig 2001.[page needed]
- ^ Röhrs, "The Classical Idea of the University", Tradition and Reform of the University under an International Perspective p.20
- ^ Rüegg 2004, pp. 5–6.
- ^ Rüegg 2004, p. 12.
- ^ Rüegg 2004, p. 13.
- ^ Rüegg 2004, p. 16.
- ^ Rüegg 2004, pp. 17–18.
- ^ Rüegg 2004, p. 31.
- ^ 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). . Encyclopædia Britannica. Vol. 25 (11th ed.). Cambridge University Press. p. 135.
- ^ Andy Magid, Letter from the Editor, in Notices of the AMS, November 2005, American Mathematical Society, p.1173. [1] Archived 2016-03-03 at the Wayback Machine
- ^ "020 OCCUPATIONS IN MATHEMATICS". Dictionary Of Occupational Titles. Archived from the original on 2012-11-02. Retrieved 2013-01-20.
- ISBN 1-59017-016-4
- ^ Hardy 2012
- ISBN 0-521-33702 X
- ISBN 0-262-73007-3
- ISBN 0-684-14391-7
- ISBN 0-520-05986-7
- 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. 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.
- 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
- ISBN 978-0-88385-578-2
External links
- Occupational Outlook: Mathematicians. Information on the occupation of mathematician from the US Department of Labor.
- 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.
- The MacTutor History of Mathematics archive. A comprehensive list of detailed biographies.
- The Mathematics Genealogy Project. Allows scholars to follow the succession of thesis advisors for most mathematicians, living or dead.
- Weisstein, Eric W. "Unsolved Problems". MathWorld.
- Middle School Mathematician Project Short biographies of select mathematicians assembled by middle school students.
- Career Information for Students of Math and Aspiring Mathematicians[permanent dead link] from MathMajor