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Occupation type | Academic |
Description | |
Competencies | Mathematics, analytical skills and critical thinking skills |
Education required | Doctoral degree, occasionally master's degree |
Fields of employment | universities, private corporations, financial industry, government |
Related jobs | statistician, actuary |
Mathematics | ||
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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.
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 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".^{ [2] } 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).^{ [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,^{ [4] } 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[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 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.^{ [7] } 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.^{ [8] } According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge.^{ [9] } 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.^{ [10] } 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."^{ [11] }
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.
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.^{[ citation needed ]}
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 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.
Many professional mathematicians also engage in the teaching of mathematics. Duties may include:
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 ).
According to the Dictionary of Occupational Titles occupations in mathematics include the following.^{ [14] }
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.
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.
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline.
A scientist is a person who researches to advance knowledge in an area of the natural sciences.
Godfrey Harold Hardy was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of population genetics.
John Edensor Littlewood was a British mathematician. He worked on topics relating to analysis, number theory, and differential equations and had lengthy collaborations with G. H. Hardy, Srinivasa Ramanujan and Mary Cartwright.
Abram Samoilovitch Besicovitch was a Russian mathematician, who worked mainly in England. He was born in Berdyansk on the Sea of Azov to a Karaite Jewish family.
Béla Bollobás FRS is a Hungarian-born British mathematician who has worked in various areas of mathematics, including functional analysis, combinatorics, graph theory, and percolation. He was strongly influenced by Paul Erdős since the age of 14.
David Gale was an American mathematician and economist. He was a professor emeritus at the University of California, Berkeley, affiliated with the departments of mathematics, economics, and industrial engineering and operations research. He has contributed to the fields of mathematical economics, game theory, and convex analysis.
Dame Mary Lucy Cartwright was a British mathematician. She was one of the pioneers of what would later become known as chaos theory. Along with J. E. Littlewood, Cartwright saw many solutions to a problem which would later be seen as an example of the butterfly effect.
Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific society devoted to applied mathematics, and roughly two-thirds of its membership resides within the United States. Founded in 1951, the organization began holding annual national meetings in 1954, and now hosts conferences, publishes books and scholarly journals, and engages in advocacy in issues of interest to its membership. Members include engineers, scientists, and mathematicians, both those employed in academia and those working in industry. The society supports educational institutions promoting applied mathematics.
The Mathematical Tripos is the mathematics course that is taught in the Faculty of Mathematics at the University of Cambridge. It is the oldest Tripos examined at the university.
European universities date from the founding of the University of Bologna in 1088 or the University of Paris. The original medieval universities arose from the Roman Catholic Church schools. Their purposes included training professionals, scientific investigation, improving society, and teaching critical thinking and research. External influences, such as Renaissance humanism, the discovery of the New World (1492), the Protestant Reformation (1517), the Age of Enlightenment, and the recurrence of political revolution, enhanced the importance of human rights and international law in the university curricula.
The Department of Mathematics at the University of Manchester is one of the largest unified mathematics departments in the United Kingdom, with over 90 academic staff and an undergraduate intake of roughly 400 students per year and approximately 200 postgraduate students in total. The School of Mathematics was formed in 2004 by the merger of the mathematics departments of University of Manchester Institute of Science and Technology (UMIST) and the Victoria University of Manchester (VUM). In July 2007 the department moved into a purpose-designed building─the first three floors of the Alan Turing Building─on Upper Brook Street. In a Faculty restructure in 2019 the School of Mathematics reverted to the Department of Mathematics. It is one of five Departments that make up the School of Natural Sciences, which together with the School of Engineering now constitutes the Faculty of Science and Engineering at Manchester.
Carlos Conca is a Chilean applied mathematician, engineer and scientist. He is the first Chilean scientist to be recognized by the French government with a distinction in the field of Exact and Natural Sciences.
Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models.
Mary Fanett Wheeler is an American mathematician. She is known for her work on numerical methods for partial differential equations, including domain decomposition methods.
Gunther Alberto Uhlmann Arancibia is a mathematician whose research focuses on inverse problems and imaging, microlocal analysis, partial differential equations and invisibility.
Jianqing Fan is a statistician, financial econometrician, and data scientist. He is currently the Frederick L. Moore '18 Professor of Finance, Professor of Operations Research and Financial Engineering, Professor of Statistics and Machine Learning, and a former Chairman of Department of Operations Research and Financial Engineering (2012–2015) and a former director of Committee of Statistical Studies (2005–2017) at Princeton University, where he directs both statistics lab and financial econometrics lab since 2008.
Weinan E is a Chinese mathematician. He is known for his pathbreaking work in applied mathematics and machine learning. His academic contributions include novel mathematical and computational results in stochastic differential equations; design of efficient algorithms to compute multiscale and multiphysics problems, particularly those arising in fluid dynamics and chemistry; and pioneering work on the application of deep learning techniques to scientific computing. In addition, he has worked on multiscale modeling and the study of rare events.
Henri Berestycki is a French mathematician who obtained his PhD from Université Paris VI – Pierre and Marie Curie University in 1975. His Dissertation was titled Contributions à l'étude des problèmes elliptiques non linéaires, and his doctoral advisor was Haïm Brezis. He was an L.E. Dickson Instructor in Mathematics at the University of Chicago from 1975–77, after which he returned to France to continue his research. He has made many contributions in nonlinear analysis, ranging from nonlinear elliptic equations, hamiltonian systems, spectral theory of elliptic operators, and with applications to the description of mathematical modelling of fluid mechanics and combustion. His current research interests include the mathematical modelling of financial markets, mathematical models in biology and especially in ecology, and modelling in social sciences. For these latter topics, he obtained an ERC Advanced grant in 2012.
Adrian Constantin is a Romanian-Austrian mathematician who does research in the field of nonlinear partial differential equations. He is a professor at the University of Vienna and has made groundbreaking contributions to the mathematics of wave propagation. He is listed as an ISI Highly Cited Researcher with more than 160 publications and 11000 citations.