Product Code Database
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with , data, quantity, structure, space, models, and change.
The number of known mathematicians grew when Pythagoras of Samos () established the Pythagorean school, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number"..
Archimedes was one of the greatest figures in the history of mathematics. He made significant contributions to geometry, providing proofs for the area of a circle and the volume and surface area of a sphere. He also gave a good approximation of π using polygons. He also developed the method of exhaustion, which is an early form of integral calculus. He furthered the study of centers of mass and mathematical statics. His precise methods had a strong impact on later mathematics and mathematical physics. Euclid and Apollonius were prominent ancient Greek mathematicians, with Euclid's Elements establishing geometry through axioms and logical proofs and laying the foundation of the axiomatic method, while Apollonius' Conics systematically developed the theory of ellipses, parabolas, and hyperbolas, significantly advancing the study of curves and influencing later geometry.
The first woman mathematician recorded by history was Hypatia of Alexandria ( – 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, Mathematics and astronomy of Ibn al-Haytham.
Noteworthy mathematicians from this time period include Aryabhata, who applied trigonometry to astronomy; Brahmagupta, credited with the first systematic explanation of and zero; and the mathematician and astronomer Bhāskara II. Mādhava of Sangamagrāma is considered to be the founder of the Kerala school of astronomy and mathematics in the Medieval India. He made pioneering contributions to the study of infinite series, trigonometry, geometry and algebra.
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 "encouraging productive thinking."Röhrs, "The Classical Idea of the University", Tradition and Reform of the University under an International Perspective p.20 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.".
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.
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.Andy Magid, Letter from the Editor, in Notices of the AMS, November 2005, American Mathematical Society, p.1173. [1] 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.
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).
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.
|
|
