ETYM French mathématiques, pl., Latin mathematica, sing., Greek mathe science. Related to Mathematic, and -ics.
A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement; SYN. math, maths.
Science of relationships between numbers, between spatial configurations, and abstract structures. The main divisions of pure mathematics include geometry, arithmetic, algebra, calculus, and trigonometry. Mechanics, statistics, numerical analysis, computing, the mathematical theories of astronomy, electricity, optics, thermodynamics, and atomic studies come under the heading of applied mathematics.
Early history.
Prehistoric human beings probably learned to count at least up to ten on their fingers. The Chinese, Hindus, Babylonians, and Egyptians all devised methods of counting and measuring that were of practical importance in their everyday lives. The first theoretical mathematician is held to be Thales of Miletus (c. 580 BC) who is believed to have proposed the first theorems in plane geometry. His disciple Pythagoras established geometry as a recognized science among the Greeks.
The later school of Alexandrian geometers (4th and 3rd centuries BC) included Euclid and Archimedes. Our present decimal numerals are based on a Hindu–Arabic system that reached Europe about AD 100 from Arab mathematicians of the Middle East such as Khwarizmi.
Europe.
Western mathematics began to develop from the 15th century. Geometry was revitalized by the invention of coordinate geometry by René Descartes 1637; Blaise Pascal and Pierre de Fermat developed probability theory; John Napier invented logarithms; and Isaac Newton and Gottfried Leibniz invented calculus, later put on a more rigorous footing by Augustin Cauchy. In Russia, Nikolai Lobachevsky rejected Euclid's parallelism and developed a non-Euclidean geometry; this was subsequently generalized by Bernhard Riemann and later utilized by Einstein in his theory of relativity. In the mid-19th century a new major theme emerged: investigation of the logical foundations of mathematics. George Boole showed how logical arguments could be expressed in algebraic symbolism. Gottlob Frege and Giuseppe Peano considerably developed this symbolic logic.
The present.
In the 20th century, mathematics has become much more diversified. Each specialist subject is being studied in far greater depth and advanced work in some fields may be unintelligible to researchers in other fields. Mathematicians working in universities have had the economic freedom to pursue the subject for its own sake. Nevertheless, new branches of mathematics have been developed which are of great practical importance and which have basic ideas simple enough to be taught in secondary schools. Probably the most important of these is the mathematical theory of statistics in which much pioneering work was done by Karl Pearson. Another new development is operations research, which is concerned with finding optimum courses of action in practical situations, particularly in economics and management. As in the late medieval period, commerce began to emerge again as a major impetus for the development of mathematics.
Higher mathematics has a powerful tool in the high-speed electronic computer, which can create and manipulate mathematical “models” of various systems in science, technology, and commerce.
Modern additions to school syllabuses such as sets, group theory, matrices, and graph theory are sometimes referred to as “new” or “modern” mathematics.
Traditionally the subject of mathematics is divided into arithmetic, which studies numbers, geometry, which studies space, algebra, which studies structures, analysis, which studies infinite processes (in particular, calculus), and probability theory and statistics, which study random processes. + prikaži više