![]() Mathematics is used in science for modeling phenomena, which then allows predictions to be made from experimental laws. These results include previously proved theorems, axioms, and-in case of abstraction from nature-some basic properties that are considered as true starting points of the theory under consideration. A proof consists of a succession of applications of deductive rules to already established results. These objects consist of either abstractions from nature or-in modern mathematics-entities that are stipulated with certain properties, called axioms. ![]() Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. ![]() These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. Mathematics (from Ancient Greek μάθημα máthēma: 'knowledge, study, learning') is an area of knowledge that includes such topics as numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes.
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