The result of a proof is called a theorem. A proof consists of a succession of applications of some deductive rules to already known results, including 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. These objects are either abstractions from nature (such as natural numbers or lines), or (in modern mathematics) abstract entities of which certain properties, called axioms, are stipulated. Most of mathematical activity consists of discovering and proving (by pure reasoning) properties of abstract objects. There is no general consensus about its exact scope or epistemological status. Mathematics (from Ancient Greek μάθημα ( máthēma) 'knowledge, study, learning') is an area of knowledge, which includes the study of such topics as numbers ( arithmetic and number theory), formulas and related structures ( algebra), shapes and spaces in which they are contained ( geometry), and quantities and their changes ( calculus and analysis). 3rd century BC Greek mathematician Euclid (holding calipers), as imagined by Raphael in this detail from The School of Athens (1509–1511)
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