SCOPE OF MATHEMATICS
Mathematics 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 ). There is no general consensus about its exact scope or epistemological status. Most of mathematical activity consists of discovering and proving (by pure reasoning) properties of abstract objects . 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. 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 properti...