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mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") includes study of such topics as quantity (number theory), structure (algebra),  space (geometry), and change (mathematical analysis). It has no generally accepted definition.

mathematicians seek and use patterns to formulate new conjectures; they resolve truth or falsity of conjectures by mathematical proof. When mathematical structures are good models of real phenomena, mathematical reasoning can be used to provide insight or predictions about nature. Through use of abstraction and logic, mathematics developed from counting, calculation, measurement, and systematic study of shapes and motions of physical objects. practical mathematics has been human activity from as far back as written records exist. research required to solve mathematical problems can take years or even centuries of sustained inquiry.