Mathematics (from Greek μάθημα máthēma , "knowledge, study, learning") includes the study of such topics as quantity ( number theory ), structure ( algebra ), space ( geometry ), [1] and change ( mathematical analysis ). It has no generally accepted definition . Mathematicians seek and use patterns to formulate new conjectures ; they resolve the 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 the use of abstraction and logic , mathematics developed from counting , calculation , measurement , and the systematic study of the shapes and motions of physical objects . Practical mathematics has been a human activity from as far back as written records ...
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