Mathematicians seek out patterns
and use them to formulate new conjectures. Mathematicians resolve the truth or
falsity of conjectures by mathematical proof. When mathematical structures are
good models of real phenomena, then mathematical reasoning can 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 exist.
The research required to solve mathematical problems can take years or even
centuries of sustained inquiry.
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