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Maths involves the study of such topics as quantity, structure, space, and change. It has no generally accepted definition.
Mathematicians look for and use formulas to formulate new assumptions; the truth or falsity of such a solution is solved by mathematical proof. If mathematical structures are good models of real phenomena, mathematical reasoning can be used to gain insight or predictions about nature. Using abstraction and logic, Maths evolved from counting, calculating, measuring, and systematically studying the shapes and motions of physical objects. Practical Maths has been a human activity since written records. The research needed to solve mathematical problems can take years or even centuries of continuous research.
Strong arguments first appeared in Greek Maths, especially in Euclid's elements. Since the pioneering work of Giuseppe Pean, David Hilbert, and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as the determination of truth by consistent deduction from appropriately chosen axioms and definitions. Maths developed at a relatively slow pace until the Renaissance, when mathematical innovations in interaction with new scientific discoveries led to a rapid increase in the rate of mathematical discoveries that persists to the present day.
Maths is essential in many areas, including science, engineering, medicine, finance, and the social sciences. Applied Maths has led to completely new mathematical disciplines, such as statistics and game theory. Mathematicians deal with pure Maths without thinking of any application, but practical applications for what began as pure Maths are often discovered later.