Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of quantity, structure, space, and change.[2] Mathematicians seek out patterns[3][4] and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proof. The research required to solve mathematical problems can take years or even centuries of sustained inquiry. Since the pioneering work of Giuseppe Peano (1858–1932), David Hilbert(1862–1943), and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth byrigorous deduction from appropriately chosen axioms and definitions. When those mathematical structures are good models of real phenomena, then mathematical reasoning often provides insight or predictions.
Through the use of abstraction and logical reasoning, mathematics developed from counting, calculation, measurement, and the systematic study of theshapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. Rigorous arguments first appeared in Greek mathematics, most notably in Euclid's Elements. Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that continues to the present day.[5]
Galileo Galilei (1564–1642) said, 'The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth'.[6] Carl Friedrich Gauss (1777–1855) referred to mathematics as "the Queen of the Sciences".[7] Benjamin Peirce (1809–1880) called mathematics "the science that... [continues]

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