The Hedgehog, the Fox, and the Magister's Pox

Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe. In... an older and closely related meaning , "science" refers to the body of reliable knowledge itself, of the type that can be logically and rationally explained . Since classical antiquity science as a type of knowledge was closely linked to philosophy. In the early modern era the words "science" and "philosophy" were sometimes used interchangeably in the English language. By the 17th century, natural philosophy was considered a separate branch of philosophy. However, "science" continued to be used in a broad sense denoting reliable knowledge about a topic, in the same way it is still used in modern terms such as library science or political science. In modern use, "science" more often refers to a way of pursuing knowledge, not only the knowledge itself.
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Mathematics is the study of quantity, structure, space, and change. Mathematicians seek out patterns 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 , David Hilbert , and others on axiomatic systems in the late 19th century, it has become customary to view mathematical research as establishing truth by rigorous 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 the shapes 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.
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