A Rumor of War

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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A biography is a detailed description or account of someone's life. It entails more than basic facts , a biography also portrays a subject's... experience of these events. Unlike a profile or curriculum vitae , a biography presents a subject's life story, highlighting various aspects of his or her life, including intimate details of experience, and may include an analysis of a subject's personality. Biographical works are usually non-fiction, but fiction can also be used to portray a person's life. One in-depth form of biographical coverage is called legacy writing. Biographical works in diverse media—from literature to film—form the genre known as a biography. An authorized biography is written with the permission, cooperation, and, at times, participation of a subject or a subject's heirs. An autobiography is about a life of a subject, written by that subject or sometimes with a collaborator. The Early Middle Ages saw a decline in awareness of the classical culture in Europe. During this time, the only repositories of knowledge and records of the early history in Europe were those of the Roman Catholic Church.
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Reference is a relation between objects in which one object designates, or acts as a means by which to connect to or link to, another object. The... first object in this relation is said to refer to the second object. The second object – the one to which the first object refers – is called the referent of the first object. The term reference is used in many spheres of human knowledge, adopting shades of meaning particular to the contexts in which it is used. References can take on many forms, including: a thought, a sensory perception that is audible , visual , olfactory, or tactile, emotional state, relationship with other, spacetime coordinate, symbolic or alpha-numeric, a physical object or an energy projection; but, other concrete and abstract contexts exist as methods of defining references within the scope of the various fields that require an origin, point of departure, or an original form. This includes methods that intentionally hide the reference from some observers, as in cryptography. The following sections give specific usages of reference in different subjects.
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