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Mathematics

Mathematics arises from many different kinds of problems. At first these were found in [commerce] , [land measurement] , [architecture] and later [astronomy] ; nowadays, all sciences suggest problems studied by mathematicians, and many problems arise within mathematics itself. For example, the [physicist] [Richard Feynman] invented the [path integral formulation] of [quantum mechanics] using a combination of mathematical reasoning and physical insight, and today's [string theory] , a still-developing scientific theory which attempts to unify the four [fundamental forces of nature] , continues to inspire new mathematics. Some mathematics is only relevant in the area that inspired it, and is applied to solve further problems in that area. But often mathematics inspired by one area proves useful in many areas, and joins the general stock of mathematical concepts. A distinction is often made between [pure mathematics] and [applied mathematics] . However pure mathematics topics often turn out to have applications, e.g. [number theory] in [cryptography] . This remarkable fact that even the "purest" mathematics often turns out to have practical applications is what [Eugene Wigner] has called " [the unreasonable effectiveness of mathematics] ."

As in most areas of study, the explosion of knowledge in the scientific age has led to specialization: there are now hundreds of specialized areas in mathematics and the latest [Mathematics Subject Classification] runs to 46 pages. Several areas of applied mathematics have merged with related traditions outside of mathematics and become disciplines in their own right, including [statistics] , [operations research] , and [computer science] .

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