Mathematics is the science that provides the tools to obtain accurate conclusions from the assumptions, so for correct reasoning. Since the strict assumptions may affect various areas of human thought and must be made in science, technology, and even in the humanities, mathematics range is wide and is still growing.
Many areas of science and technology, at some point begins to define his idea of a sufficiently high precision to be able to use mathematical methods to them, which often initiates another forum theoretical or applied mathematics. This was the case for example of classical mechanics, statistical mechanics, economics (econometrics), linguistics (mathematical linguistics), game theory, and even some areas of political science (theory of voting). Currently, the standard in science is experimental confirmation of the existence of the observed using the methods of statistics, which is the branch of mathematics. This allows you to distinguish between the actual results from the random convergence. Leonardo da Vinci said in the Treatise on Painting: "No human studies can not be called real science if it can not be demonstrated mathematically."
Theoretical mathematics, pure mathematics sometimes called, is often developed without a clear link to the specific applications. In this embodiment, it is considered by some mathematicians as a form of art. However, some theoretical mathematics departments have found their practical application, when it turned out that they needed a modern physics or computer science. School understanding of mathematics as a science only of numbers and geometrical concepts, has become obsolete in the nineteenth century with the progress of algebra and set theory. Part of the logic of mathematics is indispensable.
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Nikolai Lobachevsky found that "There is no branch of mathematics, no matter how abstract, which one day would not be applied to real-world events," the statement ahead of a half-century, the progress of physics, which act on the branches of mathematics, before the era considered to be the domain pure thought, niezbrukanej applications.
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