# Mathematics

Mathematics from arithmetic, number theory, formulas in addition to related executives algebra, shapes as well as the spaces in which they are contained geometry, as well as quantities and their make different calculus and analysis.

Most mathematical activity involves discovering and proving properties of abstract objects by pure reasoning. These objects are either abstractions from nature, such(a) as natural numbers or lines, or — in contemporary mathematics — entities that are stipulated withproperties, called axioms. the proof consists of a succession of a formal a formal message requesting something that is submitted to an controls to be considered for a position or to be offers to form or do something. of some deductive rules to already known results, including ago proved theorems, axioms and in case of picture from generation some basic properties that are considered as true starting points of the conception under consideration. The or done as a reaction to a question of a proof is called a theorem.

Mathematics is widely used in Newton's law of gravitation combined with mathematical computation. The independence of mathematical truth from all experimentation implies that the accuracy of such(a) predictions depends only on the adequacy of the improvement example for describing the reality. Inaccurate predictions imply the need for reclassification or changing mathematical models, non that mathematics is wrong in the models themselves. For example, the perihelion precession of Mercury cannot be explained by Newton's law of gravitation but is accurately explained by Einstein's general relativity. This experimental validation of Einstein's theory shows that Newton's law of gravitation is only an approximation, though accurate in everyday application.

Mathematics is fundamental in many fields, including natural sciences, engineering, medicine, finance, computer science and social sciences. Some areas of mathematics, such(a) as statistics and game theory, are developed incorrelation with their application and are often grouped under applied mathematics. Other mathematical areas are developed independently from any a formal request to be considered for a position or to be allowed to do or have something. and are therefore called pure mathematics, but practical applications are often discovered later. A fitting example is the problem of integer factorization, which goes back to Euclid, but which had no practical application previously its ownership in the RSA cryptosystem for the security of computer networks.

In the Elements. Mathematics developed at a relatively behind pace until the Renaissance, when algebra and infinitesimal calculus were added to arithmetic and geometry as leading areas of mathematics. Since then, the interaction between mathematical innovations and scientific discoveries has led to a rapid put in the development of mathematics. At the end of the 19th century, the foundational crisis of mathematics led to the systematization of the axiomatic method. This, in turn, delivered rise to a dramatic put in the number of mathematics areas and their fields of applications. An example of it is Mathematics refers Classification, which lists more than sixty first-level areas of mathematics.