Periods of development of mathematics

Аннотация

This article provides information about the stages of development of mathematical science ancient times and the work being done today to develop the field of mathematics. Keywords: A.N.Kolmogorov , elementary mathematics , Khwarizmi , M.Merson, analytic geometryю Most mathematicians of history prefer the periodicity of the development of mathematics recommended by A.N.Kolmogorov. The main reason for this is tha Kolmogorov’s periodization is based on important methods , ideas, and results of mathematics. The division of the development of mathematics into such special periods does not completely solve the essence of the history of mathematics but will be an additional tool for a better understanding of the objective laws of mathematical development. 1. The emergence of Mathematics. This period began in the 6th century BC. That is during this period mathematics became an independent science with its own subject and methods. The beginning of the period dates back to the earliest period – the primitive community system – collection of mathematical facts. 2. The period of elementary mathematics (the period of mathematics of variables). It lasted from the 6th to the 5th centuries BC to the 17th century BC. During this period great achievements were made in the study of variables. Mathematics courses taught in secondary schools can give some idea. The creation of the science of algebra by the Uzbek scientist Muhammad ibn Muso al- Khwarizmi (780-850) , the creation of analytical geometry by Dascartes , the beginning of the development of infinitely small quantities. In general , the concept of elementary mathematics is difficult to define. There is no clear definition of it but it is correct to distinguish such a period in the history of mathematics and it makes easier to study its history. 3. Mathematics of variable quantities. The definitive creation of analytic geometry begins with the emergence of differential and integral calculus by I.Newton (1642-1727) and Leibniz (1646-1716). The end of this period goes back to the end of the 19th century. At the same time all the scientific foundations of mathematics, called classical mathematics were formed. 4.Modern mathematics. It dates back to the mid-19th century. This period is ,characterized by the growing role of mathematical abstraction , the widespread use of mathematical modeling in mathematics. It was during 175 Scientific research results in pandemic conditions (COVID-19) this period that what I called classical mathematics became much narrower to apply to itself , to other areas of mathematics. The reason is that mathematics has split into many branches. The axiomatic method was widely developed in it . As a result, a new mathematical concept – a mathematical structure – emerged. The concept of mathematical structure helps to teach a unit of mathematical facts and methods that seem too far apart at first glance creates different mathematical structures. In recent years various branches of mathematics and even some mathematical subjects have begun to be interpreted as the material of those structures. Therefore, modern mathematics can be described as a science of mathematical structures and their models. Mathematics like all other sciences, is constantly evolving. There are two reasons for this : first , its development requires daily life and practice. Second , development is required by the internal needs of mathematics. The rapid development of mathematics with pictures has a great influence on the development of technology , economics , production management , as well as the development of other neighboring disciplines. Mathematics (Greek thematics, mathema-knowledge science ) is a science of knowledge based on clear logical observations. In today`s mathematics , calculations, even operations on formulas, take up very little space. Mathematics in the oldest branch of science and has a long history of development and at the same time the answer to the question “What is mathematics?” . Has changed and deepened. In Greece mathematics is understood as geometry. In the 9th and 13th centuries the concept of mathematics was expanded by algebra and trigonometry. From the 17th and 18th centuries analytical geometry , differential and integral calculus became central to mathematics and until the early 20 th century it was defined as “ the science of quantitative relations and spatial forms”. In the late 19th and 20th centuries, various geometries ( such as Lobachevsky geometry, projective geometry , Riemannian geometry ), algebras (Bull algebra, quaternion algebra, Kelly algebra ), infinitely dimensional spaces, etc. were very diverse in content, often artificial in nature. As objects began to be studied , the above definition of mathematics became too narrow. During this period as a result of the formation of a specific style and language of observation based on mathematical logic and set theory , the idea emerged in mathematics that feature is strictly logical obs