ПЕРИОДИЗАЦИЯ А.Н. КОЛМОГОРОВА КАК ОСНОВА ПРЕДСТАВЛЕНИЙ ОБ ИСТОРИИ РАЗВИТИЯ МАТЕМАТИЧЕСКОЙ НАУКИ

Abstract

The periodization of the development of mathematical science was proposed by A.N. Kolmogorov. He identifies four periods in the development of mathematics. The basis of periodization includes assessment of the content, level of achievements and features of mathematical research: its most important methods, results, ideas. Particular attention is paid to the development of probability theory structured according to Kolmogorov periods. The prerequisites for the formation of probability theory began to appear during the second millennium BC — the first period. During the period of accumulation of knowledge (before 600 BC), the concept of “chance” — the main concept in the science in question – began to develop. Until the third period, the concept was invariably associated with the philosophical category “fate,” that is, a certain predetermined process, which contradicts modern ideas about chance. Probability Theory received its unofficial name precisely from the period of elementary mathematics (before the 15–16th centuries) — the second period. The next period was called by Kolmogorov “Mathematics of Variables” (XVII–XVIII centuries). Since the beginning of the period of modern mathematics (since the 19th century), random variables and the patterns associated with them have come to the fore in probability theory. This is due to the general scientific growth in the 19th century. The main problems that arose by the end of the third period are being solved: all the basic concepts, rules for their application, and theorems are clearly defined. By the beginning of the 20th century — the fourth period–there was a need to formalize the acquired knowledge. Andrei Nikolaevich built a system based on modern and already developed by that time set theory and measure theory. The periodization of the development of mathematical science, proposed by A.N. Kolmogorov, with the rapid progress of mathematical knowledge and the emergence of information technologies in the future may require adjustments to the last stage of development of the history of mathematics or will lead to the emergence of a new stage of periodization.