In our time, few argue that the theoretical and empirical knowledge of the sociologist should closely interact with each other in the process of solving any sociological problem: empirical knowledge must confirm the correctness of the theoretical, theoretical – provide a basis for obtaining the empirical. However, no constructive rules for the practical organization of such interaction have yet been developed. In this article, such rules are proposed for a situation where new empirical knowledge is obtained through the use of mathematical methods in traditional ways for sociology. Namely, it is shown that for the effective interaction of the theoretical and empirical stages of research it is required that the process of applying the mathematical apparatus boils down to the construction of a series of such mathematical models of social reality that can be considered carriers of the sociologist’s theoretical knowledge of the phenomenon being studied. This can be facilitated by: (a) the introduction into scientific use of a specific view of mathematics, according to which it is understood in two ways: not only traditionally, as a rigorous formal science, but also as a scientific branch aimed at developing rules for constructing a model of the reality being studied, written in mathematical language; (b) the consideration of all models embodied in mathematical methods as results of a generalized measurement, ensuring that the interpretation of the above models corresponds to the a priori theoretical views of the sociologist; (c) use of methodological principles of application in the sociology of the mathematical apparatus developed, in particular, by (1) well-known American methodologist P.F. Lazarsfeld; (2) Russian mathematician A.A. Chuprov; (3) creators of the data analysis; (4) the author of this article. According to the author’s intention, the article should show that the possibility of successful application of theoretical knowledge for obtaining empirical and back is not accidental arises precisely on the basis of using a mathematical apparatus, since such use requires a clear formulation of ideas about both types of knowledge.