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This article describes those interaction between applied sciences (mathematics and information technology) and sociologists in the 1960's and 1980's which influenced the subsequent development of Russian sociology. The object of research is scientific articles and other texts (popular science articles, memoirs, interviews) of those participating in past and present interdisciplinary interaction. The main trait of the interdisciplinary cooperation between sociologists and mathematicians is the paradigmatization of sociology as a field of science. Precise sciences played a special role in this process, as they participated in the formation of the language, thematic repertoire and methodological arsenal of sociology. As shown by our analysis, the demand for cooperation was formed by three tasks: of the methodological, instrumental and practical (socio-engineering) variety. The article describes three cases of cooperation. Number one — when it was formed by the organizational and intellectual leadership of mathematicians (Novosibirsk school). Number two — when leadership positions were held by sociologists (Leningrad school). And number three — when "game rules" were set by external agents — the cooperation of sociologists and mathematicians in the name of solving industrial tasks. The typical tasks which scientists collectively solved in each of these three cases were identified and systematized. The article offers conclusions about the significance of this period for the development of sociology. Further development of this topic, in our opinion, lies within giving direction to the analysis of cooperation mechanisms between sociologists and researchers in the field of precise sciences, as well as its institutionalization.

This article considers the subject of interdisciplinary interaction among specialists working in exact and social sciences as a practice of exchanging ideas about social reality; mutual adaptation of these ideas; empirical verification of the universal formal logic rules applied to specific tasks of sociological research. Such formulation of the subject goes beyond the problem of adapting educational programs to "literacy classes" for potential partners. It is maintained that in inter-professional communication it is important to formulate conceptual systems of common use not "in general", not for all possible cases, but with regard to the problem addressed by consolidated effort. For such conceptual systems we use the term "common language area" according to the ideas of epistemologists (Ilya Kasavin). Elements of these conceptual systems include paradigms, concepts, tools and procedures mobilized for collaborative work. Readers are offered a description of the experience of cooperation between mathematicians and sociologists in 1990 – 2010s in the qualitative analysis of sociological data — which is an area of concern for both sociology and exact methods. To find a cooperative solution, we needed to develop a system of basic propositions regarding the object and purpose of the research; to put together a structure of sociological data suitable for using the proposed formal tool; to carry out empirical verification of the formalized language of logic-mathematical reasoning. This work has made it possible to explicate the opportunities and limitations when it comes to interpreting results. The article draws conclusions about the specifics of communication in a team of specialists, including sociologists and mathematicians, and about the development of a common language area in the field of cooperation that deals with qualitative analysis of sociological data. Our experience of cooperation in using formalized qualitative analysis of sociological data shows that, when it comes to the need to solve a common problem, partner role relations turned out to be the most effective (rather than role pairs such as "teacher-student" or "seller-buyer").