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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").