At the round table the problem was discussed of using mathematical methods in the analysis of historical process, or methods of historical macrosociology. On the one hand, it is obvious that in the history different societies have certain regularity, which can be examined by statistical methods. This applies to demographic waves as well as to certain economic realities, etc. For instance, we can point to the Kondratieff’s waves. If we take it for granted, it appears that it is possible to speak about the corresponding laws. However two problems appear straight away – the quality of data on which to rely, and the ratio of the peculiarities of the history of some particular societies and the general laws which characterize any society. Economists, the most advanced in application of mathematics, are building system models, while historians are just approaching to this. There is inductive approach to these issues as well, when historians use statistics to analyze certain specific processes. Also such issues were discussed such as the transformation of professional history into applied political science, which is certainly counterproductive from the point of view of science as such, and the problem of the access to the archives. In addition, it was indicated that there is a deep connection between historical research and such complex discipline as adaptology. Participants also discussed the problems of interpretation of historical data and the status of social sciences in general.