  The paper discusses fundamental problems in mathematical description of
social systems based on physical concepts, with so-called statistical social
systems being the main subject of consideration. Basic properties of human
beings and human societies that distinguish social and natural systems from
each other are listed to make it clear that individual mathematical formalism
and physical notions should be developed to describe such objects rather then
can be directly inherited from classical mechanics and statistical physics. As
a particular example systems with motivation are considered. Their
characteristic features are analyzed individually and the appropriate
mathematical description is proposed. Finally the paper concludes that the
basic elements necessary for describing statistical social systems or, more
rigorously, systems with motivation are available or partly developed in modern
physics and applied mathematics.
