Kilka uwag o formalnych zasadach matematycznego modelowania zjawisk ekonomicznych i interakcji społecznych

Mathematics as an abstract science was derived from studies and analyses of the material word. However, “pure” mathematics very often creates its imaginary objects which develop independently, lead their own “imaginary” lines and very seldom have their equivalent in the surrounding reality. Nevertheless a completely new aspect of mathematics is highlighted when it is used for describing real phenomena, since – due to its highly formalized language – it enables practitioners, including economists, to specify relations and operations between objects under study. In order to achieve this goal the appropriate models have been created. Theconstruction of new models in economic science (and in many other domains) aims simplifying and formalizing many problems which, in fact, may increase the probability of finding relevant solutions. Furthermore, from the economic point of view, due to the high precision with highlighted above models work, essential conclusions are to be drawn, which subsequently may prove relevant for the progress of science. The aim of this paper is to present how modeling economic phenomena and social interactions have been developed within many years by using formalized language of mathematics economic phenomena and social interactions which have been developed within many years by using formalized language of mathematics.