Mathematical representation became a practical tool with the emergence of computer science
Although mathematical model representation always was related to practical computational tasks, it gained its enormous significance with two interrelated developments: first, the degree of complexity of systems to be implemented and observed which far exceeded previously viable possibilities of human overview and calculations; and secondly, the emergence of highly advanced computational technologies which made it possible to handle this complexity problem.
These new, more serious problems and their technical solutions had repercussions on the development of mathematics and the real tasks represented by mathematics, they connected the procedures and validation standards developed in natural sciences to the examination of scientific fields where stricter mathematical representation was impossible earlier. Biology, medicine, psychology, economics, sociology, historical science and archaeology are all examples of the potential of mathematical-computer science representations.