On the Interaction Between Soft and Hard Sciences: the Role of Mathematical Sciences: Looking Ahead to Research Perspectives

Abstract

This paper deals with a study of the conceivable contributions of mathematical sciences to the modeling of complex systems constituted by several interacting living entities, where interactions are nonlocal and nonlinearly additive. The first part of the presentation provides some reasonings and speculations on the specific features of living systems which have to be taken into account in the modeling approach. The second part is proposed as a review of known results focused on a modeling strategy. Some open problems are treated in the third part where hints to tackle them are brought to the readers attention in view of research perspectives. Some free speculations on the complex interplay between soft and hard sciences follows.