Toward a mathematical theory of living systems focusing on developmental biology and evolution: a review and perspectives.

This review paper is devoted to present a personal perspective, based on a critical analysis of the existing literature, about the conceptual difficulties that mathematics meets when attempting to describe the complexity of living matter focusing on the challenging goal of developing a mathematical theory for living systems. The authors propose a personal path, starting from the identification of a number of common features of living systems that can be viewed as sources of complexity, firstly in general, and subsequently focusing specifically on evolution problems. Further, three key questions are posed addressing to a mathematical theory. Finally, the tools of the kinetic theory of active particles are critically analyzed to understand how far this approach still is from the achievement of the afore said ambitious objective.