At the end of the 17th and at the beginning of the 18th century, ageing constitutes an issue specific to medicine. Indeed, on the one hand, ageing portrays a normal process of the living; and on the other hand, the old age is often followed by specific pathologies. Is it really possible to dissociate the old age from the pathology? If so, how can we think of the old age and explain both the necessity and the normality of it? If not, what is the cause of this dysfunction? This is what is at stake among the modern medical controversies, which argue along with the respective partisans of the iatromecanism (Descartes), the empirical medicine (Sydenham) and the animist medicine (Stahl). Furthermore, it progressively appears that the issue of aging must also be addressed within the social field, which is determined by sanitary, economic and strategic challenges. Indeed, doctors, economists and philosophers (Graunt, Petty, Leibniz) have been trying to assess the old age with the new methods of Arithmetic Policy. Thus, in this paper, we want to draw the modern constitution of the systems of knowledge that the old age requires, as a medical category located at the borderline between epistemological, practical and social challenges.