The ArgumentThe development of modern mathematical biology took place in the 1920s in three main directions: population dynamics, population genetics, and mathematical theory of epidemics. This paper focuses on the first trend which is considered the most significant. Modern mathematical theory of population dynamics is characterized by three aspects (the first two being in a somewhat critical relationship): the emergence of the mathematical modeling approach, the attempt at establishing it in a reductionist-mechanist conceptual framework, and the revival of Darwinism. The (...) first section is devoted to the analysis of the concept of mathematical model and the second one presents an example of a mathematical model (Van der Pol's model of heartbeat) which is a good prototype of that concept. In section 3 the main trends of mathematization of biology and the cultural and scientific contexts in which they found their development are discussed. Sections 4 and 5 are devoted to the contributions of V. Volterra and A. J. Lotka, to the analysis of the differences of their scientific conceptions, and to a discussion of a case study: the priority dispute concerning the discovery of the Volterra-Lotka equations. The historical analysis developed in this paper is also intended to detect the roots of some recent trends of mathematization of biology. (shrink)

We can distinguish between two different ways in which mathematics is applied in science: when mathematics is introduced and developed in the context of a particular scientific application; when mathematics is used in the context of a particular scientific application but it has been developed independently from that application. Nevertheless, there might also exist intermediate cases in which mathematics is developed independently from an application but it is nonetheless introduced in the context of that particular application. In this paper I (...) present a case study, that of the Lagrange multipliers, which concerns such type of intermediate application. I offer a reconstruction of how Lagrange developed the method of multipliers and I argue that the philosophical significance of this case-study analysis is twofold. In the context of the applicability debate, my historically-driven considerations pull towards the reasonable effectiveness of mathematics in science. Secondly, I maintain that the practice of applying the same mathematical result in different scientific settings can be regarded as a form of crosschecking that contributes to the objectivity of a mathematical result. (shrink)

In the interwar years the Gran Paradiso ibex population followed two subsequent, contrasting trends: a steady rise once the national park was established in 1922, followed by a precipitous fall after the Fascist regime took direct control of conservation in 1934, which almost led to the colony’s extinction. This paper addresses the issue of how models taken from population ecology may inform historical narratives. The data for the interwar years were analyzed using a statistical model based on climate and population (...) density, which has proved reliable for most of the post-World War II period. The article highlights the pivotal role of anthropic variables in determining the inter-war trends and how these are best analyzed using historical scholarship. (shrink)

ArgumentMy contribution focuses on two aspects strictly related each other. On one hand, the progressive marginalization of Volterra from Italian scientific and political life after the rise of Fascism – because of his public anti-Fascist stance, both as a senator and as a professor – until his definitive exclusion on racial grounds in 1938. On the other hand, the reactions of his French colleagues and friends to this ostracism, and the support he received from them. As it emerges from several (...) sources (Volterra's correspondence, institutional documentation, conference proceedings, etc.), it was mainly thanks to their support that he was able to escape the complete isolation and the “civil death” to which the regime condemned many of its adversaries. (shrink)