The correspondence between Felice Casorati and Angelo Genocchi: scientific renewal and new teaching approaches in post-unification Italy

Abstract

The aim of this article is to analyse the correspondence between the mathematicians Angelo Genocchi (1817-1889) and Felice Casorati (1835-1890), in order to investigate the impact that they had on the innovation of mathematics teaching and research in Italy after its Unification. The correspondence covers twenty years (1865-1886), with a total of 26 letters, of which 11 were sent by Casorati and 15 by Genocchi, plus a letter from Emil Weyr to Casorati. Recent historiography, which also agrees with the opinion of Vito Volterra, brings out a portrait of Casorati as a man who “lived almost exclusively for his pupils and his school”. The same cannot be said of Genocchi: an innovator, but one to be downplayed, according to other historians. Therefore, it is precisely to shed light on this ambiguity that the analysis of the correspondence with Casorati is inserted, whose topics are solely concerned with teaching and research. It is also intended to highlight how Genocchi’s contribution improved mathematical teaching at the University of Turin, as well as the original results he achieved in number theory. In this regard, after retracing their respective biographies, the panorama of mathematical teaching at the dawn of Unity will be given, without neglecting the Analysis courses they held in Pavia and Turin. Casorati and Genocchi interacted rather well one with another: a first example is the Casorati’s treatise Teorica delle funzioni a variabile complessa to which Genocchi made a notable contribution, and the active commitment of both in supporting excellent young scholars, both for candidacies in competitions and for career opportunities abroad. Finally, evidence from this correspondence will clarify how their divergences in practical approach to the subjects were due to cultural and generational factors, as their objectives are often aligned, at least in their teaching and research intentions.