Abstract

The Italian Risorgimento and the subsequent unification of Italy took place during a period of not only political, but general renewal of the country, and Italian scientists linked themselves to the more advanced fields of European research. This paper focuses on the central figure of Francesco Brioschi and his correspondences with Enrico Betti and Placido Tardy. The scientific themes discussed in their letters are analyzed: the theory of invariants of binary forms, the resolution of fifth degree algebraic equations by elliptic functions, and the theory of fractional integrals. The epistolary relationships of these three mathematicians with their foreign colleagues are also described, which allows for a reconstruction of the frequent journeys undertaken by Italian scholars abroad, as well as those of foreign scholars to Italy. Of particular importance, for the number of letters and their contents, are Brioschi’s correspondences with Felix Klein and Charles Hermite. The main collections come from the Polytechnic of Milan, the Scuola Normale of Pisa, the University Library of Genoa, and the Historical Archives of Göttingen University.