The renewal of mathematical research in Italy: the correspondences Brioschi-Betti (1857-1890) and Brioschi-Tardy (1853-1893)

The Italian Risorgimento and the following unification of Italy was a period of general, not only political, 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 means of elliptic functions, and the theory of fractional integrals. The epistolary relationships of these three mathematicians with their foreign colleagues is also described, which allows a reconstruction of the frequent journeys abroad undertaken by Italian scholars, as well as those of foreign scholars to Italy. Of particular importance for number of letters and 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