Three algebraists at the Gioenia Academy: Cipolla, Scorza, and Spampinato

Abstract

The article discusses three renowned algebraists -Gaetano Scorza, Michele Cipolla, and Nicolò Spampinato- who were members of the Gioenia Academy and professors at the University of Catania. In the first half of the twentieth century, they significantly influenced the course of mathematical research both in Italy and abroad. After briefly describing the intellectual fervor that animated mathematical research in Catania among this group of scholars, as well as the main lines of their work, the article focuses on the notion of infinity. The study and debate on this concept within the Gioenia Academy link the authors to the three aforementioned algebraists, demonstrating the contribution that Catania’s mathematical community made to the emerging theory of algebras at the beginning of the twentieth century. In particular, the treatment of infinity in the context of real variables highlights the complexity and significance of Spampinato’s studies on the same issue in the case of complex variables. From this perspective, Spampinato explores infinity in multi-unit algebras, eventually showing that in the field of n complex variables, the same notion of infinity is obtained as with the projective viewpoint. This approach connects the different conceptions of infinity in both the complex field and the multi-unit algebraic case.