G. Peano and M. Gramegna on ordinary differential equations

In the context of the theory of infinite matrices and linear operators, two articles by Peano and by Gramegna on systems of linear differential equations have interesting implications for the reconstruction of research on functional analysis between 1887 and 1910. With the aim of evaluating their historical value, linked to logic and vector calculus, this paper provides a detailed analysis of their treatment, demonstrating the modernity of the analytic tools used. In this paper we also reveal the negative consequences that Gramegna’s note had on Peano’s lectureship in Higher Analysis, leading to his dismissal, which marked the beginning of the progressive decline of his school.