A Matter of Style and Praxis. Segre vs. Peano on the Concept of Rigour in Mathematics Education

Between the late 19th century and the 1920s, many of the greatest Italian mathematicians showed a particular sensitivity regarding educational issues, sometimes spurred by their own scientific activity, at other times by interests of a pedagogical and epistemological type or by some kind of social commitment. It is in this context that we may consider the reflections of the members of the two Italian research ‘Schools’ flourished in Turin (those of G. Peano and C. Segre) on the possibility of introducing the results of studies on the foundations of mathematics into teaching, renovating at various levels the traditional treatment of rational arithmetic and geometry. In light of this context, this paper is intended to pinpoint the different ways in which rigour and intuition were characterized by the ‘Peanians’, in relation to both teaching practice and pedagogic theory