Characterizing a Mathematical School. Oral Knowledge and Peano’s Formulario

This article is devoted to a re-interpretation of the activity of the Peano School linked to the Formulario di Matematica, a text that has always been presented as the manifesto par excellence of this group. The choice of a new perspective, buttressing the analysis of this encyclopaedic work with that of the exchanges among the Peanians - reconstructed thanks to new archival sources - has made it possible to replace the clichés produced by historiography and to recover and properly attribute to Peanians a substantial mass of results in logic and foundations of mathematics, which circulated in the School but without ultimately filtering into the Formulario. A stark contrast emerges between the image of the Peano School generally delivered (that of a cohesive, hierarchically structured team) and the real practices of collective construction and socialization of mathematics within a network of scholars much looser than one might deem.