La scuola di Peano e il secondo problema di Hilbert

At the World Congress of Mathematics, Hilbert gave a famous lecture on the "Problems of mathematics". Peano attended the lecture and declared that the 2nd problem (the compatibility of the arithmetical axioms) had already been solved by his school. This article analyzes his declaration in the context of contemporary debates and of the work Peano and his collaborators did on the foundations of arithmetics, providing a new perspective on their work and on the competing epistemologies of mathematics of that time.