The Italian School of Algebraic Geometry and the Teaching of Mathematics in Secondary Schools: Motivations, Assumptions and Strategies

As it is well known, the Italian school of algebraic geometry was born in Turin at the end of the nineteenth century, under the guidance of Corrado Segre. It soon brought forth such significant results that it became a leading light (führende Stellung) on an international level, as F. Meyer and H. Mohrmann affirm in the Encyclopädie der mathematischen Wissenschaften. Segre inspired an atmosphere of work characterised by highly prolific, enthusiastic, and frenetic activity, which Guido Castelnuovo, remembering his years in Turin, would refer to as “Turin’s geometric orgies”. The mathematicians involved were gifted students preparing their degree theses with Segre, such as Fano, Beppo Levi, Tanturri, Severi, Giambelli, Terracini, and Togliatti. A number of newly graduated students from Italy and abroad were also drawn to Turin by Segre’s fame. Amongst these, the most famous were Castelnuovo, Amodeo, Enriques, Scorza, the English couple William H. Young and Grace Chisholm Young, and, from the United States, Julian Coolidge, E. B. Stouffer, and C. H. Sisam. The great significance of the scientific results obtained by the School has led historians of mathematics to overlook, or at best to attach only secondary importance to, the issues related to mathematics teaching that would occupy many of its members, including Segre himself, throughout their lives. Here I illustrate the reasons which led some members of the Italian School of algebraic geometry – in particular, Corrado Segre (1863-1924), Guido Castelnuovo (1865-1952), Federigo Enriques (1871-1946) and Francesco Severi (1879-1961) – to become so concerned with problems pertaining to mathematics teaching; describe the epistemological vision which inspired them; discuss the various ways in which this commitment manifested itself (school legislation, teacher training, textbooks, publishing initiatives, university lectures, etc.); make evident the influence of the reform movements abroad, particularly that of Klein; finally, show how, in this respect as well, Italian geometers projected an unquestionable image of a “School”.