Segre’s University Courses and the Blossoming of the Italian School of Algebraic Geometry

Abstract

One of the greatest architects of the “geometric Risorgimento” (Coolidge 1927, 352) in Italy, Corrado Segre provides a shining example of the role of mentor in the history of mathematics. His university courses were a veritable forge for future researchers. The years between 1891 and the beginning of the 20th century witnessed the launch in Turin, under his guidance, of the Italian School of algebraic geometry, which in a short time would assume an internationally recognised role. Undoubtedly decisive in the formation of the School was the fact that Segre had fostered the onset and consolidation of the following lines of research: hyperspatial projective geometry; research in the foundations of the hyperspatial projective geometry; birational algebraic geometry; enumerative geometry; projective differential geometry; and projective geometry in the complex domain. However, also significant was the role of his university teaching, a valuable record of which is conserved in the forty handwritten notebooks of his university lectures. These not only make it possible to reconstruct the genesis and developments of his scientific research, but also allow us to understand how his own research stimulated and closely interacted with that of his students, thus showing the importance of his teaching in the flourishing of the Italian School. Here, after a brief overview of Segre’s scientific contributions, we intend to show the close interaction between teaching and research, in order to bring out the influence of his university courses on his students and to pinpoint the moment when his role as leader began to be acknowledged; and make evident the enthusiasm, the nature of the collective work of his group of researchers, at least up to the early years of the twentieth century. We also intend to show how his vision of mathematics education—closely linked to his idea of the objectives of mathematics—was transmitted to the future teachers who attended his courses at the Scuola di Magistero (Teachers College) of the University of Turin. Finally we will try to identify the most salient features of his scientific leadership.