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Guido Castelnuovo and mathematics in Rome between the Risorgimento and the Belle Époque. (Italian. English summary) Zbl 1392.01017
The red line of this paper is to explain why Guido Castelnuovo (1865–1952), who was one of the most brilliant algebraic geometers, around 1905 abandoned almost completely his field of research and dedicated himself to the teaching of probability calculus and statistics (p. 229). Castelnuovo, jointly with Federigo Enriques, had reached important results in the study of algebraic surfaces. New methods were necessary to further develop the research. At this stage, Castelnuovo, as is well explained by the author, preferred to give his contribution to the economical and social development of Italy by educating the new leading class. For the necessities connected to the industrial development, the knowledge of probability calculus and statistics was important. This justifies Castelnuovo’s choice.
The author arrives at explaining Castelnuovo’s decision remembering the important role that mathematicians and scientists had in the attempt to make Italy a modern and industrial country starting from the Italian unification (1861).
Therefore, in Section 2, the author reminds of the political engagement of Italian mathematicians of the post-Risorgimento period to improve the Italian situation. Great mathematicians as Cremona, Betti, Casorati, Beltrami and, first of all, Brioschi, had important tasks in the educational context of the Italian policy of that time. They tried to reduce the gap between Italy and industrial countries as France, England and Germany. In this context, the attempt to make Rome a leading centre for research and education in Italy played a significant role. This situation lasted until about 1875. After that, the general crisis, which affected Europe until half the 90s of the 19th century, was particularly serious in Italy, and the gap between Italy and the advanced part of Europe became even more vast (Section 5). Things began to partially change in the last years of the 19th century and in the period of the 20th century preceding the First World War – the Belle Époque. In an ephemeral state of optimism and economical development, in Italy a situation, in a sense, comparable to that of the post-Risorgimento existed. Castelnuovo, who had become Professor at the University of Rome in 1891 (Section 4), felt both the duty to give his contribution for the development of Italy and for the improvement of the Roman scientific milieu. As to the latter question, the author clearly explains the way in which, thanks to Castelnuovo’s efforts, Vito Volterra – probably the then most important Italian mathematician – was called to the University of Rome (Section 6).
Finally, the author explains how Castelnuovo’s familiar milieu also had a significant impact on his educational-social engagement with his country (Section 8) as well as Castelnuovo and Volterra’s work in the Rome of the Belle Époque. This paper is well conceived. It is quite synthetic considering the breadth of the addressed subjects. Nonetheless, it offers a good picture to introduce the reader to an intriguing context, both from a mathematical and socio-historical point of view.

01A55 History of mathematics in the 19th century
01A60 History of mathematics in the 20th century
01A73 History of mathematics at specific universities
Biographic References:
Castelnuovo, Guido
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