Up until the French Revolution, European mathematics was an “aristocratic” activity, the intellectual pastime of a small circle of men who were convinced they were collaborating on a universal undertaking free of all space-time constraints, as they believed they were ideally in dialogue with the Greek founders and with mathematicians of all languages and eras. The nineteenth century saw its transformation into a “democratic” but also “patriotic” activity: the dominant tendency, as shown by recent research to analyze this transformation, seems to be the national one, albeit accompanied by numerous analogies from the point of view of the processes of national evolution, possibly staggered in time. Nevertheless, the very homogeneity of the individual national processes leads us to view mathematics in the context of the national-universal tension that the spread of liberal democracy was subjected to over the past two centuries. In order to analyze national-universal tension in mathematics, viewed as an intellectual undertaking and a profession of the new bourgeois society, it is necessary to investigate whether the network of international communication survived the political, social, and cultural upheavals of the French Revolution and the European wars waged in the early nineteenth century, whether national passions have transformed this network, and if so, in what way. Luigi Cremona's international correspondence indicates that relationships among individuals have been restructured by the force of national membership, but that the universal nature of mathematics has actually been boosted by a vision shared by mathematicians from all countries concerning the role of their discipline in democratic and liberal society as the basis of scientific culture and technological innovation, as well as a basic component of public education.

Mathematicians and the Nation in the Second Half of the Nineteenth Century as Reflected in the Luigi Cremona Correspondence

We describe the historical framework and the main issues (biographical, scientific, political, etc.) of the correspondences of Placido Tardy and Luigi Cremona in the libraries of Genoa, which constitute an important contribution to the reconstruction of the History of Mathematics in the Italian “Risorgimento”. In particular, we mainly deal with the Cremona-Tardy, Betti-Tardy and Cremona-Guccia correspondences. Tardy’s letters are preserved at the Genoa University Library and Cremona’s letters at the Mazzini Institute of Genoa.

The Correspondences of Luigi Cremona and Placido Tardy in the Libraries of Genoa

The Italian Risorgimento and the subsequent unification of Italy took place during a period of not only political, but general renewal of the country, and Italian scientists linked themselves to the more advanced fields of European research. This paper focuses on the central figure of Francesco Brioschi and his correspondences with Enrico Betti and Placido Tardy. The scientific themes discussed in their letters are analyzed: the theory of invariants of binary forms, the resolution of fifth degree algebraic equations by elliptic functions, and the theory of fractional integrals. The epistolary relationships of these three mathematicians with their foreign colleagues are also described, which allows for a reconstruction of the frequent journeys undertaken by Italian scholars abroad, as well as those of foreign scholars to Italy. Of particular importance, for the number of letters and their contents, are Brioschi’s correspondences with Felix Klein and Charles Hermite. The main collections come from the Polytechnic of Milan, the Scuola Normale of Pisa, the University Library of Genoa, and the Historical Archives of Gottingen University.

The Renewal of Mathematical Research in Italy: The Correspondences Between Brioschi-Betti (1857–1890) and Brioschi-Tardy (1853–1893)

Luigi Cremona (1830–1903), unanimously considered to be the man who laid the foundations of the prestigious Italian school of Algebraic Geometry, was active at the University of Bologna from October 1860, when assigned by the Minister Terenzio Mamiani (1799–1885) to cover the Chair of Higher Geometry, until September 1867 when Francesco Brioschi (1824–1897) called him to the Politecnico di Milano. The “Bolognese years” were Cremona’s richest and most significant in terms of scientific production, and, at the same time, were the years when he puts the basis for its most important interventions in the social and political life of the “newborn” kingdom of Italy. In this article we present these different aspects of Cremona’s life, with particular emphasis on the relationship of the geometer of Pavia with the academic life in Bologna, with students and colleagues.

Luigi Cremona’s Years in Bologna: From Research to Social Commitment

The involvement of some of the most prominent Italian mathematicians of the end of the nineteenth century has often been highlighted by the historians of mathematics. This article draws a general analysis of the way the position of a mathematician can be used in the political field to found a legitimating discourse, some kind of expertise, or to claim a specific way to consider political questions. It shows in particular that mathematicians in Parliament never forget their disciplinary origins and try to use it to legitimate their stands while some members of Parliament tend to consider them as outsiders whose intervention in the political field is attached to abstraction and somehow disconnected from reality.

Anna Maria Mercurio

Papers

Per la costruzione dell'unità d'Italia : le corrispondenze epistolari Brioschi-Cremona e Betti-Genocchi