I shall try to give a description of the various groups and current lines of thought which present a wide range of interests, and I apologise to the authors cited for the simplification of my outline given the restriction of space available to me.
5 Pietro Ricardi e la storiografia cit.
In Florence there is Enrico Giusti, whose main contributions have been to the analysis of the works of Galileo and the Galilean School: the doctrine of motion, the theory of proportions, Cavalieri‘s theory of indivisibles, as well as to the historical foundations of infinitesimal calculus. Enrico Giusti also deserves special mention for planning and setting up ―Il Giardino di Archimede‖, a museum of mathematics aimed at arousing young people‘s interest in mathematics and the history of mathematics. He is assisted in the running of the museum by Raffaella Petti. The research group also includes Sandra Giuntini, whose main contribution is the edition of correspondences and documents of mathematicians of the seventeenth and eighteenth centuries, Elisabetta Ulivi, who, after her first studies on the Galilean School, devoted her attention to abacus mathematics and the abacus schools in Tuscany in the 14th-16th centuries, expanding the research carried out by Arrighi, Procissi and then by Laura Toti Rigatelli and Raffaella Franci. The research group collaborates with Pier Daniele Napolitani in Pisa, who investigated the transmission and reconstruction of science of the Greek Hellenistic Age by sixteenth century mathematicians like Luca Valerio, Federico Commandino and Francesco Maurolico; he is now supervising the national edition of Maurolico‘s works. Veronica Gavagna, after an initial research on mathematical correspondences of the early twentieth century, besides taking part in the scientific publications of the Maurolico Project, is now focussing on the Caparrini and Erika Luciano are also part of the Turin group.
In Rome, Giorgio Israel co-ordinates a group, of which Ana Millan Gasca and Luca Dell‘Aglio are part, that has developed research on the history of mathematics applied to economics and social sciences, probabilities and statistics.
Israel has, moreover, been working on the reconstruction of the mathematical milieu of the Fascist period.
Mathematics in Italy between the two world wars is also the subject of research by Angelo Guerraggio from the Bocconi University of Milan. He founded a journal of mathematics and history of mathematics for circulation among enthusiasts and teachers of mathematics called Lettera Matematica Pristem (in collaboration with Simonetta di Sieno).
Massimo Galuzzi, working in the State University of Milan, has been researching the history of the solution of algebraic equations (Galois‘ theory), the School of Bourbaki and the historiography of mathematics.
In Milan, there are also Paola Gario and Umberto Bottazzini, the latter a historian of international renown who has focussed his research mainly on mathematics in nineteenth century Italy, and its relationship with the French and German schools. One of his pupils, Rossana Tazzioli, has devoted herself to the study of the history of non Euclidean geometries of that period and the first models of hyperbolic geometry. Paola Gario has studied the Italian school of geometry, with particular regard to Enriques and Castelnuovo, as well as the history of the teaching of mathematics and the formation of teachers of mathematics.
In Bergamo, Pier Luigi Pizzamiglio has devoted his studies to the bibliography and publication of classics, the history of scientific instruments, and the history of mathematics in relation to the teaching of mathematics.
The nineteenth century is also the focus of Paolo Freguglia‘s research at the University of Aquila, regarding the history of algebra and geometry in the 16th-17th centuries, the foundations of mathematics and logic in the 19th-20th centuries, the vector calculus and correlated theories (quaternions). Instead, the history of absolute differential calculus and mathematical physics of the late nineteenth and early twentieth centuries, and the foundations of the probability theory constitute the subjects of research by Luca Dell‘Aglio at the University of Calabria.
At the University of Calabria the leading historian of mathematics is Luigi Maierù, whose investigations are above all linked to sixteenth century mathematics such as the criticism of Euclid‘s Fifth Postulate, the angle of contact and the theory of conics.
The Ferrara group is composed of Luigi Pepe, Maria Teresa Borgato and Alessandra Fiocca, whose main focus has been the mathematics of the eighteenth and early nineteenth centuries through the publication of numerous unedited works above all of J.L. Lagrange. Luigi Pepe has carried out research into mathematics in eighteenth century Italy and the Napoleonic period with particular regard to Gaspard Monge‘s missions in Italy, the dissemination of infinitesimal calculus in Italy, the history of the teaching of mathematics and the scientific institutions. Maria Teresa Borgato‘s interest has focussed on the Jesuit scientists of the seventeenth century, Lagrange‘s biography, eighteenth century actuarial mathematics, and mechanics and hydraulics of the Napoleonic period. Alessandra Fiocca has studied the science of waters in the Renaissance and seventeenth–eighteenth centuries, the history of the university and Libri‘s historical works.
Francesco Barbieri and Franca Cattelani Degani, in Modena, have contributed with archival research and the publication of correspondences to the biographies of mathematicians and historians of mathematics of that city (Pietro Riccardi, and Paolo Ruffini).
Proceedings of the 4th International Conference of the ESHS, Barcelona 2010 45
In Genoa, we have the group co-ordinated by Antonio Carlo Garibaldi, which includes Giuseppina Fenaroli and Michela Malpangotto: their research works have investigated the history of the probability theory, the history of mechanics and the publication of various correspondences between mathematicians.
In Naples (and then in Salerno) Franco Palladino has been studying the mathematics correspondences in the nineteenth century and the history of mathematical models and instruments. Romano Gatto has done research into the mechanics of Galileo and the Neapolitan tradition. Giovanni Ferraro, at the University of Molise, has investigated the theory of series, the integration theory and the theory of functions in the eighteenth century.
In Palermo, Aldo Brigaglia is the co-ordinator of a group, which includes Cinzia Cerroni, whose focus is the history of algebraic geometry as well as the Circolo matematico di Palermo, a famous journal that collected important contributions from European mathematicians. Pietro Nastasi also works in Palermo studying the history of the Institute for the Applications of Calculus as well as the history of institutions during the Fascist period.
Various Italian scholars have carried out their studies mostly in other countries: Niccolò Guicciardini in Great Britain, where he worked on Newton‘s theory of fluxions and the development of calculus in that nation; Marco Panza in France where he carried out research mainly on the eighteenth century; Rossana Tazzioli, presently in Lille, has studied the relationship between Vito Volterra and French mathematicians.