Università degli Studi di Pavia

Dipartimento di Matematica ''F. Casorati''

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History of mathematics at the University of Pavia

The study of mathematics has a long and distinguished tradition in the University of Pavia. During the first centuries of existence of the university, up until the reforms enacted by emperors Maria Theresa and Joseph II between 1771 and 1786, mathematics had a secondary role, limited to the “philosophical” curriculum which prepared students to the higher studies in Theology, Law and Medicine. During this period only isolated figures stood out, like Gerolamo Saccheri, logician and precursor of non-euclidean geometry, who was professor at Pavia from 1699 to 1733. It must also be recalled that Gerolamo Cardano, one of the greatest mathematicians of the Renaissance, taught medicine at Pavia on several occasion between 1536 and 1562; there is no indication, however, that he also taught mathematics.

Things changed with the reforms, and in particular from 1786 on, when the teaching of engineering and architecture in Lombardy was concentrated in Pavia. This necessitated a significant strengthening of the mathematics courses. In fact, in 1786 Gregorio Fontana, who had succeeded Ruggero Boscovich on what was at the time the only chair of mathematics in the university, was joined by Lorenzo Mascheroni. The end of the XVIII century was a period of crisis for the University of Pavia, due to political turmoil in which both Fontana and Mascheroni were actively involved. The crisis was made worse by the death of Mascheroni in 1800 and of Fontana in 1803.

It was with Vincenzo Brunacci, professor at Pavia from 1801 to his death in 1818, that a real mathematical school began to take shape in the University of Pavia. From this school issued, among others, Gabrio Piola, Ottaviano Mossotti and Antonio Bordoni. The latter was professor of mathematics at Pavia from 1816 to 1852, succeeding Brunacci. Several important mathematicians trained under his guidance. Among these one may remember Gaspare Mainardi and Delfino Codazzi – both professors at Pavia from 1840 to 1863 and from 1865 to 1873 respectively – and particularly Francesco Brioschi, who joined Bordoni as professor at Pavia from 1850 to 1861. Luigi Cremona, Felice Casorati and Eugenio Beltrami studied in Pavia under the joint guidance of Bordoni and Brioschi. Together with Brioschi, they count among the greatest Italian mathematicians of the XIX century. From the time of Bordoni almost until the end of the century Pavia may be regarded, together with the University of Pisa, as the most important centre for mathematics in Italy and the main point of contact between Italian mathematics and the mathematics of the rest of Europe, thanks also to two scientific journeys: one in 1858 which took Brioschi, Casorati and the Pisan mathematician Enrico Betti to Berlin, Göttingen and Paris, which hosted the most prestigious mathematical schools; the other in 1864 by Casorati alone to Berlin and Dresden.

Another difficult moment for mathematics at Pavia came with the unification of Italy. As a consequence of the Casati law which reformed the universities of the newborn kingdom, the engineering courses virtually ceased at Pavia, and the institution of the Istituto Tecnico Superiore (later Politecnico) of Milan caused serious losses of students, teachers and equipment. During this period the task of ensuring the continuity of the mathematical tradition at Pavia fell essentially to Casorati, who was professor in the university from 1857 to his death in 1890. The scientific isolation that Casorati suffered in Pavia, which he repeatedly lamented in his correspondence, was interrupted in 1875 when Eugenio Beltrami moved from Rome to Pavia. The same year saw the start of the Scuola Normale, initially modeled after the Scuola Normale of Pisa, which remained vital until the end of the century and in whose activities the mathematicians of Pavia actively participated. A few years later, in 1880, another eminent mathematicians, Eugenio Bertini, was appointed to a chair in Pavia. This marked the beginning of what has been called the “golden decade” of mathematics in Pavia. During this period, on Bertini’s initiative, the Mathematical Library was created. Initially conceived as a service to the students of the Scuola Normale, it may be considered the initial nucleus of the future Institute (later Department) of Mathematics. During the same period the positive tradition began of sending abroad for a specialization period the best students who had graduated at Pavia, thanks to fellowships awarded by the Ministry of Public Education.

The premature death of Casorati in 1890 brought this happy period to an end. Within two years first Beltrami, then Bertini left Pavia, moving to Rome and Pisa respectively. However, the mathematical tradition of Pavia continued, thanks also to the presence of the Scuola Normale. The statute of the school provided for one position of internal teacher of mathematics, which was filled by promising young mathematicians who, while waiting for a professorship at a university, found the position a valid alternative to teaching in secondary schools. Among the scholars who filled the position we may mention Giacinto Morera, Tullio Levi-Civita, Tito Camillo Cazzaniga, Orazio Tedone, Roberto Bonola. The chair that had belonged to Casorati was filled first by Ernesto Pascal, professor at Pavia from 1890 to 1907, then by Giulio Vivanti (1907-1924), both distinguished analysts. Carlo Somigliana (1892-1904) succeeded Beltrami on the chair of Mathematical Physics. As for geometry, one must remember in particular Luigi Berzolari, professor at Pavia from 1899 to 1935, and Luigi Brusotti (1931-1947).

After the second World War several mathematicians have given new impetus to mathematics in the University of Pavia, among them Silvio Cinquini (professor at Pavia from 1938 to 1976), Maria Cibrario (1950-1975), Vittorio Emanuele Galafassi (1953-1964) and Enrico Magenes (1959-1993), founder of the Laboratory (later Institute) of Numerical Analysis of the CNR, now IMATI.

Dipartimento di Matematica ''F. Casorati''

Università degli Studi di Pavia - Via Ferrata, 5 - 27100 Pavia
Tel +39.0382.985600 - Fax +39.0382.985602