Democratization of mathematics through Cremona's correspondence with foreign colleagues (1860--1901) (Q2314089)

This article surveys the edition of 1221 letters written to the Italian mathematician Luigi Cremona [Correspondence of Luigi Cremona (1830--1903). Edited by Giorgio Israel. In 2 volumes. Turnhout: Brepols Publishers (2017; Zbl 1384.01003)]. These letters were found by Giorgio Israel, in 1982, at the library of the mathematical institute of ``La Sapienza'', the university of Rome. Luigi Cremona (1830--1903) is an outstanding figure of 19th-century mathematics in Italy and Europe, both for his scientific and his institutional role. He graduated in 1853 in Pavia as a civil engineer and architect and in 1860 was appointed to the new chair of higher geometry at the University of Bologna. In 1879, he was nominated senator of the Italian Kingdom, and actively took part to projects of reform in school and university programs. Cremona's correspondence treated in this article -- only a part of a larger and partially unexplored corpus -- offers a precious vista on the process of internationalization of mathematics in the second half of the 19th century through the direct voice of its protagonists. The article under review makes a brief survey of Cremona's letters preserved in Rome and in Genoa, describes certain themes discussed in them, mainly regarding the teaching and transmission of mathematics, for instance through translations of Cremona's works, and makes a description of the geographical distribution of the correspondents. The majority of the letters from abroad came from Europe (69 from Germany, 36 from France and 20 from the UK), but Cremona's network was wider, as he had exchanges with correspondents in the US, Australia and Canada. Equally represented is Eastern Europe, with countries such as the Czech territories and Hungary (at the time still part of the Habsburg empire) as well as Romania and Russia. Of particular interest are the linguistic choices made within the European network of Cremona's correspondents. As the authors remark: ``a surprising inter-European linguistic facility emerges (\dots) if compared with current exchanges among university scholars who use a single language -- English''. This linguistic plurality is an expression of patriotic commitment to develop national scientific languages, but did not seem to have hindered the process of circulation and democratization of mathematical knowledge. The apparent tension between the national movements emerging and spreading throughout Europe in the 19th century and the ``universalistic'' vocation that characterized modern science and specifically mathematics from the 16th and 17th centuries is a theme that runs through all this article. Studying the connotations of being a mathematician in 19th-century Italy can provide a way out of this tension, as the authors suggest. Cremona's correspondence shows that mathematics was conceived both as a ``patriotic'' and a ``democratic'' activity. On one hand, its patriotic aspect stemmed from the fact that the scientific and technical training which had mathematics at its core aimed to modernize the nation and to create a new kind of ruling group formed by scientists and engineers. On the other hand, its democratic aspect stemmed from the fact that science (and mathematics) was viewed as a tool to ``liberate thinking from all dogmatic constraints'', as the authors point out, and a culture, inherited from the ancient Greeks, potentially accessible to anyone and understandable by anyone thanks to its universal language: ``the national spirit, according to Cremona's letters, did not run counter to the universal spirit''. The article ends with a suggestion for future research: ``a more in-depth analysis of the penetration of mathematics into individual national cultures and, above all, of the political aspects that played such an important role among the men of the nineteenth century up until World War I is a task that essentially still remains to be carried out''. Hopefully, this suggestion will not go unheeded. For the entire collection see [Zbl 1411.01011].