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

Between the 19th and 20th centuries many common traits were shared by national mathematical communities far apart geographically (from the Czech lands to Japan), culturally (from north to south Europe) or as to the dynamism of original research (from Germany to the United States). Societies and journals in the national language were launched, thanks to the widening of the social platform of mathematics and the emergence of a national leadership; the deployment of the state school systems increased mathematical information; and mathematics played a role and received encouragement from the processes of social and economical modernization and development of state institutions. Intellectual competition among nations, much in the spirit of the 19th century, seem to prevail on the early Modern European universalism. A panorama of almost planetary diffusion of Western mathematics resulted from this evolution, and eventually a reinforcement of international circulation of knowledge, which survived two world wars. The collection of letters written to Luigi Cremona conserved at the Sapienza University of Rome throws light on several aspects of this evolution. Letters offer a point of view on the "backstage", in contrast with official proclamations; they show the interplay between national leaders and the circles in the capitals and mathematicians working in isolation; they show a variety of connected activities – research, institutional commitments, and cultural fostering, including translations and textbooks. International dialog grew out of this nebula of initiatives driven by national passion, by philosophical and political convictions; in contrast with the present European trend to entrust the circulations of ideas – and the production of knowledge – to initiatives governed from the top, and standardized (design, funding and assessment), far beyond what would be needed. The edition (in the Académie Internationale d'Histoire des Sciences series "De diversis artibus") has been carried out by a European team directed by Giorgio Israel.