Circulating Mathematics via Journals: The rise of internationalization - 1850-1920

The forms of mathematical communication are in the process of deep change, imposing a restructuring of the system of communication as it had developed since the 19th century. In the light of this process, the task to investigate, at different scales (local, national and international), the specialised mathematical periodicals that developed in the time period 1850-1920, seems particularly stimulating for historians of mathematics. Indeed along with the creation of specialized journals strongly involved in the shaping of national mathematical communities – like Crelle’s Journal für die reine und angewandte Mathematik (Berlin 1837), Liouville’s Journal de mathématiques pures et appliquées (Paris 18) or Tortolini’s Annali di scienze matematiche e fisiche (Rome 1850) – periodicals stressing the international dimension develop. The first to be mentioned here is of course Mittag-Leffler’s Acta mathematica, created in 1882, but also the Rendiconti del Circolo matematico di Palermo (Palermo 1885). In the chosen time period, small local titles exist along with “national” journals, which try of course to attract contributions from major foreign mathematicians, and the nascent international periodicals. It is also the period when the newly created national societies publish their Bulletins. The political background, especially the competition between France and Germany after 1870, creates a strong tension between the more local and global aspects of publishing and circulating mathematics via different types of journals.

In history of mathematics, journals have ever been used as major sources for research, the most important titles have been more or less extensively studied, but it is only in the last decades, in the wake of the development of the social history of mathematics, that more broad questions concerning the circulation of mathematics at different scales and in different cultural areas, its main actors – producers of mathematics, intelligencers, users, publishers… – the editorial backgrounds and strategies moved centre stage. Studies centred on one journal or a single country, are insufficient to have a good understanding of the whole dynamics of circulation.

Among the questions on the research agenda, the most important may concern the local aspects of so-called international mathematical journals and the links of more local journals to the national and international mathematical communities and institutions. Indeed, international journals are also produced locally, they depend on local human and material resources such as mathematicians, authors or subscribers, printers, postal systems, and so on. They may need the financial support of local institutions and rely on the know how of local publishing houses. The building of international reading audiences heavily depends on the mathematical and social networks of the editor and the commercial network of the publisher of the periodical. International journals may benefit from a local, regional or national tradition of publishing mathematics’ journals and rely already on a strong reading audience in a limited geographical area. That’s why they have to be studied in the broader context of the changing relations between mathematical centres (Berlin, Paris, Göttingen, Cambridge) and the periphery.

Another stimulating but yet poorly investigated question concerns the interplay between different journals. It is well known that Gösta Mittag-Leffler built his broad network of authors and readers by exchanging his journal, Acta mathematica, with other mathematical periodicals. This habit explains in part the richness of the collections kept in the library of the Institute. If the sources are available, and in the case of Mittag-Leffler’s Acta they are, their systematic study will give interesting insights in the materiality of circulating mathematics. Another source of interplay between journals between 1850 and 1920 are of course translations. No in depth study exists of the translation processes in the second half of the 19^th century. It would allow investigating precisely how certain mathematical problems, questions, results, techniques,… circulated from one cultural area to another. Why does a mathematician decide to publish a paper abroad, and how does he choose among an array of possible publishing opportunities? Do the latter depend on personal or institutional incentives? These are some of the research questions we will have to face. Case studies on the circulation of particular mathematical subjects among journals, communities and disciplines (via reprints and translations), and how they change when being translated and circulated, can also be particularly enlightening.

The purpose of the conference is to bring together in a stimulating environment a group of historians of mathematics, all engaged in a research project, Cirmath, supported by the French ANR (Agence Nationale de la Rercherche), in order to discuss the questions outlined above, while also benefitting from the rich historical collections of the MLI library, especially those concerning the early period of the journal Acta mathematica under Gösta Mittag-Leffler.