### Mathematical specialization, editorial strategies and audiences of 18th to 20th-century periodicals

###### Lisbonne — ESHS 2014 — 4 septembre 2014

###### Organizers: H. Gispert, P. Nabonnand, C.S. Roero

The history of learned journals begins in 1665 with the creation in Paris of the *Journal des sçavans* immediately followed by the *Philosophical Transactions* in London, in both of which mathematics was present, as in most learned journals created after them. From the beginning of the 18th century, mathematics has not always been enthusiastically welcomed by the editors of the Journal des savants, whereas the *Acta eruditorum* of Leipzig played the role of a specialized periodical for the mathematicians involved in Leibniz calculus. In parallel, the *Ladies’ Diary* was created in London at the beginning of the 18th century. This was an almanac whose success over a century and a half was ensured by its mathematical portion which contained arithmetical questions and “*enigmas*”. The question of an audience or a market large enough to support a journal devoted to only one discipline thus arises from the very beginning of the history of journals. This decision to place audiences at the heart of our analysis, stipulating that the creation and the success of a journal are related to the existence of an audience, makes it possible to reexamine from a fresh standpoint the question of the specialization of these journals. This may then contrast with a traditional historiography which maintains that professionalization of scientists, and in particular of mathematicians, said by some to take place at the end of the 18th century and by others at the beginning of the 19th century, is the starting point of the process of specialization of the mathematical press, rather than a new form of an existing process. Throughout the 19th and 20th centuries mathematical journals multiply, corresponding to the increases in mathematical production, in the number of mathematical practitioners, and in the variety of educational institutions. After the *Annales de mathématiques pures et appliquées* that their editor, Gergonne, presented in 1810 as the first periodical miscellany devoted to mathematics, other specialized journals were created in Germany, in France, in Italy, and then in England, to publish research papers in mathematics. In parallel another process of specialization took place, with the creation of journals whose editors, audiences, and authors belong to specific professional milieux – teachers, engineers, military officers – and further, starting from the end of the 19th century, of journals dedicated to particular mathematical fields. This symposium is devoted to these processes of specialization studied over the long term, from the very beginning of the 18th century until the first half of the 20th century. It presents research being carried out within the framework of international projects on the circulation of mathematics and its audiences in various geographical areas. The papers of the symposium’s two sessions will be dedicated to different dynamics of mathematical specialisation in and via journals, as well as to aspects of the segmentation dynamics of the journals’ audiences. Addressing the study of journals by asking questions about their audiences allows a reconsideration of an historiography too exclusively centred on authors, by also taking into account their readers and users. Conferences

###### Mathematical Publishing and Specialization over the long Term in 18th to 20th Century Journals: The Audiences

###### Hélène GISPERT (GHDSO (EA 1610), Université Paris Sud, France),

Philippe NABONNAND (Archives Henri Poincaré, Université de Lorraine),

Clara Silvia ROERO (Department of Mathematics ‘G. Peano’,Torino)

The traditional historiography of specialization of journals, in particular in mathematics, has long been presented as a linear history. Beginning with the creation of the learned journals (17th century), one would have attended a first stage of specialization with the advent of journals devoted to only one discipline – at the end of the 18th century or at the beginning of the 19th century for mathematics -, and at a second stage, with the creation of journals devoted to sub-disciplines (from the end of 19th century onwards). Such a vision, centered mainly on publications dedicated to research, does not give an account of the diversity of the mathematical journals, of their audiences (including the public of authors), of their uses, which have existed during this long time in various areas. We propose to break with this vision and consider the specialization of a journal according to the aims of its editors and the uses audience(s) to which it addresses itself could have. Then the category of specialized mathematical journal becomes more and more complex, diversifies, according to the specialization of editorial projects and to the segmentation of target audiences, communities of authors and readers who take hold of the journals. The history which one can make can be any more, in no way, a linear history. Thus, from a synchronic point of view, the editorial offer in mathematics at different times of this long term period, particularly from the 19th century, presents a range of journals and uses to write, read, learn, practice, utilize mathematics. From a diachronic point of view, taking into account the different geographical and cultural areas incites to describe editorial dynamics both in countries usually considered the center of the mathematical world of the 19th century and in those thought up to now on its margin.

ESHS 2014 — H. Gispert-P. Nabonnand – S. Roero

### Mathematical Specialisation in 18^{th} Century Journals: Early Attemps and the Question of the Audience

#### Jeanne PEIFFER (CNRS, Paris, France)

The paper will be devoted to the study of early attempts of mathematical specialisation of/in learned journals from the 18^{th} century. What may specialisation mean in a century when disciplinary communities were only about to develop and when learned periodicals were of generalist content? At the hands of examples, the paper will investigate this notion and show that the dynamics of specialisation was present in various forms since the creation of the first learned journals. Most of the latter titles included some mathematical information, as the example of the *Journal des sçavans* or *La Clef du Cabinet des Princes* show. Periodicals like the Leipzig *Acta eruditorum*, or to a lesser extent the Italian *Giornale de’ letterati*, built specific editorial strategies, which allowed the small nascent community of Leibnizian analysts to use them as their privileged means of communication. From the start, a demand for specialised journals was vivid among mathematicians. Early attempts of a disciplinary specialisation existed, as the example of Antoine Parent’s *Recherches de physique et de mathématique *(1703-1713) indicates. The reasons for its failure will be discussed, while at the same time period, the immense popularity of the British *Ladies’ Diary*, initially established (in 1704) as an almanac, was due to its mathematical questions, which awoke the curiosity of a large audience putting the journal on a firm financial basis. The link to a profession may also support a specialised journal, as is the case with *Magazin für die Bergbaukunde*, created in 1785, which offers an example of a journal addressed to a profession (mining) and partly dedicated to mathematics. In all the examples to be considered, the success of a specialisation process depends among others on the existence of an audience, may it be a lay audience or a mathematical profession.

### Mathematical Work and Mathematical Publics as Reflected in German-Language Periodical LIterature, 1785-1830.

#### Tom ARCHIBALD (Dept of mathematics, Simon Fraser University, Canada)

With the professionalization of research mathematics in universities during the nineteenth century, the distinctions between research and practical production became quite clear. This was not at all the case in the immediately preceding period, and the very nature of creative research in the mathematical sciences during that period is quite murky. What are the differences between research and practice? between mathematical creation and recreation? Looking at the periodicals that published mathematical literature in German in the years from the death of Frederick II until the eve of the establishment of the Zollverein, we gain an understanding of the publics that engaged with periodical literature containing or specializing in mathematical articles. This period spans the Napoleonic Wars, decisive for the European history of the period. It also begins with what are generally considered the first specialized mathematical periodicals, edited by C. F. HIndenburg , and concludes with the early years of Crelle’s journal. By looking at these and other periodicals, we look not only at the publics for mathematics, but also at the role of publication in the career strategies of various mathematical writers of this period. We will examine shifts in publication practice by authors, in the nature of mathematical articles, and in the role of mathematical publishersalmanac, was due to its mathematical questions, which awoke the curiosity of a large audience putting the journal on a firm financial basis. The link to a profession may also support a specialised journal, as is the case with Magazin für die Bergbaukunde, created in 1785, which offers an example of a journal addressed to a profession (mining) and partly dedicated to mathematics. In all the examples to be considered, the success of a specialisation process depends among others on the existence of an audience, may it be a lay audience or a mathematical profession.

ESHS 2014 — Présentation Tom Archibald

### A Journal for Sailors and Mathematicans Practitioners: *The Nautical Almanac and Astronomical Ephemeris* (1727-1828)

#### Martina SCHIAVON (Archives Henri Poincaré, Université de Lorraine)

The “Nautical Almanac and Astronomical Ephemeris” was published from 1767 by Nevil Maskelyne via the *Board of longitude*, the commission instituted in 1714 by Queen Ann to solve the longitude problem on sea. The Almanac is an annually published ephemeris giving the positions of heavenly bodies for stated points in time and has provided essential data to navigators, geographers and astronomers. The tables also contained everything essential for a “general use” and its users had practically to be skilled on mathematical and even technical knowledge. This talk will consider the Almanac in relation with the *Board of longitude* and the strategies developed by Maskelyne to diffuse astronomical method in longitude computation. Keeping my attention on audiences, I’ll consider how, in 1828, the specialization of the Almanac asked by some of its audiences, i.e. mathematician practitioners or astronomers, eventually caused the dismantling of the *Board of longitude*.

### Adapting publishing strategies to the diversity of editorial offer. The case of mathematics in France (1810-1835).

#### Caroline EHRHARDT (Department of mathematics and history of sciences, Université Paris 8)

This talk aims at looking at the importance of publishing in scholarly life in France at the beginning of the 19th century. At a time when the role of the académie des sciences was changing, when publishing houses producing textbooks started emerging, and when science gained a stronger presence in the general press, how did mathematicians gain their scientific legitimacy ? I will examine how the emergence of various publishing venues allowed the coexistence of several procedures whereby scientific contributions are validated and accepted. Using printed sources aimed at different groups of readers (academic publications, journals, textbooks and periodicals for students and teachers), I will analyze the publishing strategies used by aspiring scholars and show how they could paradoxically attempt to address a non academic readership to make their work accepted and their scientific contribution validated by the mathematical community.

ESHS 2014 — Présentation Caroline Ehrhardt

### Searching for mathematics within French engineering journals in the 19^{th} century

#### Kostas CHATZIS (IFSTTAR/LATTS (CNRS/Ecole des Ponts ParisTech/Univ. Marne-la-Vallée))

It is now a well-established fact that a significant minority of *polytechniciens *in the long 19^{th} century availed themselves of the teaching they received while at *Ecole polytechnique* and its various applications schools, to conduct pioneering work in various areas of mathematics. Vast swathes of mathematics produced by graduates of *Ecole polytechnique* were published in the many engineering journals that were founded in the first third of the 19^{th} century. Among these journals, *Annales des Ponts et Chaussées (APC)* probably stands out from the rest in respect of the quantity of (high-level) mathematics it contained. It must be noted, though, that most of this mathematical production, far from constituting an autonomous body of knowledge, was rather a key component of practice-oriented studies dealing with the various scientific and technical areas embraced by the *Ponts et Chaussées* engineer of the time, such as hydraulics and strength of materials, road and water systems, or bridges and buildings. The case of nomography illustrates well this interplay and intermingling of mathematics and engineering concerns within *APC* in the 19^{th} century. Charged with the repetitive and highly time-consuming task of estimating “cut and fill” volumes, *Ponts et Chaussées* engineers had recourse massively to various original calculation techniques over the 19^{th} century and the early 20^{th} century. Although geared towards practical applications, these estimation techniques nevertheless formed a fertile breeding ground for the creation of a new mathematical area called nomography. Building on the many articles tackling the “cut and fill” issue that were published in *APC*, this proposal aims at analysing the long road to nomography, and in doing so, at casting light on the ways engineering journals functioned as significant sites of knowledge production and diffusion in the field of mathematics during the 19^{th} century.

ESHS 2014 — Présentation Kostas Chatzis

### Teaching and divulgation of mathematics in savoyard and italian pedagogic periodicals (1845-1920)

#### Chiara PIZZARELLI (Department of Mathematics ‘G. Peano’, Torino)

In the last years of the 19th century, the Italian Kingdom saw the flourishing of periodicals specialized in mathematics teaching, such as the *Bollettino della Mathesis* (1896-1920) and the *Periodico di Matematica* (1886-1918). However, the very roots of this scientific and educational fervor, which involved scientists and pedagogues of high level, date back to the second half of 19th century. From the study of the pedagogic periodicals’ succession –risen up after the liberties brought on by the Albertine Statute in Sardinia Kingdom – and, in particular, focusing on their initiatives to increase teachers’ pedagogical competences and scientific knowledge, we gain an overview of the growing participation of specialized editors, mainly pedagogues, increasingly supported by scientists and professors from the Faculty of Mathematical and Physical Sciences of Turin. By sustaining an innovative pedagogical approach influenced by foreign experiences, and promoting its direct application into the schools, periodicals such as the *Giornale della Società d’Istruzione e di Educazione* (1849-54) and *L’Istitutore* (1852-93) addressed teachers who not only needed a concrete support and a professional education upgrade, but also a specialized and distinguished milieu of collaboration and free divulgation of ideas and knowledge. By analyzing the evolution of readers’ typology and topics – and its switch from an initial orientation on the political liaisons and debates to an increasing clustering of mainly technical topics suitable to specific scholastic levels and disciplines – we gather a brand new way of promoting scientific divulgation, aimed to the enhancement of education in both a theoretical and pragmatical aspect. An evolution, which can be considered as the root of mathematics’ teachers associationism as well as the start of a more modern way of teaching Mathematics in the Italian Kingdom of the first years of the 20th century.

### Some aspects of the diffusion of tensor analysis in post-Unitarian Italy journals

#### Luca DELL’AGLIO (Department of Mathematics, University of Calabria)

The subject of this communication concerns the way in which the papers in tensor analysis were published in Italian scientific journals in the various stages of the development of the theory, both before and after its use in general relativity. This subject can be viewed as an historical example of the relationships between the process of specialization of scientific thought at work throughout the nineteenth century and the presence of cultural and scientific Academies with their journals covering many different research fields. In effect, the explicit appearance and the first developments of tensor analysis were essentially connected to the school of G. Ricci-Curbastro and T. Levi-Civita in Padua in the late 19th and early 20th century, with the journals *Atti del Reale Istituto Veneto di scienze, lettere ed arti* and *Rendiconti della Reale Accademia dei Lincei. Classe di Scienze fisiche, matematiche e naturali* as its principal means of diffusion. On the other hand, as regards the development of the theory in Italy, it is also possible to observe an increasing presence of papers published in journals more specifically devoted to mathematical subjects; an aspect that is testified by the role played in this context by the *Rendiconti del Circolo Matematico di Palermo*, in which for example the paper by Levi-Civita on parallel transport were published in 1917.

**Where publishing Mathematics in France before Gergonne’s Journal (1810-1832)?**

**Norbert VERDIER (GHDSO – Université de Paris Sud)**