Séminaire – Histoire des sciences, histoire du texte

Reorganisations
Org. Arilès Remaki

Erika Luciano , (Dipartimento di Matematica G. Peano, Università di Torino)
The archive(-s) of the Formulario di Matematica : logics and practices of a collective organization and reorganization of sources
Résumé :
The encyclopaedic treatise Formulario di Matematica is usually considered the manifesto of the School of Peano. Published from 1894 to 1908, its five volumes constitute a publication that escapes the common bibliographic classifications : they are not reprints, because the discussion becomes increasingly extensive ; they are not sequels, because the text restarts each time ; and they are not subsequent editions, because sometimes “temporary editorial demands made it necessary to highlight the latest results, without reproducing some fundamental contents, considered classic by that time”.
In its last version, the Formulario included over 5000 propositions written in ideographic language, accompanied with historical annotations and bibliographic references.
The publication of these texts asked Peano and his protégés to do a demanding and continuing work of organization and reorganization of their archives. In this paper, we will analyze the collective activity of classification, ordering, indexing, composition and decomposition of archive materials performed within the School of Peano in relation to the construction of the Formulario di Matematica through the dozen years of its publication.

Célestin Xiaohan Zhou , (The Institute for the History of Natural Sciences, Chinese Academy of Sciences)
Reorganization of Text from Ancient Mathematical Classic : Yang Hui’s (ca. 1261 CE) Mathematical Methods Explaining in Detail The Nine Chapters and Reclassifications
Résumé :
The Nine Chapters on Mathematical Procedures was compiled in the first century CE. Scholars of the third century and seventh century wrote commentaries on this work, both of which were regarded as inseparable parts from the text of The Nine Chapters, because all these layers of texts were handed down as classical mathematical work. In the eleventh century, scholar Jia Xian resumed to make the third layer of commentary on the texts completed before him. According to historical records known to us and extant mathematical works, before the thirteenth century, The Nine Chapters were mainly learned in the official education system and were circulated among literati and scholars with expertise. Yang Hui of the thirteenth century played a key role in the popularization of The Nine Chapters among more general mathematics learners and the populace. In this regard, Yang’s Mathematical Methods Explaining in Detail The Nine Chapters and Reclassifications (1261 CE) are influential during the following several centuries. On the basis of a unique incomplete edition of Yang’s works mentioned above, this talk tries to address the following questions : What are the differences between Yang’s categories and reclassifications of text of The Nine Chapters from those of the former commentaries to this work ? What was Yang’s goal of reclassification and how did Yang achieve his goal of reclassification through reorganization of text ? More concretely, what were his criteria for reclassifications ? Mathematical methods Yang supplemented compose the subcategories that are subordinate to the structure of the original text. How did he arrange the order of mathematical problems and methods in each category and subcategory ? How did Yang use his added analogical problems or modified problems to exemplify the new mathematical methods he introduced in the works ?

Arilès Remaki , (Sphere, ERC Philiumm, Université Paris Cité, CNRS)
Did Leibniz rearrange his own drafts ?
Résumé :
Leibniz’s mathematical drafts are very different from one another. This difference lies not only in the content of the draft, nor even in its function (draft letter, draft work, simple notes, etc.), but in the philological nature of the material. Some documents are completely isolated, without title or date, and with few or no references to other manuscripts. Others, on the other hand, have a very complete heading, in which Leibniz indicates the title, date and possibly the place of the document in a larger series.
The first, natural hypothesis is that these two types of document reflect two different practices in Leibniz’s work. Organised drafts that have a more significant content and isolated drafts that Leibniz kept by mistake, or with little conviction.
A second hypothesis emerges from a close study of the manuscripts. It seems that the headings of many of the texts were added afterwards. Although it is impossible to determine the exact chronology of these operations, the fact that Leibniz reordered his manuscripts a posteriori testifies to a radically different practice, and calls into question the presence of the heading as a criterion of the importance of the content.
The presentation will attempt to show the material traces that support the second hypothesis, and will present the concrete consequences that the discovery of such a practice has for the exegesis of Leibnizian drafts.