Routine Controversies : Mathematical Challenges in Mersenne's Correspondence

Mathematical challenges punctuate the history of early modern mathematics. While cultural historians have attempted to contextualize these challenges among contemporary practices, in particular duels or advertisements in a competitive market, thus emphasizing their interpersonal and social dimensions, historians of mathematics have generally treated them as somewhat childish remnants of a pre-scientific age, that the advent of modern science and its Baconian ideal of efficient collaboration would soon bring to an end. However, the number of challenges did not decrease but rather multiplied inside one of the first scientific organizations aiming at cooperative work--Marin Mersenne's network. This paradox has suggested the focus of this article : to examine the role of challenges in the economy of mathematical exchange (and mathematical creation) in early modern France. Through examples of successful, but also of unsuccessful challenges, we shall see how challenges operated, not only as "mises en sc\`ene" of methodological oppositions, but also, and primarily, as links in a mathematical environment structured inside correspondences around the resolution of problems. This situation also exemplifies how controversies may have been a constitutive part of normal scientific activities--and not their disruption--while shaping their development in specific, limited directions

Les autres de l'un : deux enqu\^etes prosopographiques sur Charles Hermite

Prosopography is usually used to globally describe a large population of ordinary subjects. It is thus opposed to biography, as a genre devoted to exceptional individuals. I show in this article how to use prosopography to study a single person, an exceptional mathematician, Charles Hermite. I construct several prosopographies (f.i. that of the authors quoted by Hermite, or that of the people writing number-theoretical texts between 1870 and 1914) and show how they allow to capture singular characteristics of Hermite, f.i. his role as a mediator, his mathematical reactions to specific themes, etc

LONG-TERM HISTORY AND EPHEMERAL CONFIGURATIONS

International audienceMathematical concepts and results have often been given a long history, stretching far back in time. Yet recent work in the history of mathematics has tended to focus on local topics, over a short term-scale, and on the study of ephemeral configurations of mathematicians, theorems or practices. The first part of the paper explains why this change has taken place: a renewed interest in the connections between mathematics and society, an increased attention to the variety of components and aspects of mathematical work, and a critical outlook on historiography itself. The problems of a long-term history are illustrated and tested using a number of episodes in the nineteenth-century history of Hermitian forms, and finally, some open questions are proposed

Langage et expérimentation mathématiques au XVIIe siècle

Catherine Goldstein, chargée de recherche au CNRS La mise en texte de nouveaux domaines du savoir a constitué un problème important pour les mathématiciens de la période moderne. Dans certains cas, comme celui de l’algèbre, ces domaines ont d’abord été perçus comme savoir-faire ou comme technique, leur légitimation comme sciences mathématiques exigeant une reconfiguration de leurs objets, de leurs modes de classification, de leurs argumentations. Dans d’autres, des pratiques spécifiques (tabl..

L’expérience des nombres en France (1625-1665)

Catherine Goldstein, chargée de recherche au CNRS Ce séminaire a eu lieu conjointement avec le séminaire collectif du centre Koyré « Lieux de science et savoirs locaux : Paris au XVIIe siècle » (C. G., Antonella Romano, Dinah Ribard et Stéphane Van Damme), la thématique commune étant d’étudier les processus d’élaboration locale des savoirs scientifiques et de constitution de lieux de savoir, ainsi que les opérations de localisation elles-mêmes. Le point de départ du séminaire a été la corresp..

Langage et expérimentation mathématiques au XVIIe siècle

Catherine Goldstein, chargée de recherche au CNRS La mise en texte de nouveaux domaines du savoir a constitué un problème important pour les mathématiciens de la période moderne. Dans certains cas, comme celui de l’algèbre, ces domaines ont d’abord été perçus comme savoir-faire ou comme technique, leur légitimation comme sciences mathématiques exigeant une reconfiguration de leurs objets, de leurs modes de classification, de leurs argumentations. Dans d’autres, des pratiques spécifiques (tabl..