La journée d’étude Histoire et philosophie des mathématiques aura lieu le vendredi 22 novembre 2019, à l’Université de Nantes, sur le campus Tertre.
Cette journée est co-organisée par le CAPHI, le Laboratoire de mathématiques Jean Leray, le Centre François Viète et la MSH Ange Guépin, dans le cadre d’une série de rencontres interdisciplinaires sur le thème Espaces empiriques, espaces conceptuels. Approches croisées : philosophie et mathématiques.
Lieu et horaires :
Université de Nantes, Faculté des lettres et sciences humaines
IGARUN, salle 991-992, 9h-17h.
Vincenzo De Risi, CNRS, SPHère, Paris — Max Planck, Berlin
"Drawing Lines through Rivers and Cities. The Axiomatization of Space in the Early Modern Age"
Abstract : "The talk explores the history of the foundations of geometry from the times of Euclid to the 19th century. In particular, we will consider the evolution of the notion of an axiom from antiquity to the modern age, and the parallel transformation of geometry from a science of figures (as it was in Euclid) into a science of space (as it is considered in the 19th century). We will see how the latter important transformation of the object of geometry reflected on the consideration of the axiomatic method in general, and this eventually produced the discovery of non-Euclidean geometry and non-Euclidean space in the works of Bolyai, Lobachevsky and Gauss."
José Ferreirós Dominguez, Universidad de Sevilla.
"What is (was) the problem of space? «
Abstract : "The talk will discuss the rather extreme changes in what has been called 'the space problem', paying particular attention to discussions in the 18th century, the mid-19th century, and the early 20th century. Such changes are indicative of the general evolution of the discipline mathematics, of the shifts in its consideration as a field of inquiry and the changing contexts in which it has been developed and understood."
Michael Friedman, Humboldt-Universität, Berlin
"On visualizations and non-visualizations of branch points and curves"
Abstract: "How can one imagine the “bending” of algebraic, complex, projective curves or surfaces? The talk will aim to describe the different ways branch points and branch curves were visualised at the turn of the 19th century. On the one hand, for branch points of complex curves one finds an abundance of visualisation techniques employed: Riemann, Neumann, Klein and von Dyck all promoted numerous forms of visualisation, either in form of two-dimensional illustrations or three-dimensional material models. On the other hand, For branch (and ramification) curves of complex surfaces, there were hardly any visual representations: When the Italian school of algebraic geometry studied branch curves systematically, at the beginning of the century, only partial illustrations can be seen (if at all), and branch curves were generally made a tool rather than an object to be researched and visualised."