Emmylou Haffner

CNRS · ITEM

In this chapter we present Richard Dedekind’s conception of continuity and his various approaches to continuous domains in a historical context. In addition to his seminal work on foundations of irrational numbers ( Stetigkeit und irrationale Zahlen , 1872), we also include a discussion of more mathematical texts (both published and unpublished) in...

Mathematical and philosophical thought about continuity has changed considerably over the ages. Aristotle insisted that continuous substances are not composed of points, and that they can only be divided into parts potentially; a continuum is a unified whole. The most dominant account today, traced to Cantor and Dedekind, is in stark contrast with...

Article en libre accès : https://journals.openedition.org/philosophiascientiae/2552

When Dedekind introduced the notion of a module, he also defined their divisibility and related arithmetical notions (e.g. the LCM of modules). The introduction of notations for these notions allowed Dedekind to state new theorems, now recognized as the modular laws in lattice theory. Observing the dualism displayed by the theorems, Dedekind pursue...

http://eman-archives.org/Dedekind/ Ce projet présente l’édition numérique génétique de manuscrits du mathématicien allemand Richard Dedekind (1831-1916). Nous nous concentrons ici sur les recherches ayant mené à la création du concept de Dualgruppe, présenté dans deux articles de 1897 et 1900. Cet aboutissement est atteint, nous dit Dedekind, « non...

In this paper, I present and analyse Dedekind’s and Weber’s editorial work which led to the edition of Riemann’s Gesammelte Werke in 1876. With several examples, I suggest that this editorial work is to be understood as a mathematical activity in and of itself and provide evidence for it.

In this paper, I study Richard Dedekind and Heinrich Weber's 1882 Theorie der algebraischen Funktionen einer Veränderlichen, with a focus on the inherently arithmetical aspects of their work. I show that their paper provides an arithmetical rewriting of Riemannian function theory, i.e. a rewriting built on elementary arithmetical notions such as di...

http://eliecartanpapers.ahp-numerique.fr Base de données iconographique et textuelle des cahiers de brouillon d'Élie Cartan (fonds 38J, Académie des Sciences)

In 1882, Richard Dedekind and HeinrichWeber offer an arithmetico-algebraic re-definition of the Riemann surface, using concepts and methods introduced by Dedekind in algebraic number theory. In an attempt to investigate Dedekind’s works beyond the mere idea of a “conceptual approach”, this works proposes to identify the elements of practice specifi...

Dans cet article, je considère la pratique et la conception de la ri­gueur chez Richard Dedekind qui se dégagent de l’étude d’une sélection de ses travaux les plus importants. Une analyse des mentions multiples de réquisits de rigueur dans les textes de Dedekind amène à constater qu’il lie très étroi­tement la rigueur à la généralité. La première p...