Strategical use(s) of arithmetic in Richard Dedekind and Heinrich Weber's Theorie der algebraischen Funktionen einer Veränderlichen
Fiche du document
2016
- handle: 10670/1.e116yh
- halshs: halshs-01432645
- doi: 10.1016/j.hm.2016.09.002
Ce document est lié à :
info:eu-repo/semantics/altIdentifier/doi/10.1016/j.hm.2016.09.002
info:eu-repo/semantics/OpenAccess
Sujets proches
PapersCiter ce document
Emmylou Haffner, « Strategical use(s) of arithmetic in Richard Dedekind and Heinrich Weber's Theorie der algebraischen Funktionen einer Veränderlichen », HAL-SHS : histoire, philosophie et sociologie des sciences et des techniques, ID : 10.1016/j.hm.2016.09.002
Métriques
Partage / Export
Résumé
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 divisibility. I start with contextual elements concerning what is “arithmetical”, to put Dedekind and Weber's works into perspective from that viewpoint. Then, through a detailed analysis of the 1882 paper and using elements of their correspondence, I suggest that Dedekind and Weber deploy a strategy of rewriting parts of mathematics using arithmetic, and that this strategy is essentially related to Dedekind's specific conception of numbers and arithmetic as intrinsically linked to the human mind.