Strategical use(s) of arithmetic in Richard Dedekind and Heinrich Weber's Theorie der algebraischen Funktionen einer Veränderlichen

Emmylou Haffner (1)

1 SPHERE (UMR_7219) - Sciences, Philosophie, Histoire

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.

Mots clés: arithmétique; Riemann; weber; Dedekind; 19e siècle; histoire des mathématiques

Domaines: Histoire, Philosophie et Sociologie des sciences; Histoire et perspectives sur les mathématiques [math.HO]

Emmylou Haffner. Strategical use(s) of arithmetic in Richard Dedekind and Heinrich Weber's Theorie der algebraischen Funktionen einer Veränderlichen. Historia Mathematica, 2016, 44 (1), pp.31-69. ⟨10.1016/j.hm.2016.09.002⟩. ⟨halshs-01432645⟩