Strategical Use(s) of Arithmetic in Richard Dedekind and Heinrich Weber's Theorie Der Algebraischen Funktionen Einer Veränderlichen (2017)
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.
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