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

Abstract : 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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https://halshs.archives-ouvertes.fr/halshs-01432645
Contributor : Emmylou Haffner Connect in order to contact the contributor
Submitted on : Thursday, January 20, 2022 - 4:10:27 PM
Last modification on : Saturday, January 22, 2022 - 3:37:07 AM
Long-term archiving on: : Thursday, April 21, 2022 - 6:09:02 PM

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

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