In this article we answer some questions that we have made on and around the historical emergence of elliptic functions in the first half of the nineteenth century. First, we want to determine the most relevant forces that produced tensions in the discipline during the period considered. To do this, we propose an explanatory hypothesis on the overturning in the field of mathematical thinking that resulted when the functions were preferred instead of the elliptic integrals. This hypothesis is rooted in the state of “Analysis” and “Algebra” during the emergence time. Then we show that the constructions of Abel and Jacobi for the elliptic functions support our working hypothesis. Finally, we outline some conclusions concerning our reflections.
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