Article ID: CBB608935808

From Gauss to Riemann Through Jacobi: Interactions Between the Epistemologies of Geometry and Mechanics? (2020)

unapi

The aim of this paper is to argue that there existed relevant interactions between mechanics and geometry during the first half of the nineteenth century, following a path that goes from Gauss to Riemann through Jacobi. By presenting a rich historical context we hope to throw light on the philosophical change of epistemological categories applied by these authors to the fundamental principles of both disciplines (which they came to regard as hypotheses or conventions). We intend to show that presentations of the changing status of the principles of mechanics as a mere epiphenomenon of the emergence of non-Euclidean geometries are inaccurate, that the relations between the two disciplines were richer than what is usually considered in the literature. These claims will be based on historical and philosophical arguments, starting from the fact that disciplinary boundaries at the time were not rigid as we are used today. It is widely known that the main figures we target worked in different areas, which is a first piece of evidence for the plausibility of our main thesis.

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Authors & Contributors
Cogliati, Alberto
Pulte, Helmut
Marc Joly
Klein, Christian Felix
de Saint-Gervais, Henri Paul
Yan, Chenguang
Concepts
Geometry
Discipline formation
Mechanics
Mathematics
Epistemology
Philosophy
Time Periods
19th century
20th century
20th century, early
18th century
Places
Germany
Spain
France
Europe
Denmark
Vienna (Austria)
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