Article ID: CBB608935808

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

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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
Pulte, Helmut
Cogliati, Alberto
Torretti, Roberto
Coxeter, H. S. M.
Sinaceur, Mohammed Allal
Bottazzini, Umberto
Journals
Historia Mathematica
Ziran Kexueshi Yanjiu (Studies in the History of Natural Sciences)
Revue d'Histoire des Sciences
Annals of Science: The History of Science and Technology
Mitteilungen, Gauss- Gesellschaft E.V. Göttingen
Kwartalnik Historii Nauki i Techniki
Publishers
Reidel
Stanford University Press
Real Academia de Ingeniería
E.N.S.
Concepts
Geometry
Discipline formation
Mechanics
Epistemology
Mathematics
Medicine
People
Riemann, Georg Friedrich Bernhard
Gauss, Carl Friedrich
Poincaré, Jules Henri
Jacobi, Karl Gustav Jakob
Dedekind, Richard
Lagrange, Joseph Louis
Places
Germany
France
Central Europe: Germany, Austria, Switzerland
Vienna (Austria)
Spain
Europe
Times
19th century
20th century
20th century, early
18th century
21st century
Institutions
École de Santé de Paris
École Normale Supérieure, Paris
Société française de physique
Université de France
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