From Gauss to Riemann Through Jacobi: Interactions Between the Epistemologies of Geometry and Mechanics? (2020)
Paz, María de (Author)
Ferreirós, José (Author)
Journal for General Philosophy of Science
Volume: 51
Issue: 1
Pages: 147-172
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.
...MoreSimilar Citations
Book
de Saint-Gervais, Henri Paul;
Poincaré, Henri;
Klein, Christian Felix;
(2010)
Uniformisation des surfaces de Riemann retour sur un théorème centenaire
Chapter
Bottazzini, Umberto;
(1994)
Geometry and “metaphysics of space” in Gauss and Riemann
Book
Alberto Cogliati;
(2024)
La geometria non euclidea. Una breve storia dall’antichità a Poincaré
Article
Laugwitz, Detlef;
(1999)
Bernhard Riemann: Ein Schüler von Gauss?
Article
Pulte, Helmut;
(1994)
C.G.J. Jacobis Vermächtnis einer “konventionalen” analytischen Mechanik: Vorgeschichte, Nachschriften und Inhalt seiner letzen Mechanik-Vorlesung
Article
Pulte, Helmut;
(1998)
Jacobi's criticism of Lagrange: The changing role of mathematics in the foundations of classical mechanics
Book
Torretti, Roberto;
(1978)
Philosophy of geometry from Riemann to Poincaré
Article
Cogliati, Alberto;
(2014)
Un réexamen du Commentatio Mathematica de Riemann
Article
Sinaceur, Mohammed Allal;
(1990)
Dedekind et le programme de Riemann
Article
Deng, Mingli;
Yan, Chenguang;
(2006)
The Rudiments of the Idea of Riemann for Geometry
Article
Wojcik, W.;
(2007)
Bernard Riemann's New Philosophy Project
Article
Giovanelli, Marco;
(2008)
Kant, Helmholtz, Riemann und der Ursprung der geometrischen Axiome
Thesis
Jenne Praeger O'Brien;
(2023)
Making the Manifold Bernhard Riemann’s Habilitation Lecture, Mathematics, and German Universities
Article
Alberto Cogliati;
(2018)
Sulla ricezione del "Theorema Egregium," 1828-1868
Article
Coxeter, H. S. M.;
(1977)
Gauss as a geometer
Article
Chen, Huiyong;
(2011)
Study on the Approach to Realize the Thought of Gauss' Non-Euclidean Geometry
Book
Gray, Jeremy;
(1999)
The symbolic universe: Geometry and physics, 1890-1930
Book
Scrimieri, Giorgio;
(1992)
Fondazione della geometria, da Bernhard Riemann a Hermann Weyl. Über die Hypothesen, welche der Geometrie zu Grunde liegen
Article
Darrigol, Olivier;
(2015)
The Mystery of Riemann's Curvature
Chapter
Castellana, Mario;
(1991)
Enriques interprete di Riemann: Geometrie e filosofia
Be the first to comment!