Article ID: CBB608935808

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


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.

Citation URI

Similar Citations

Book de Saint-Gervais, Henri Paul; Poincaré, Henri; Klein, Christian Felix; (2010)
Uniformisation des surfaces de Riemann retour sur un théorème centenaire (/isis/citation/CBB001551391/) unapi

Chapter Bottazzini, Umberto; (1994)
Geometry and “metaphysics of space” in Gauss and Riemann (/isis/citation/CBB000056277/) unapi

Article Laugwitz, Detlef; (1999)
Bernhard Riemann: Ein Schüler von Gauss? (/isis/citation/CBB000082271/) unapi

Book Torretti, Roberto; (1978)
Philosophy of geometry from Riemann to Poincaré (/isis/citation/CBB000008239/) unapi

Article Giovanelli, Marco; (2008)
Kant, Helmholtz, Riemann und der Ursprung der geometrischen Axiome (/isis/citation/CBB001034987/) unapi

Article Wojcik, W.; (2007)
Bernard Riemann's New Philosophy Project (/isis/citation/CBB000931659/) unapi

Article Deng, Mingli; Yan, Chenguang; (2006)
The Rudiments of the Idea of Riemann for Geometry (/isis/citation/CBB000630902/) unapi

Article Cogliati, Alberto; (2014)
Un réexamen du Commentatio Mathematica de Riemann (/isis/citation/CBB001451431/) unapi

Article Sinaceur, Mohammed Allal; (1990)
Dedekind et le programme de Riemann (/isis/citation/CBB000045268/) unapi

Article Chen, Huiyong; (2011)
Study on the Approach to Realize the Thought of Gauss' Non-Euclidean Geometry (/isis/citation/CBB001210056/) unapi

Article Coxeter, H. S. M.; (1977)
Gauss as a geometer (/isis/citation/CBB000014884/) unapi

Article Alberto Cogliati; (2018)
Sulla ricezione del "Theorema Egregium," 1828-1868 (/isis/citation/CBB513903674/) unapi

Chapter João Príncipe; (2014)
Henri Poincaré: The Status of Mechanical Explanations and the Foundations of Statistical Mechanics (/isis/citation/CBB035763250/) unapi

Book Winter, Sarah; (1999)
Freud and the Institution of Psychoanalytic Knowledge (/isis/citation/CBB000410064/) unapi

Book Silva Suárez, Manuel; (2011)
Técnica e ingeniería en España: VI, El ochocientos: De los lenguajes al patrimonio (/isis/citation/CBB001210051/) unapi

Authors & Contributors
Pulte, Helmut
Cogliati, Alberto
Torretti, Roberto
Coxeter, H. S. M.
Sinaceur, Mohammed Allal
Bottazzini, Umberto
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
Stanford University Press
Real Academia de Ingeniería
Discipline formation
Riemann, Georg Friedrich Bernhard
Gauss, Carl Friedrich
Poincaré, Jules Henri
Jacobi, Karl Gustav Jakob
Dedekind, Richard
Lagrange, Joseph Louis
Central Europe: Germany, Austria, Switzerland
Vienna (Austria)
19th century
20th century
20th century, early
18th century
21st century
École de Santé de Paris
École Normale Supérieure, Paris
Société française de physique
Université de France

Be the first to comment!

{{ comment.created_by.username }} on {{ comment.created_on | date:'medium' }}

Log in or register to comment