Article ID: CBB001551387

The Mystery of Riemann's Curvature (2015)

unapi

Bernhard Riemann's habilitation lecture of 1854 on the foundations of geometry contains a stunningly precise concept of curvature without any supporting calculations. Another memoir of 1861 contains formulas in which we may recognize our Riemann tensor, though in a different context and without much geometrical interpretation. The first text is mysterious by the lack of formulas, the second by the excess of formulas. The purpose of this essay is to investigate this double mystery and the stimulating effect it had on some of Riemann's early readers, from Richard Dedekind to Tullio Levi-Civita. Use is made of some heretofore unexploited manuscript sheets by Riemann.

...More
Citation URI
https://data.isiscb.org/isis/citation/CBB001551387/

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/)

Book Gray, Jeremy; (1999)
The symbolic universe: Geometry and physics, 1890-1930 (/isis/citation/CBB000083033/)

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

Book Thomas Sonar; Karin Reich; (2014)
Der Briefwechsel, Richard Dedekind-Heinrich Weber (/isis/citation/CBB718714957/)

Book Alberto Cogliati; (2020)
Ars inveniendi (/isis/citation/CBB525882872/)

Article Plotnitsky, Arkady; (2009)
Bernhard Riemann's Conceptual Mathematics and the Idea of Space (/isis/citation/CBB001031505/)

Article Knobloch, Eberhard; (2002)
Leibniz's Rigorous Foundation of Infinitesimal Geometry by Means of Riemannian Sums (/isis/citation/CBB000300359/)

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

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

Article Błaszczyk, Piotr; Katz, Mikhail G.; Sherry, David; (2013)
Ten Misconceptions from the History of Analysis and Their Debunking (/isis/citation/CBB001252715/)

Book Charlotte Victorine Pollet; (2020)
The empty and the full: Li Ye and the way of mathematics : geometrical procedures by section of areas (/isis/citation/CBB703705286/)

Article Brazil, Marcus; Graham, Ronald L.; Thomas, Doreen A.; Zachariasen, Martin; (2014)
On the History of the Euclidean Steiner Tree Problem (/isis/citation/CBB001214201/)

Book Berlinski, David; (2013)
The King of Infinite Space: Euclid and His Elements (/isis/citation/CBB001213232/)

Book Lohr, Alfred; (2013)
Der Computus Gerlandi: Edition, Ubersetzung und Erläuterungen (/isis/citation/CBB001551218/)

Article Pavel Šišma; Laurent Mazliak; (2016)
The Moravian Crossroad: Mathematics and Mathematicians in Brno Between German Traditions and Czech Hopes (/isis/citation/CBB759227619/)

Article Ferreirós Domínguez, José; (1992)
Sobre los orígenes de la matemática abstracta: Richard Dedekind y Bernhard Riemann (/isis/citation/CBB000040253/)

Authors & Contributors
Reich, Karin
Cogliati, Alberto
Charlotte Victorine Pollet
Klein, Christian Felix
de Saint-Gervais, Henri Paul
Lohr, Alfred
Concepts
Mathematics
Mathematicians
Geometry
Infinitesimals
Biographies
Science and politics
Time Periods
19th century
20th century, early
20th century
Yuan Dynasty (China, ca. 1260-1368)
Song Dynasty (China, 960-1279)
Modern
Places
Germany
China
St. Petersburg (Russia)
Prague (Czechia)
Russia
Comments

Be the first to comment!

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

Log in or register to comment