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Article Dans Une Revue Historia Mathematica Année : 2014

The mystery of Riemann's curvature

Olivier Darrigol

Résumé

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

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Dates et versions

halshs-01502007 , version 1 (04-04-2017)

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Olivier Darrigol. The mystery of Riemann's curvature. Historia Mathematica, 2014, 42 (1), pp.47-83. ⟨10.1016/j.hm.2014.03.001⟩. ⟨halshs-01502007⟩
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