On the genesis of the concept of covariant differentiation

Luca Dell’ Aglio

Revue d'histoire des mathématiques (1996)

  • Volume: 2, Issue: 2, page 215-264
  • ISSN: 1262-022X

Abstract

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The purpose of this paper is to reconsider the genesis of the concept of covariant differentiation, which is interpreted as arising out of two traditions running through 19th-century research work. While the first tradition, of an algebraic nature, was responsible for the “algorithmic” emergence of the concept, the second, analytical in character, was essentially concerned with the import of covariant differentiation as a broader kind of differentiation. The methodological contrast that these two traditions exhibit, concerning the use of algebraic and variational methods, was mainly evidenced in Ricci-Curbastro’s work, and was a significant factor in the genesis of tensor analysis. The emergence of the notion of covariant differentiation in his research work may, indeed, be interpreted as the resolution of that methodological contrast into the definitive form of a conceptual synthesis.

How to cite

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Dell’ Aglio, Luca. "On the genesis of the concept of covariant differentiation." Revue d'histoire des mathématiques 2.2 (1996): 215-264. <http://eudml.org/doc/252048>.

@article{Dell1996,
abstract = {The purpose of this paper is to reconsider the genesis of the concept of covariant differentiation, which is interpreted as arising out of two traditions running through 19th-century research work. While the first tradition, of an algebraic nature, was responsible for the “algorithmic” emergence of the concept, the second, analytical in character, was essentially concerned with the import of covariant differentiation as a broader kind of differentiation. The methodological contrast that these two traditions exhibit, concerning the use of algebraic and variational methods, was mainly evidenced in Ricci-Curbastro’s work, and was a significant factor in the genesis of tensor analysis. The emergence of the notion of covariant differentiation in his research work may, indeed, be interpreted as the resolution of that methodological contrast into the definitive form of a conceptual synthesis.},
author = {Dell’ Aglio, Luca},
journal = {Revue d'histoire des mathématiques},
keywords = {G. Ricci-Curbastro; tensor analysis; covariant derivative; history of},
language = {eng},
number = {2},
pages = {215-264},
publisher = {Société mathématique de France},
title = {On the genesis of the concept of covariant differentiation},
url = {http://eudml.org/doc/252048},
volume = {2},
year = {1996},
}

TY - JOUR
AU - Dell’ Aglio, Luca
TI - On the genesis of the concept of covariant differentiation
JO - Revue d'histoire des mathématiques
PY - 1996
PB - Société mathématique de France
VL - 2
IS - 2
SP - 215
EP - 264
AB - The purpose of this paper is to reconsider the genesis of the concept of covariant differentiation, which is interpreted as arising out of two traditions running through 19th-century research work. While the first tradition, of an algebraic nature, was responsible for the “algorithmic” emergence of the concept, the second, analytical in character, was essentially concerned with the import of covariant differentiation as a broader kind of differentiation. The methodological contrast that these two traditions exhibit, concerning the use of algebraic and variational methods, was mainly evidenced in Ricci-Curbastro’s work, and was a significant factor in the genesis of tensor analysis. The emergence of the notion of covariant differentiation in his research work may, indeed, be interpreted as the resolution of that methodological contrast into the definitive form of a conceptual synthesis.
LA - eng
KW - G. Ricci-Curbastro; tensor analysis; covariant derivative; history of
UR - http://eudml.org/doc/252048
ER -

References

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