Some remarks on the history of Ricci’s absolute differential calculus

The article offers a general account of the genesis of the absolute differential calculus (ADC), paying special attention to its links with the history of differential geometry. In relatively recent times, several historians have described the development of the ADC as a direct outgrowth either of t...

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Bibliographic Details
Published in:Archive for history of exact sciences 2024-11, Vol.78 (6), p.717-761
Main Author: Cogliati, Alberto
Format: Article
Language:English
Subjects:
Astronomy
Differential calculus
Differential geometry
History and Philosophical Foundations of Physics
History of Mathematical Sciences
History of Science
Mathematics
Mathematics and Statistics
Observations and Techniques
Philosophy of Science
Tensors
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Summary:The article offers a general account of the genesis of the absolute differential calculus (ADC), paying special attention to its links with the history of differential geometry. In relatively recent times, several historians have described the development of the ADC as a direct outgrowth either of the theory of algebraic and differential invariants or as a product of analytical investigations, thus minimizing the role of Riemann’s geometry in the process leading to its discovery. Our principal aim consists in challenging this historiographical tenet and analyzing the intimate connection between the development of Riemannian geometry and the birth of tensor calculus.
ISSN:0003-9519
1432-0657
DOI:10.1007/s00407-024-00336-2