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

Abstract

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.