Abstract
In this paper we present for the first time a part of the correspondence between Tullio Levi-Civita and Jan Arnoldus Schouten, in the period from May 1918 to April 1919. These letters recount the story of the common and independent discovery of a geometrical interpretation of the covariant derivative. Furthermore, they offer the occasion to reflect upon the quite diverging technical choices adopted by the two mathematicians. The transcription of the letters along with some commentary remarks is preceded by two introductory sections in which the relevant contributions of Levi-Civita and Schouten are dealt with.
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