According to the YouTube video "Evariste Galois a documentary" by MsrEvaristeGalois, when the young Evariste Galois was taking his entrance exam for the Ecole Polytechnique, his examinateurs asked Galois to explain the theory of arithmetical logarithms. According to the video, Galois refused, claiming there is no such thing as arithmetical logarithm, apparently angering the examining professors.
Does anyone know what arithmetical logarithms supposedly are?
According to the Encyclopédie (mid-eighteenth century), real logarithms belong to arithmetic, while logarithms of negative or complex numbers belong to analysis. "la première partie de l’article Logarithme, considérée comme élémentaire, est classée en Arithmétique ; c’est la seconde partie, consacrée au problème des logarithmes des nombres négatifs et aux développements en séries entières, qui est classée en Analyse." (https://journals.openedition.org/rde/4728?lang=en, paragraph 105). English translation by Google-translate: "the first part of the article Logarithm, considered as elementary, is classified in Arithmetic; it is the second part, devoted to the problem of the logarithms of negative numbers and to expansions in whole series, which is classified in Analysis."