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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?

Blue
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Jim Newton
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    Not very clear... see Laura Toti Rigatelli, Evariste Galois 1811–1832 (1996), page 45: "This examination has become something of a legend in the history of mathematics. GALOIS was asked to describe the theory of logarithms. He did not keep to the traditional textbooks and was criticized by the examiners. A heated discussion began, during which GALOIS, who was sure he was right, threw the backboard duster at one of them. Needless to say, he was not admitted. Since the examination could only be taken twice, his greatest dream had now faded away for ever." – Mauro ALLEGRANZA Apr 20 '22 at 09:27
  • Thus, IMO "arithmetical logarithms" must be simply "logarithms". – Mauro ALLEGRANZA Apr 21 '22 at 06:53
  • See this related post: "if a set of numbers is in geometric progression, then their logarithms are in arithmetic progression." – Mauro ALLEGRANZA May 05 '22 at 12:18

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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."

MasB
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