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Article ID: CBB388966363

The sexagesimal place-value notation and abstract numbers in mathematical cuneiform texts (2022)

Proust, Christine (Author)

Historia Mathematica
Volume: 59
Pages: 54-70

URI: https://www.sciencedirect.com/science/article/pii/S0315086022000088

DOI: 10.1016/j.hm.2021.12.001

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Number theory; number concept Historiography Cuneiform inscriptions Mathematics 20th century, early 19th century Thureau-Dangin, François

The discovery at the end of the 19th century of the mathematical cuneiform texts posed to historians the question of the nature of the numbers used in them, i.e. that of the sexagesimal place-value notation. This notation, although familiar to us today since it is the one we use to measure time, has, in the cuneiform texts, specificities which still raise challenges of interpretation. One of these specificities is the fact that the cuneiform writing does not indicate the order of magnitude of the numbers (for example, 1, 60, 1/60 or any other power of 60 are written in the same way). This article outlines the way in which historians of the late 19th and early 20th centuries interpreted this specificity. The focus here is on the interpretation proposed by the Assyriologist François Thureau-Dangin, who in 1930 considered numbers in sexagesimal place-value notation as “abstract numbers”, as opposed to “concrete numbers”. Résumé La découverte à la fin du 19e siècle des premières tablettes mathématiques cunéiformes a posé aux historiens la question de la nature des nombres qui y étaient utilisés, c'est-à-dire celle de la notation sexagésimale positionnelle. Cette notation, quoique familière aujourd'hui puisque c'est celle que nous utilisons pour la mesure du temps, revêt dans les textes cunéiformes des spécificités qui soulèvent encore aujourd'hui des défis d'interprétation. Une de ces spécificités est le fait que l'écriture cunéiforme n'indique pas l'ordre de grandeur des nombres (par exemple, 1, 60, 1/60 ou toute autre puissance de 60 s'écrivent de la même façon). Cet article retrace la façon dont les historiens de la fin du 19e siècle et du début du 20e siècle ont interprété cette spécificité. L'accent est mis ici sur l'interprétation de François Thureau-Dangin, qui, en 1930, considérait les nombres en notation sexagésimale positionnelle comme des « nombres abstraits », qu'il opposait aux « nombres concrets ».

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