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Article ID: CBB729622687

Explicit and Less Explicit Algorithmic Thinking, 1200-1500. Jordanus de Nemore, and the Contrast between Barthelemy de Romans et Chuquet (2018)

Høyrup, Jens (Author)

Bollettino di Storia delle Scienze Matematiche
Volume: 38
Issue: 1
Pages: 9-30

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Algebra Mathematics Algorithms Medieval 13th century 15th century 14th century France

An introductory section discusses the utility of the algorithm concept in the historiographic analysis of non-recent mathematics, in particular the sense that can be given to claims that a particular mathematical culture was of algorithmic type. It concludes that the adequacy of this epithet when applied to a mathematical culture does not depend on whether texts used in teaching are built up around paradigmatic examples but on whether the production of rules or algorithms was regarded as a central activity for those whom we would count as “mathematicians” (that is, producers of mathematical knowledge). Three medieval examples of attitudes to algorithms follow. First, Jordanus de Nemore’s "De numeris datis" is shown to develop a method to combine algorithms and deductivity, in an alternative to algebra. Second, Barthélemy de Romans’ graphic schemes for organizing the complex algorithms used to solve the sophisticated variants of the problem of the “unknown heritage” are discussed. Third is considered Nicholas Chuquet’s dismissal of these schemes and algorithms, in favour of the algebraic tool.

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