Explicit and less explicit algorithmic thinking, 1200–1500: Jordanus de Nemore, and the contrast between Barthélemy de Romans et Chuquet: Contribution to the workshop “Pratiques algorithmiques dans les mathématiques pré modernes”, Université de Lille 3, 12 14 octobre 2011. Preprint, 18 October 2011. Preprint.

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.