### Abstract

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.

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.

Original language | English |
---|---|

Number of pages | 22 |

Publication status | Published - 18 Oct 2011 |

## Cite this

Høyrup, J. (2011).

*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.*