### Resumé

Now, instead, it has become customary to classify pre-Modern practical arithmetic as “algorithmic mathematics”. In so far as any computation in several steps can be claimed to follow an underlying algorithm (just as it can be explained from an “underlying theorem”, for instance from proportion theory, or from a supposedly underlying algebraic calculation), this can no doubt be justified. Traditionally, however, historians as well as the sources would speak of a rule.

The paper first goes through some of the formative appeals to the algebraic interpretation – Eisenlohr, Zeuthen, Neugebauer – as well as some of the better argued attacks on it (Rodet, Mahoney). Next it asks for the reasons to introduce the algorithmic interpretation, and discusses the adequacy or inadequacy of some uses. Finally, it investigates in which sense various pre-modern mathematical cultures can be characterized globally as “algorithmic”, concluding that this characterization fits ancient Chinese and Sanskrit mathematics but neither early second-millennium

Mediterranean practical arithmetic (including Fibonacci and the Italian abbacus tradition), nor the

Old Babylonian corpus.

Originalsprog | Engelsk |
---|---|

Tidsskrift | AIMS Mathematics |

Vol/bind | 3 |

Udgave nummer | 1 |

Sider (fra-til) | 211-232 |

ISSN | 2473-6988 |

DOI | |

Status | Udgivet - 2018 |

### Citer dette

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**When is the algorithm concept pertinent – and when not? Thoughts about algorithms and paradigmatic examples, and about algorithmic and non-algorithmic mathematical cultures.** / Høyrup, Jens.

Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review

TY - JOUR

T1 - When is the algorithm concept pertinent – and when not?

T2 - Thoughts about algorithms and paradigmatic examples, and about algorithmic and non-algorithmic mathematical cultures

AU - Høyrup, Jens

PY - 2018

Y1 - 2018

N2 - Until some decades ago, it was customary to discuss much pre-Modern mathematics as “algebra”, without agreement between workers about what was to be understood by that word. Then this view came under heavy fire, rarely with more precision.Now, instead, it has become customary to classify pre-Modern practical arithmetic as “algorithmic mathematics”. In so far as any computation in several steps can be claimed to follow an underlying algorithm (just as it can be explained from an “underlying theorem”, for instance from proportion theory, or from a supposedly underlying algebraic calculation), this can no doubt be justified. Traditionally, however, historians as well as the sources would speak of a rule.The paper first goes through some of the formative appeals to the algebraic interpretation – Eisenlohr, Zeuthen, Neugebauer – as well as some of the better argued attacks on it (Rodet, Mahoney).Next it asks for the reasons to introduce the algorithmic interpretation, and discusses the adequacy or inadequacy of some uses. Finally, it investigates in which sense various pre-modern mathematical cultures can be characterized globally as “algorithmic”, concluding that this characterization fits ancient Chinese and Sanskrit mathematics but neither early second-millennium Mediterranean practical arithmetic (including Fibonacci and the Italian abbacus tradition), nor the Old Babylonian corpus.

AB - Until some decades ago, it was customary to discuss much pre-Modern mathematics as “algebra”, without agreement between workers about what was to be understood by that word. Then this view came under heavy fire, rarely with more precision.Now, instead, it has become customary to classify pre-Modern practical arithmetic as “algorithmic mathematics”. In so far as any computation in several steps can be claimed to follow an underlying algorithm (just as it can be explained from an “underlying theorem”, for instance from proportion theory, or from a supposedly underlying algebraic calculation), this can no doubt be justified. Traditionally, however, historians as well as the sources would speak of a rule.The paper first goes through some of the formative appeals to the algebraic interpretation – Eisenlohr, Zeuthen, Neugebauer – as well as some of the better argued attacks on it (Rodet, Mahoney).Next it asks for the reasons to introduce the algorithmic interpretation, and discusses the adequacy or inadequacy of some uses. Finally, it investigates in which sense various pre-modern mathematical cultures can be characterized globally as “algorithmic”, concluding that this characterization fits ancient Chinese and Sanskrit mathematics but neither early second-millennium Mediterranean practical arithmetic (including Fibonacci and the Italian abbacus tradition), nor the Old Babylonian corpus.

U2 - 10.3934/Math.2018.1.211

DO - 10.3934/Math.2018.1.211

M3 - Journal article

VL - 3

SP - 211

EP - 232

JO - AIMS Mathematics

JF - AIMS Mathematics

SN - 2473-6988

IS - 1

ER -