### Abstract

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, often with

no more precision.

Now it has instead 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),

this is certainly 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.

mathematics as “algebra”, without agreement between workers about what was

to be understood by that word. Then this view came under heavy fire, often with

no more precision.

Now it has instead 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),

this is certainly 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 |
---|---|

Publikationsdato | 1 sep. 2015 |

Antal sider | 27 |

Status | Udgivet - 1 sep. 2015 |

Begivenhed | International Conference on the History of Ancient Mathematics and Astronomy: Algorithms in the Mathematical Sciences in the Ancient World - Northwest University, Xi'an, China, Xi'an, Kina Varighed: 23 aug. 2015 → 29 aug. 2015 |

### Konference

Konference | International Conference on the History of Ancient Mathematics and Astronomy |
---|---|

Lokation | Northwest University, Xi'an, China |

Land | Kina |

By | Xi'an |

Periode | 23/08/2015 → 29/08/2015 |

Andet | In memory of Professor Li Jimin (1938-1993) |

## Citer dette

Høyrup, J. (2015).

*When is the algorithm concept pertinent – and when not? Thoughts about algorithms and paradigmatic examples, and about algorithmic and non-algorithmic mathematical cultures*. Afhandling præsenteret på International Conference on the History of Ancient Mathematics and Astronomy, Xi'an, Kina.