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

Publikation: KonferencebidragPaperForskning

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.
OriginalsprogEngelsk
Publikationsdato1 sep. 2015
Antal sider27
StatusUdgivet - 1 sep. 2015
BegivenhedInternational 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. 201529 aug. 2015

Konference

KonferenceInternational Conference on the History of Ancient Mathematics and Astronomy
LokationNorthwest University, Xi'an, China
LandKina
ByXi'an
Periode23/08/201529/08/2015
AndetIn 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.