Tactics: In search of a long-term mathematical project (1844–1896)

Abstract

This paper tackles the history of tactics, a field of investigation at the crossroads of algebra, combinatorics and recreational mathematics. Tactics was only taken up by mathematicians now and then between the 1850s and the 1900s, and its emergence was a process of mathematization of questions linked to the notions of "order" and "position". To understand the long-term history of this field of investigation-one that became neither a theory nor a discipline-the paper analyzes the different historical configurations in which tactics took on its scientific meaning. It thus investigates how, under the banner of tactics, a continuity could be claimed by mathematicians that were, finally, working in very different scientific and historical context. RésuméCet article aborde l'histoire de la tactique, un domaine de recherche au croisement de l'algèbre, des combinatoires et des récréa-tions mathématiques. Entre les années 1850 et les années 1900, la tactique n'a été étudiée que de manière épisodique par certains mathématiciens, qui cherchaient à mathématiser les notions d'"ordre" et de "position". Pour comprendre dans la longue durée l'histoire de ce thème de recherche, qui n'est finalement devenu ni une théorie ni une discipline, cet article propose d'analyser les différentes configurations historiques dans lesquelles les travaux portant sur la tactique ont pris sens. Il s'agit donc de comprendre comment, sous la bannière de la tactique, des mathématiciens ont pu se réclamer d'une continuité avec des travaux antérieurs, tout en travaillant dans un contexte scientifique et historique radicalement différent.

Enumeration of Sets of Mutually Orthogonal Latin Rectangles

“…The existence of a set of n − 1 MOLS, for n = p r , for a prime p, was demonstrated in a somewhat forgotten paper from 1896 by Moore [30]. See Ehrhardt [15] for a historical discussion of Moore's paper and the wider context of 19th-century design theory.…”

Enumeration of Sets of Mutually Orthogonal Latin Rectangles

“…However the existence of a set of (n − 1) MOLS, for n = p r , for a prime p, was demonstrated in a somewhat forgotten paper from 1896 by Moore [27]. See [15] for a historical discussion of that paper and the wider context of 19thcentury design theory.…”