Thomas Harriot on Combinations

Maclean, Ian

Revue d'histoire des mathématiques, Tome 11 (2005) no. 1, pp. 57-88.

Thomas Harriot (1560 ?-1621) est célèbre pour ses travaux novateurs tant dans le domaine de l'algèbre que de la philosophie naturelle. Dans cet article, on se propose d'examiner sa pensée sur les combinaisons dans trois contextes ; celui du langage (les anagrammes), celui de la philosophie naturelle (les atomes) et celui de la théorie des nombres. On considérera cette pensée dans le cadre de trois débats historiographiques, à savoir : 1) si ou non, il existe deux mentalités opposées au seuil de la modernité, à savoir l'occulte et la scientifique ; 2) si à cette époque les « sciences mathématiques » sont distinctes de la philosophie naturelle ; et 3) si cette philosophie comprend, au-delà d'une étude de la nature elle-même, celle des attributs du créateur de la nature. Du cas Harriot, on concluera que ce mathématicien est capable d'une pensée mathématique fort abstraite, libérée de l'idéologie sociale, religieuse et politique de son temps (sans que ce contrat s'étende à ce qu'il a à dire sur l'alchimie, ou sur les problèmes des mathématiques appliquées, comme celui de la longitude), et qu'il est capable, comme bien de ses contemporains, de compartimenter son esprit de façon à s'engager mentalement selon des modes fort divers dans les différents domaines de son univers intellectuel.

Thomas Harriot (1560?-1621) is known today as an innovative mathematician and a natural philosopher with wide intellectual horizons. This paper will look at his interest in combinations in three contexts: language (anagrams), natural philosophy (the question of atomism) and mathematics (number theory), in order to assess where to situate him in respect of three current historiographical debates: 1) whether there existed in the late Renaissance two opposed mentalities, the occult and the scientific; 2) whether all mathematical science was clearly demarcated from natural philosophy at that time; and 3) whether all enquiry into nature (including that pursued through mathematics) entailed a consideration of the attributes of God Himself. The paper argues from the case of Harriot that as a man capable of highly abstract mathematical thought, his work on combinations of all kinds is scarcely marked at all by the social, political and religious context from which it arose (which is not to say that his work on alchemy or on practical mathematics is unmarked in the same way), and that he, like many of his contemporaries, was capable of compartmentalising his mind, and of according different modes and degrees of intellectual commitment to different areas of his mental universe.

Keywords: renaissance, combinations, anagrams, atomism, number theory
Mot clés : renaissance, combinaisons, anagrammes, atomisme, théorie des nombres

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