Small Skills, Big Networks: Marin Mersenne as Mathematical Intelligencer

Abstract

Writing in August 1634, the French polymath Nicolas-Claude Fabri de Peiresc reflected upon Marin Mersenne's endeavours. Mersenne, Peiresc asserted, had forced himself into frontiers that are a little more in fashion of the times than these prolix treaties of the schools that so few men handle outside of the colleges.1 Peiresc was quite prescient to realize the novel claims that Mersenne was promoting. From the middle of the 1620s until his death in 1648, Mersenne encouraged discussion on a number of new mathematical concepts, ideas that lacked a secure home within the Aristotelian university curriculum.2 By mathematics, I am referring to mixed mathematics, the application of arithmetic and geometry often to physical processes, and related topics in natural philosophy: examples include Galilean mechanics, the question of whether a void exists in nature, and analysis of conic sections and their spatial counterparts.3 For Peiresc and others, Mersenne was an exemplar of new, heterodox ideas: though he was a member of the religious Minim order, he was respected widely as a mathematician, he lived a gregarious life in cosmopolitan Paris, and he was an intimate friend of the famed French mathematician Rene Descartes as well as a correspondent with the Italian Galileo Galilei and the Dutch Christiaan Huygens.4 But while Mersenne is still remembered as a mathematician and correspondent of famous mathematicians, Peiresc's description of Mersenne as trend-conscious or even a trendsetter has been effectively forgotten. In this essay I want to show that, far from accidental, Mersenne's trendiness framed much of his work as a mathematician and indefatigable network builder. It was also a sign of the limitations of his mathematical skills.Only recently have historians of science begun to examine epistolary culture as a genre, highlighting interactions in formerly unrecognizable communities and social threads that support scientific advancements. Compared to correspondences that have been well studied, Mersenne's is unlike what preceded or followed it. It does not resemble the Latin astronomical correspondence of Tycho Brahe, which contains fewer than 500 letters.5 Nor can it be likened to the humanistic and astrologically inflected letters of his other astronomical forerunner, Johannes Kepler.6 Mersenne's writings also differ from Henry Oldenburg's later multidisciplinary and generally vernacular correspondence of 3,139 letters (a handful later discovered), much of which was written during his tenure as secretary of the Royal Society.7 Yet Mersenne's seventeen-volume correspondence has salient characteristics.8 Though numbering 1,871 entries in its sixteen main volumes, the Mersenne correspondence actually contains 1,896 items.9 Of these, 803 items were addressed to Mersenne and a scant 318 items - roughly one-sixth of the correspondence - originated from Mersenne's hand.10 Though only approximately 59% of the correspondence was to or from Mersenne, additional letters were included merely because they bore Mersenne's name in context, thus exaggerating Mersenne's image as mailbox of Europe and Secretary-General of the Republic of relative to (better-edited correspondences of) his understudied contemporaries.11 Many of Mersenne's letters seem to have been lost - especially those sent to Descartes, who was itinerant in the Netherlands during much of Mersenne's communicative heyday. Nevertheless, Mersenne's epistolary traffic soared as his own book production subsided in the mid1630s.12 Whenever possible, Mersenne opted for vernacular correspondence unless he was citing books or other classical sources (he wrote in French and Latin). Also notable is its international flavour, with a preponderance of writing on mathematical topics. Letters in his network often crossed from Catholic lands to the Protestant Netherlands, fostering talk between individuals of different faiths. While these exchanges occurred throughout the Thirty Years' War, there is little evidence of that conflict causing problems; if anything, Mersenne's correspondents usually accessed the ordinary post [