Small Skills,Big Networks: Marin Mersenne as Mathematical Intelligencer

de Peiresc Nicolas-Claude Fabri to Mersenne Marin , 13 August 1634, Correspondance du P. Marin Mersenne, ed. by Tannery Paul de Waard Cornelis Beaulieu Armand (Paris, 1945–88), iv, no. 368, 287. Henceforth cited as CM: “[vous serés astrainé dans ces] bornes-là qui sont un peu plus à la mode du temps que ces prolixes traités des escholes que peu des gents manient hors des colleges”.

For general overviews, see Porter Roy , “The scientific revolution and universities”, in de Ridder-Symoens Hilde (ed.), A history of the university in Europe, ii, Universities in early modern Europe (1500–1800) (Cambridge, 1996), 531–62; Gascoigne John , “A reappraisal of the role of the universities in the scientific revolution”, in Lindberg David C. Westman Robert S. (eds), Reappraisals of the scientific revolution (Cambridge, 1990), 207–60.

The most comprehensive discussion of this genre of mathematics can be found in Dear Peter , Discipline and experience: The mathematical way in the scientific revolution (Chicago, 1995). See also Meli Domenico Bertolini , Thinking with objects: The transformation of mathematics in the seventeenth century (Baltimore, 2006).

I would like to note a methodological quagmire: Because Mersenne generally used letters for distance communication, his correspondence does not reveal transparently whom his often-local intimates were. Context clues indicate that Mersenne's best friends included the mathematician and philosopher Pierre Gassendi and the astronomer and priest Ismaël Boulliau. Substantial details, however, cannot be gleaned from the correspondence about Mersenne's quotidian interactions with them.

Mosley Adam , Bearing the heavens: Tycho Brahe and the astronomical community of the late sixteenth century (Cambridge, 2007), especially 31–115; Mosley Adam Jardine Nicholas Tybjerg Karin , “Epistolary culture, editorial practices, and the property of Tycho's Astronomical letters”, Journal for the history of astronomy, xxxiv (2003), 2003–51.

Grafton Anthony , Defenders of the text: The traditions of scholarship in an age of science, 1450–1800 (Cambridge, MA, 1991), 178–213.

See, most importantly, Hall Marie Boas , Henry Oldenburg: Shaping the Royal Society (Oxford, 2002), 125–56. See also Iliffe Rob , “Making correspondents network: Henry Oldenburg, philosophical commerce, and Italian science, 1660–72”, in Beretta Marco Clericuzio Antonio Principe Lawrence M. (eds), The Accademia del Cimento and its European context (Sagamore Beach, MA, 2009), 211–28. An important analysis of Oldenburg's correspondence is Steven Shapin, O Henry, review of ” The correspondence of Henry Oldenburg”, ed. and trans. by Hall A. Rupert Hall Marie Boas , Isis, lxxviii (1987), 1987–24.

The correspondence editor, Tannery Paul , saw Mersenne as a paragon for a new historical style: One without tight geographic borders, one lacking an intellectual figurehead. Tannery's death in 1904 prevented him from completing a Mersenne correspondence. It was not until 1945 that this project continued until completion, first by Cornelis de Waard and then Armand Beaulieu. For details, see the preface by Cornelis de Waard, CM, i, especially p. xiv: “Ces lettres… émanent de correspondants, la plupart très peu connus, et résidant dans les villes les plus diverses, leur publication soulève des questions d'histoire locale qu'il est extrêmement difficile de résoudre…”.

In addition to the 1,871 entries, there are two missed entries that are included in the final, supplemental volume of the Mersenne correspondence. These are no. 1872 and no. 1873. There are also fourteen items in the correspondence that share an index number with another item but are suffixed with “bis”. Eight of them are letters from Marin Mersenne to Theodore Haak that were discovered by surprise as publication of the Mersenne correspondence was underway. They date to years in the correspondence that had been already printed and are contained at the conclusion of volume 11 of the correspondence. The others are all contained immediately after their indexical twin and complement their partner in some fashion. Finally, I have counted item no. 1257 ten times, as it is a set of dedications for Mersenne's Cogitata physico mathematica (1644) that Mersenne sent to various individuals, each for specific sections of his text. Item no. 1257 is numbered no. 1257A through no. 1257I in the correspondence, with a no. 1257A bis. This gives a total of 1,886 items. Because over 99% of the items in the Mersenne correspondence were letters or sent as letters, I refer to entries as “items” rather than “letters” here and in the following sentence.

A note of clarification: My count here includes all items in which Mersenne either is definitively or is presumed by the editors to be a sender or a recipient of an item, including all cases in which Mersenne served as an intermediary. I am also counting dedications of Mersenne's Cogitata physico mathematica (1644) ten times (nos. 1257A − 1257I, and no. 1257A bis) and dedicatory letter manuscripts for an optics project (no. 1841) as part of the outgoing items from Mersenne.

For an excellent source complete with maps and charts that compares the impact of the Mersenne correspondence with correspondence volumes of Peiresc, Boulliau and Oldenburg, see Hatch Robert A. , “Between erudition and science: The archive and correspondence network of Ismaël Boulliau”, in Hunter Michael (ed.), Archives of the scientific revolution: The formation and exchange of ideas in seventeenth-century Europe (Woodbridge, UK and Rochester, NY, 1998), 49–71. One can also compare data on Mersenne with that of his contemporary Samuel Hartlib. Analysis of the Hartlib correspondence can be found in Greengrass Mark , “Archive refractions: Hartlib's papers and the workings of an intelligencer”, in Hunter Michael (ed.), Archives of the scientific revolution: The formation and exchange of ideas in seventeenth-century Europe (Woodbridge, UK and Rochester, NY, 1998), 35–47. Some two thousand letters to Hartlib are now published in electronic form (CD ROM).

Of the correspondence entries prior to 1637, over 35% of the letters involve Peiresc, who was central to Mersenne's literary endeavours. Over 69% of the Mersenne correspondence, however, dates from 1637 onwards. The subset of entries from these later years contains a much larger and more geographically diverse pool of correspondents than the preceding years. Overall, more than 60% of Mersenne's correspondents were mathematicians, philosophers, physicists, astronomers, or medical doctors.

Discussions on war were rare and hardly mentioned obstructed information flow. A rare, poignant example concerning management of stymied mail is Constantijn Huygens to René Descartes, 14 August 1640, CM, x, no. 906, 4–5: “Le perpetuel mouvement de ceste armée m'a faict negliger de vous envoyer de certaines theses philosophiques et pour la plus part mathematiques, que le Pere Mersenne me mande avoir [esté] disputées à Paris, où on s'en prend aussi à vostre matiere subtile et autres positions; et maintenant qu'il seroit temps de vous les communiquer, je les trouve esgarees, mes gens me faisant croire que, parmi d'autres pacquets de reserve, je les auroy envoyées dans mon bateau. Elles paroistront en quelque endroit, et vous les aurez, si tanti est, et n'aymez mieux d'attendre à les veoir à vostre arrivee à Paris, où le Pere Mersenne vous en cornera bien d'autres…”.

A useful discussion of Mersenne and his correspondence network can be found in Hans Bots, “Marin Mersenne, ‘secrétaire général’ de la République des Lettres (1620–1648)”, in Berkvens-Stevelinck Christiane Bots Hans Häseler Jens (eds), Les grands intermédiaires culturels de la République des Lettres: Études de réseaux de correspondances du XVIe au XVIIIe siècles (Paris, 2005), 165–81. There has been scholarly opposition to studying Mersenne's correspondence. Even before the completion of Mersenne's correspondence, P. J. S. Whitmore surmised that it would yield little new intellectual material for historians. See Whitmore P. J. S. , The order of Minims in seventeenth century France (The Hague, 1967), 142: “It is difficult at this moment to write about Mersenne; le Père Lenoble's Mersenne ou le Mécanisme gives such a complete exposition of his work and influence that it will remain the definitive work at least until the edition of the Correspondance is complete; even then it is unlikely that any new material will come to light that will alter the findings of Lenoble”.

The most profound discussion of this is Biagioli Mario , Galileo courtier: The practice of science in the culture of absolutism (Chicago, 1994). On Kepler as a court mathematician, see Max Caspar, Kepler, ed. and trans. by Hellman C. Doris (London, 1959; New York, 1993), 116–208. Citations are to the Dover edition. See also Smith Pamela H. , The business of alchemy: Science and culture in the Holy Roman Empire (Princeton, NJ, 1994).

Literature on this subject is extensive. Key examples relevant to this paper for continental Europe include Stroup Alice , A company of scientists: Botany, patronage, and community at the seventeenth-century Parisian Royal Academy of Sciences (Berkeley, 1990), especially 3–61, 169–226; Lux David S. , Patronage and royal science in seventeenth century France: The Académie de Physique in Caen (Ithaca, NY, 1989); Hahn Roger , The anatomy of a scientific institution: The Paris Academy of Sciences, 1666–1803 (Berkeley, 1971), 1–57. For a classical study see Brown Harcourt , Scientific organizations in seventeenth century France (1620–1680) (Baltimore, 1934; New York, 1967). Relevant studies on Italy include Luciano Boschiero, Experiment and natural philosophy in seventeenth-century Tuscany (Dordrecht, 2007), especially 1–48, 115–40; Middleton W. E. Knowles , The experimenters: A study of the Accademia del Cimento (Baltimore, 1971).

Two recent studies have attempted to address this issue from different angles. The more critical of the two is Licoppe Christian , La formation de la pratique scientifique: Le discours de l'expérience en France et en Angleterre (1630–1820) (Paris, 1996), 19–52. Licoppe, however, restricts the majority of his discussion to experimental science. More vague is Volker Remmert, Widmung, welterklärung und wissenschaftslegitimierung: Titelbilder und ihre funktionen in der wissenschaftlichen revolution (Wiesbaden, 2005). Remmert's analysis says little about social interaction of mathematicians and is instead an analysis of frontispieces to mathematical texts.

Though Mersenne was never referred to as such by his contemporaries, the term had appeared in English vernacular as early as 1581. On this matter, see The Oxford English dictionary, 2nd edn, prep. Simpson J. A. Weiner E. S. C. , vii (Oxford, 1989), 1070, s.v. “Intelligencer”.

Amama Sixtinus to Rivet André , June 1626, CM, i, no. 61, 476.

Amama Sixtinus to Rivet André , 13/23 February 1628, CM, ii, no. 94, 27. The response to Mersenne is the entirety of the previous letter: Sixtinus Amama to Marin Mersenne, 23 February 1628, CM, ii, no. 93, 21–25.

For more on this intellectual climate, see Israel Jonathan I. , The Dutch Republic: Its rise, greatness, and fall, 1477–1806 (Oxford, 1995), 565–91.

On the importance of long distance networks for strengthening knowledge claims, see, most importantly, Cook Harold J. Lux David S. , “Closed circles or open networks?: Communicating at a distance during the scientific revolution”, History of science, xxxvi (1998), 179–211. See also Harris Steven J. , “Networks of travel, correspondence, and exchange”, in Park Katharine Daston Lorraine (eds), The Cambridge history of science, iii, Early modern science (Cambridge, 2006), 341–62.

Mersenne Marin to Rivet André , 23 May 1638, CM, vii, no. 672, 216. See also Descartes René to Mersenne Marin , 17/27 May 1638, CM, vii, no. 674, 240. For more on Beeckman and Mersenne, see van Berkel Klaas , Isaac Beeckman (1588–1637) en de mechanisering van het wereldbeeld (Amsterdam, 1983). Consult chapter 3 of the forthcoming English edition for details.

On Mersenne correcting Rivet's work, see the first paragraph of Marin Mersenne to André Rivet, 25 December 1628, CM, ii, no. 121, 150–1. More than once Mersenne offered Rivet's son lodging. See, for example, Marin Mersenne to André Rivet, 5 April 1629, CM, ii, no. 129, 228. See also Mersenne Marin to Rivet André , 23 August 1629, CM, ii, no. 134, 265.

Mersenne Marin to Rivet André , 25 December 1628, CM, ii, no. 121, 151–2: “Vous aurez donc, s'il vous plaist, soin d'entretenir nostre amitié avec Msr Amama et de luy prier de me faire s&çavoir de temps en temps ce qui s'imprimera de bon dans leur Academie”.

Mersenne Marin to Rivet André , 30 October 1628, CM, ii, no. 116, 104: “[j]'auray… un soin particulier d'entretenir nostre communication, tant pour les livres et autres choses qui concernent la litterature que pour tout ce que vous jugerez vous pouvoir apporter du contentement”.

Mersenne Marin to Rivet André , 28 February 1629, CM, ii, no. 126, 205: “le plus excellent esprit”.

Most of the data concerning Mersenne's interactions with the Elzevirs can be gleaned from his exchanges with Rivet. There is only one letter in the entire Mersenne correspondence between Mersenne and the Elzevirs, and it summarizes their interactions well. See Bonaventure Elzevir Abraham to Mersenne Marin , 8 March 1638, CM, vii, no. 657, 107.

Mersenne Marin to Rivet André , 25 December 1628, CM, ii, no. 121, 152.

For more on Elzevir culture, see Davies D. W. , The world of the Elseviers, 1580–1712 (The Hague, 1954), especially 76–96. For information on Jan Maire, see Breugelmans Ronald , Fac et spera: Joannes Maire, publisher, printer and bookseller in Leiden 1603–1657. A Bibliography of His Publications (Houten, Netherlands, 2003).

For a good summary, see Soman Alfred , “Press pulpit and censorship in France before Richelieu”, Proceedings of the American Philosophical Society, cxx (1976), 439–63.

See, for example, Théodore Deschamps to Marin Mersenne, 26 March 1642, CM, xi, no. 1075, 86.

For more details on the genesis and development of these ideas, see Gaukroger Stephen , Descartes: An intellectual biography (Oxford, 1995), 225–92.

For the first serious conversation, see Descartes René to Mersenne Marin , 15 April 1630, CM, ii, no. 155, 423–4. Progress reports to Mersenne were as follows: Descartes to Marin Mersenne, 25 November 1630, CM, ii, no. 173, 560–1; Descartes René to Mersenne Marin , October or November 1631, CM, iii, no. 208, 213; Descartes René to Mersenne Marin , 5 April 1632, CM, iii, no. 218, 290–1; Descartes René to Mersenne Marin , 1 August 1632, CM, iii, no. 222, 314; Descartes René to Mersenne Marin , November or December 1632, CM, iii, no. 229, 346.

Descartes René to Mersenne Marin , 23 July 1633, CM, iii, no. 263, 459.

On at least two occasions Descartes expresses his anxieties to Mersenne. See Descartes René to Mersenne Marin , 28 November 1633, CM, iii, no. 291, 557–8. See also Descartes René to Mersenne Marin , end of February 1634, CM, iv, no. 317, 50.

For a comprehensive English language discussion of the Discourse, its development, and its publication history, see MacLean Ian , introduction to A discourse on the method of correctly conducting one's reason and seeking truth in the social sciences, by Descartes René , 2nd edn (Oxford, 2008).

Mersenne himself recognized this. See Mersenne Marin to Descartes René , 1 August 1638, CM, viii, no. 691, 2. An excellent article covering the full range of Descartes's authorial strategies is Jean-Pierre Cavaillé, “‘Le plus éloquent philosophe des derniers temps’: Les stratégies d'auteur de René Descartes”, Annales HSS, ii (1994), 1994–67.

Descartes René to Mersenne Marin , March 1636, CM, vi, no. 547, 43.

On the economy and efficacy of Dutch printing houses, see Johns Adrian , The nature of the book: Print and knowledge in the making (Chicago, 1998), 447–8.

Mersenne Marin to Rivet André , 20 January 1638, CM, vii, no. 645, 27: “ne parle que philosophiquement”.

Here Mersenne is referring to Fermat's objections to the Dioptrique, Morin's questions concerning the nature of light, and Guillaume Gibieuf's discussions concerning the existence of God.

Descartes René to Mersenne Marin , around 20 April 1637, CM, vi, no. 601, 233–4.

Descartes René to Mersenne Marin , March 1636, CM, vi, no. 547, 43.

The Dutch privilege was granted on 20 December 1636.

Huygens Constantijn to Descartes René , 5 January 1637, CM, vi, no. 578, 164.

The porter was likely Johan van Euskercken, secretary to the Dutch ambassador in Paris.

Mersenne Marin to Descartes René , 15 February 1637, CM, vi, no. 584, 186–7.

Mersenne Marin to Descartes René , 15 February 1637, CM, vi, no. 584, 187.

See Descartes René to Mersenne Marin , around 17 May 1637, CM, vi, no. 609, 257. See also Descartes René to Mersenne Marin , around 17 May 1637, CM, vi, no 610, 262. The French privilege had already been granted, but the documentation did not arrive in Leiden until 1 June 1637.

Descartes René to Mersenne Marin , around 17 May 1637, CM, vi, no. 609, 257–8.

Descartes René to Mersenne Marin , 6 June 1637, CM, vi, no. 616, 277.

Descartes René to Mersenne Marin , 6 June 1637, CM, vi, no. 616, 278.

Descartes René to Mersenne Marin , 13 November 1639, CM, viii, no. 780, 611. More explicit directions were given later in the summer of 1640. For this, see Descartes René to Mersenne Marin , 30 July 1640, CM, ix, no. 899, 521.

The genesis of the plan is found in Descartes René to Mersenne Marin , 30 September 1640, CM, x, no. 921, 116. The actualization of the plan is in René Descartes to Marin Mersenne, 11 November 1640, CM, x, no. 939, 233.

On shipping the Meditations to Mersenne, see Descartes René to Mersenne Marin , 11 November 1640, CM, x, no. 938, 228. See also Descartes René to Huygens Constantijn , 11 November 1640, CM, x, no. 940, 235. On declaring Mersenne the godfather of the work, see Descartes René to Mersenne Marin , 11 November 1640, CM, x, no. 939, 232: “Je vous envoye enfin mon écrit de Metaphysique, auquel je n'ay point mis de titre, afin de vous en faire le parain, et vous laisser la puissance de le baptiser”.

Descartes René to Mersenne Marin , 4 March 1641, CM, x, no. 986, 530.

Many of these objections are beyond the scope of mathematics, but Mersenne's intervention in collecting them is indicative of his engagement with the print world. For a recent and concise summary of the objections to Descartes and his replies, see Ariew Roger Cress Donald , introduction to Meditations, objections, and replies, by Descartes René (Indianapolis, 2006).

Mersenne Marin to Rivet André , 1 November 1641, CM, x, no. 1040, 774. It seems that the text was slow to reach the Netherlands after having been printed in Paris. Mersenne was irked that Rivet had not yet received a copy of the book in late November, since it had finished printing in Paris on 28 August 1641. See Mersenne Marin to Rivet André , 25 November 1641, CM, x, no. 1045, 798.

Descartes René to Mersenne Marin , 31 December 1640, CM, x, no. 956, 362.

Descartes René to Mersenne Marin , 17 November 1641, CM, x, no. 1042, 780.

Descartes René to Mersenne Marin , 17 November 1641, CM, x, no. 1042, 779–80.

See Goldgar Anne , Impolite learning: Conduct and community in the Republic of Letters, 1680–1750 (New Haven, CT and London, 1995), 41–53.

Descartes René to Mersenne Marin , 31 March 1638, CM, vii, no. 661, 120.

Huygens Constantijn to Mersenne Marin , 26 August 1639, CM, viii, no. 759, 491.

Mersenne Marin to Rivet André , 15 July 1640, CM, ix, no. 892, 483.

Rivet André to Huygens Constantijn , 6 August 1640, CM, x, no. 903, 1.

Huygens Constantijn to Rivet André , 20 August 1640, CM, x, no. 908, 17.

Literature on Peiresc has mushroomed in recent years. Seminal items concerning Peiresc and networks include Miller Peter N. , Peiresc's Europe: Learning and virtue in the seventeenth century (New Haven, CT, 2000); Wilding Nick , “Writing the book of nature: Natural philosophy and communication in early modern Europe” (Ph.D. diss., European University Institute, 2000); Brentjes Sonja , Travellers from Europe in the Ottoman and Safavid empires, 16th–17th centuries: Seeking, transforming, discarding knowledge (Farnham, UK and Burlington, VT, 2010), vii, 1–56.

On Mersenne's plea, see Mersenne Marin to de Peiresc Nicolas-Claude Fabri , 20 March 1634, CM, iv, no. 324, 81–82. On Peiresc funding the work, see de Peiresc Nicolas-Claude Fabri to Mersenne Marin , 8 July 1634, CM, iv, no. 358, 236. On the dedication to Peiresc, see Mersenne Marin to de Peiresc Nicolas-Claude Fabri , 1 July 1635, CM, v, no. 453, 268. Mersenne also sought Peiresc's prepublication advice. See Mersenne Marin to de Peiresc Nicolas-Claude Fabri , 17 September 1635, CM, v, no. 484, 404. Though this gives a flavour of their interactions concerning the production of Harmonie universelle, further supporting details can be found in intervening letters between Mersenne and Peiresc.

Gauvin Jean-François , “Habits of knowledge: Artisans, savants and mechanical devices in seventeenth-century French natural philosophy” (Ph.D. diss., Harvard University, 2008), 28–119.

Blair Ann M. , Too much to know: Managing scholarly information before the modern age (New Haven, CT and London, 2010), 173–229.

Mersenne Marin to de Peiresc Nicolas-Claude Fabri , 20 March 1634, CM, iv, no. 324, 82: “Je n'espère maintenant plus rien de la musique des Grecs, ni des Orientaux, après avoir attendu 2 ou 3 ou 4 ans après sans aucun fruit…. Je croy que nous les surpassons tous en ceste matiere”.

Beaugrand Jean to Mersenne Marin , 20 February 1632, CM, iii, no. 213, 254, 256.

Little is known about this academy. For a brief, empirical sketch, see Fletcher Colin , “Mersenne: Sa correspondance et l'academia parisiensis”, in Goldstein Catherine Gray Jeremy Ritter Jim (eds), L'Europe mathématique/Mathematical Europe (Paris, 1996), 145–53.

Only four letters from Mersenne himself discuss the Academia Parisiensis. The most explicit, which names members, is Marin Mersenne to Nicolas-Claude Fabri de Peiresc, around 1 September 1635, CM, v, no. 476, 371. Supporting details are found in Marin Mersenne to Nicolas-Claude Fabri de Peiresc, 23 May 1635, CM, v, no. 435, 209; Marin Mersenne to Nicolas-Claude Fabri de Peiresc, 15 July 1635, CM, v, no. 460, 301–2; Marin Mersenne to Nicolas-Claude Fabri de Peiresc, 20 August 1635, CM, v, no. 472, 353.

Fermat Pierre to Mersenne Marin , 26 April 1636, CM, vi, no. 550, 51.

Galilei Galileo to Diodati Élie , 17 August 1638, CM, viii, no. 695, 32. Galileo later complained to the mathematician Bonaventura Cavalieri that neither he nor his colleagues could read Mersenne's handwriting. See Galilei Galileo to Cavalieri Bonaventura , 24 February 1640, CM, ix, no. 823, 125.

de Peiresc Nicolas-Claude Fabri to Dupuy Pierre , 6 February 1634, CM, iv, no. 309, 31.

Doni Giovanni Battista to Mersenne Marin , 8 April 1634, CM, iv. no. 326, 87.

Hine William L. , “Mersenne and Copernicanism”, Isis, lxiv (1973), 18–32.

A recent, comprehensive discussion of Galileo in France can be found in Lewis John , Galileo in France: French reactions to the theories and trial of Galileo (New York, 2006). Specifics regarding Galileo's condemnation are found on pages 131 and 183.

Mersenne Marin to de Peiresc Nicolas-Claude Fabri , 4 December 1634, CM, iv, no. 393, 406–7.

For a comprehensive study of Élie Diodati, his friends, and his social network, see Garcia Stéphane , Élie Diodati et Galilée: Naissance d'un réseau scientifique dans l'Europe du XVII^e siècle (Florence, 2004).

There is no direct correspondence between the two men in the Mersenne correspondence. Though both men lived in Paris, Diodati's language in his letter to Galileo on 16 May 1634 (see ref. 87) indicates that Diodati and Mersenne did not know each other well.

See Mersenne Marin to Rivet André , 3 March 1635, CM, v, no. 411, 81. The accompanying editorial note on the following page and page 273 of this volume clarifies that the key anticipated work is indeed Galileo's Dialogue. Mersenne heralded the arrival of the work to Peiresc on the first of July. See Mersenne Marin to de Peiresc Nicolas-Claude Fabri , 1 July 1635, CM, v, no. 453, 270.

Diodati Élie to Galilei Galileo , 16 May 1634, CM, iv, no. 339, 156. Mersenne's translation appeared in 1634 under the title Les mechaniques de Galilée.

Mersenne Marin to Rivet André , 20 November 1638, CM, viii, no. 708, 222. Mersenne already had tried to coax such ideas out of Rivet in the winter of 1634. See Mersenne Marin to Rivet André , 8 February 1634, CM, iv, no. 311, 37–38.

Mersenne Marin to Rivet André , 20 December 1638, CM, viii, no. 712, 239.

Mersenne Marin to Rivet André , 20 November 1638, CM, viii, no. 708, 221–2. See also Mersenne Marin to Rivet André , 15 September 1636, CM, vi no. 569, 138. Mersenne had been aware that such a work was underway for a while. See, for example, Descartes René to Mersenne Marin , around 1 May 1634, CM, iv, no. 329, 98–99.

Castelli Benedetto to Galilei Galileo , 30 November 1635, CM, v, no. 519, 510.

Cavalieri Bonaventura to Rocca Giannantonio , 11 November 1635, CM, v, no. 506, 466.

Marr Alexander , Between Raphael and Galileo: Mutio Oddi and the mathematical culture of late Renaissance Italy (Chicago, 2011), 109–30.

Mersenne Marin to Galilei Galileo , 27 November 1637, CM, vi, no. 633, 339–40.

Shortly after Mersenne informed Galileo that Descartes's work was coming, Galileo's cousin in Lyon, Roberto Galilei, wrote to Galileo supplying the same message. See Galilei Roberto to Galilei Galileo , 23 December 1637, CM, vi, no. 635, 343. Hereafter, Roberto seems to have mistaken Mersenne as the author of the Discourse. On the loss of the materials, see Galilei Roberto to Galilei Galileo , 22 June 1638, CM, vii, no. 679, 287. On the recovery of the materials, see Santini Antonio to Galilei Galileo , 21 September 1641, CM, x, no. 1032, 751. Additional letters from Roberto Galilei to Galileo Galilei in volumes six and seven of the Mersenne correspondence provide more details.

Baliani Giovanni Battista to Mersenne Marin , 1 October 1640, CM, x, no. 922, 130.

Marin Mersenne to Bonaventura Cavalieri, 1 March 1641, CM, x, no. 984, 519–20.

Biagioli Mario , Galileo's instruments of credit: Telescopes, images, secrecy (Chicago, 2006), 21–75.

The most explicit reference is René Descartes to Marin Mersenne, 31 March 1641, CM, x, no. 995, 579–80: “Je vous envoye un escrit pour le libraire, que vous ne trouverez pas daté de Leyde, à cause que je n'y demeure plus, mais en une maison qui n'en est qu'à demi-lieuë, en laquelle je me suis retiré pour travailler plus commodement à la Philosophie et ensemble aux experiences. Il n'est point besoin pour cela de changer l'adresse de vos lettres, ou plutost il n'est point besoin d'y mettre aucune adresse que mon nom, car le messager de Leyde s&çait assez le lieu où il les doit envoyer”.

Descartes René to Mersenne Marin , January 1638, CM, vii, no. 643, 12.

Fermat Pierre to Mersenne Marin , 3 June 1636, CM, vi, no. 557, 94.

On Mersenne not understanding the concepts, see Fermat Pierre to Mersenne Marin , 24 June 1636, CM, vi, no. 562, 108. For Mersenne seeking Descartes's thoughts, see Descartes René to Mersenne Marin , second half of June 1637, CM, vi, no. 619, 289.

Descartes René to Mersenne Marin , 5 or 12 October 1637, CM, vi, no. 628, 314–15.

Beaugrand Jean to Mersenne Marin , the beginning of March 1638, CM, vii, no. 655, 88. For a discussion on specific mathematical rules that Beaugrand felt were copied, see the numbered passages in the body of the letter. Key areas of contention include eliminating the term of second highest degree in a polynomial, ridding fractional coefficients of polynomials, and lessons for how to reduce quartic polynomials to cubic equations.

Descartes René to Mersenne Marin , 29 June 1638, CM, vii, no. 681, 302, 309.

See the entirety of Fermat Pierre to Mersenne Marin , April or May 1637, CM, vi, no. 607, 247–54.

Fermat Pierre to Mersenne Marin , April or May 1637, CM, vi, no. 607, 252.

Descartes's initial reply intimates that Fermat is unnamed. See Descartes René to Mersenne Marin , 5 or 12 October 1637, CM, vi, no. 629, 316. More explicit evidence is in René Descartes to Marin Mersenne, January 1638, CM, vii, no 643, 10.

Descartes René to Mersenne Marin , 6 June 1637, CM, vi, no. 616, 279–80.

Letters 628 and 629 probably arrived together. Although Fermat's name was not mentioned on the actual critique, letter 629, Descartes acknowledges that its author is Fermat in the previous letter. See Descartes René to Mersenne Marin , 5 or 12 October 1637, CM, vi, no. 628, 314.

For the rebuttal, see the entirety of Fermat Pierre to Mersenne Marin , November 1637?, CM, vi, no. 631, 321–32. Descartes told Mersenne it was not necessary to rush delivery of the rebuttal. See Descartes René to Mersenne Marin , end of December 1637, CM, vi, no. 636, 347.

In actuality, Descartes's method sought to find normal lines to curves, from which tangents could be easily derived.

Desargues Gérard to Mersenne Marin , 4 April 1638, CM, vii, no. 663, 151.

For a full epistemic account of the debate over maxima and minima between Fermat and Descartes, see Mahoney Michael Sean , The mathematical career of Pierre Fermat (1601–1665) (Princeton, NJ, 1973), 143–213. Another insightful epistemic study on Fermat is Giovanna Cleonice Cifoletti, La méthode de Fermat: Son statut et sa diffusion: Algèbre et comparaison de figures dans l'histoire de la méthode de Fermat (Paris, 1990), especially 10–18, 61–74, 93–128.

Descartes René to Mersenne Marin , January 1638?, CM, vii, no. 644, 16, 18, 20.

Descartes René to Mersenne Marin , 1 March 1638, CM, vii, no. 654, 78.

Descartes René to Mersenne Marin , 1 March 1638, CM, vii, no. 654, 78.

Descartes René to Mydorge Claude , 1 March 1638, CM, vii, no. 653, 59.

Fermat Pierre to Mersenne Marin , February 1638, CM, vii, no. 652, 49; Pierre Fermat to Marin Mersenne, 20 April 1638, CM, vii, no. 665, 170.

See the entirety of Roberval against Descartes, first half of April 1638, CM, vii, no. 664, 158–68.

Descartes finally acknowledged receipt of this material two months after it had debuted. See Descartes René to Mersenne Marin , 3 June 1638, CM, vii, no. 676, 254. Around this same time, Roberval remarked that this delay seemed odd. See de Roberval Gilles Personne to Fermat Pierre , 1 June 1638, CM, vii, no. 675, 247.

Fermat Pierre to Mersenne Marin , 20 April 1638, CM, vii, no. 665, 171.

See, for example, Descartes René to Mersenne Marin , 17/27 May 1638, CM, vii, no. 674, 236.

Descartes first described the mathematical properties of the folium curve to Fermat in January of 1638. See Descartes René to Mersenne Marin , January 1638?, CM, vii, no. 644, 18–19 for technical details. It seems that Fermat actually found the tangent to this curve and told Roberval, but not Descartes. See Gilles Personne de Roberval to Pierre Fermat, 1 June 1638, CM, vii, no. 675, 249; René Descartes to Marin Mersenne, 27 July 1638, CM, vii, no. 690, 422–3. A final, lengthy discussion is found in René Descartes to Marin Mersenne, 23 August 1638, CM, viii, no. 696, 40–45. Using modern mathematical notation, the folium is defined by the equation x³ + y³ — 3axy = 0, where a is a constant.

For the best source on the roots of peer review, see Biagioli Mario , “From book censorship to academic peer review”, Emergences, xii (2002), 11–45. Biagioli, however, asserts that the origins of scientific peer review are to be found in published journals of scientific institutions postdating this era. My example is limited to manuscript circulation, and it is unlikely that scribal publication of these letters had a serious role in the peer review process aside from using Mersenne as a repository for holding copies of letters.

Descartes René to Mersenne Marin , 5 or 12 October 1637, CM, vi, no. 628, 315.

Descartes René to Mersenne Marin , 17/27 May 1638, CM, vii, no. 674, 236.

Descartes René to Mersenne Marin , 17/27 May 1638, CM, vii, no. 674, 237.

Descartes René to Mersenne Marin , 29 June 1638, CM, vii, no. 681, 294.

Claims to originality were rooted in Renaissance culture, though they were not protected through copyright law until 1710 in the Statute of Anne. On the notion of originality in Renaissance literature, see Quint David , Origin and originality in Renaissance literature: Versions of the source (New Haven, CT and London, 1983). For information concerning letter writing, see Braunmuller A. R. , “Editing Elizabethan letters”, Text: Transactions of the Society for Textual Scholarship, i (1981), 1981–99. On legal notions of literary property and their development in the eighteenth century, see, most importantly, Rose Mark , Authors and owners: The invention of copyright (Cambridge, MA, 1993).

Fermat Pierre to Mersenne Marin , November 1637?, CM, vi, no. 631, 322.

Fermat Pierre to Mersenne Marin , November 1637?, CM, vi, no. 631, 322.

Descartes René to Mersenne Marin , January 1638, CM, vii, no. 643, 10.

Descartes René to Mersenne Marin , January 1638, CM, vii, no. 643, 11.

Descartes René to Mersenne Marin , 1 March 1638, CM, vii, no. 654, 80: “Gardez-vous aussi de mettre les originaux entre les mains des amis de Monsieur de Fermat, sans en avoir des copies, de peur qu'ils ne vous les rendent plus; et vous luy envoyerez, s'il vous plaist, mes réponses, si-tost que vous les aurait fait copier”.

Descartes René to Mersenne Marin , 1 March 1638, CM, vii, no. 654, 80: “Une autre fois je vous prie de retenir des copies de tout ce que vous m'envoyerez et desirerez ravoir”.

Descartes René to Mersenne Marin , 11 October 1638, CM, viii, no. 700, 101 and said other times before and after in this letter with slight variations in wording: “entierement basti en l'air”.

Descartes René to Mersenne Marin , 11 October 1638, CM, viii, no. 700, 103–4: “Et premierement, touchant Galilée, je ne l'ay jamais vû, ny n'ay eu aucune communication avec luy, et que par consequent je ne s&çaurois en avoir emprunté aucune chose”.

Debeaune Florimond to Mersenne Marin , 13 November 1638, CM, viii, no. 706, 172: “Tout ce qui est fascheux, est que Mr Descartes parle ambiguement”.

For a full account on hyperbolic lenses, see Burnett D. Graham , Descartes and the hyperbolic quest: Lens making machines and their significance in the seventeenth century (Philadelphia, 2005).

Descartes René to Mersenne Marin , 31 March 1638, CM, vii, no. 661, 123; Descartes René to Mersenne Marin , November or December 1632, CM, iii, no. 229, 345.

Descartes René to Mersenne Marin , 25 January 1638, CM, vii, no. 647, 38; Descartes René to Huygens Constantijn , 25 January 1638, CM, vii, no. 648, 43.

Descartes René to Mersenne Marin , 25 December 1639, CM, viii, no. 797, 702–3. Descartes later reflected more explicitly on Debeaune's ability. See Descartes René to Mersenne Marin , 21 January 1641, CM, x, no. 969, 425.

Descartes René to Mersenne Marin , 11 March 1640, CM, ix, no. 837, 198. Further details can be deduced from the following letter, René Descartes to Constantijn Huygens, 12 March 1640, CM, ix, no. 838, 202.

Deschamps Théodore to Mersenne Marin , 26 March 1642, CM, xi, no. 1075, 87–88.

An implicit reference is Deschamps Théodore to Mersenne Marin , 29 August 1640, CM, x, no. 913, 78–79. Deschamps was more explicit in his later requests. See Deschamps Théodore to Mersenne Marin , 18 April 1642, CM, xi, no. 1084, 121. See also Deschamps Théodore to Mersenne Marin , 5 May 1642, CM, xi, no. 1093, 140.

Deschamps Théodore to Mersenne Marin , 22 December 1642, CM, xi, no. 1150, 383, 390. Deschamps had already mentioned sending these lenses to Mersenne two months earlier with the promise of better lenses to come. See Deschamps Théodore to Mersenne Marin , 31 October 1642, CM, xi, no. 1139, 316–17.

The delivery of the lenses can be surmised from Deschamps Théodore to Mersenne Marin , 1 March 1643, CM, xii, no. 1169, 87. On Mersenne's disappointment, see Deschamps Théodore to Mersenne Marin , 17 June 1643, CM, xii, no. 1192, 217.

Deschamps Théodore to Mersenne Marin , 8 May 1644, CM, xiii, no. 1271, 127.

René Descartes to Marin Mersenne for Thomas Hobbes, 21 January 1641, CM, x, no. 970, 427.

Rivet André to Mersenne Marin , 29 April 1638, CM, vii, no. 667, 185.

Rivet André to Mersenne Marin , 23 May 1638, CM, vii, no. 672, 212.

Mersenne Marin to Rivet André , 23 January 1638, CM, vii, no. 646, 33.

Magiotti Raffaello to Galilei Galileo , 25 April 1637, CM, vi, no. 604, 241: “il P. Mersenio de' Minimi, che ha veduto il libro de Motu [Two new sciences] con l'altre osservationi… egli vuole scompuzzare ogni cosa. Questo frate stampa grandi e molti libracci, cercando con lo sgradire altrui d'acquistarsi reputatione, e forse gli riuscirà appresso della marmaglia”.

Using modern mathematical notation, the cycloid is defined by the parametric equations x = r(t — Sin t), y = r(1 — Cos t) where r is the radius of the circular wheel and t is the parameter.

Mersenne's correspondent, Blaise Pascal, wrote a detailed history of the cycloid in 1658. For further details see Pascal Blaise , Œuvres complètes, ed. by Mesnard Jean , iv (Paris, 1992), 214–45. A slight continuation of the history exists in Latin and occupies pages 246–52 of the text.

Descartes René to Mersenne Marin , 30 April 1639, CM, viii, no. 737, 410: “Il faut que je rie de ce que vous m'avez desja envoyé 5 ou 6 fois sa fa&çon pour trouver la tangente de la Roulete, toujours differemment, et tousjours avec faute, ce qui ne s&çauroit venir de vostre plume”.

Fermat Pierre to Mersenne Marin , 27 January 1643, CM, xii, no. 1162, 33: “Je vous rends mille grâces… des propositions que vous m'avez fait la faveur de m'envoyer. Celles de la parabole, de l'hélice et du conoïde parabolique sont si visiblement fausses que ce seroit perdre le temps que les refuter”.

Garber Daniel , “On the frontlines of the scientific revolution: How Mersenne learned to love Galileo”, Perspectives on science, xii (2004), 135–63.

See Galilei Galileo , Dialogue concerning the two chief world systems: Ptolemaic and Copernican, ed. and trans. by Drake Stillman (New York, 2001), 257; Galilei Galileo , Two new sciences, ed. and trans. by Drake Stillman (Madison, 1974), 147, 167–9.

Palmerino Carla Rita , “Experiments, mathematics, physical causes: How Mersenne came to doubt the validity of Galileo's law of free fall”, Perspectives on science, xviii (2010), 50–76.

Mersenne Marin to Descartes René , 28 April 1638, CM, vii, no. 666, 174: “Or agréez s'il vous plaist, que je vous propose deux difficultez, dont je suis en controverse avec ledit sieur de Roberval, lesquelles vous me ferez plaisir de resoudre, se vous le pouvez”.

Lenoble Robert , Mersenne ou la naissance du mécanisme (Paris, 1943), 336–82 on mechanics, 451–4 on mathematics.

See Descartes René to Mersenne Marin , 11 October 1638, CM, viii, no. 700, 94–103. Critiques are from the first part of the letter.

Marin Mersenne in the name of the Mathematicians of Paris to the friends of Galileo in Italy, 1 July 1643, CM, xii, no. 1194, 220–7.

See Biagioli Mario Galison Peter , (eds), Scientific authorship: Credit and intellectual property in science (New York, 2002).

For theoretical implications, see Foucault Michel , “What is an author?”, in Rabinow Paul (ed.), The Foucault reader (New York, 1984), 101–20. Though Foucault's concept of the “author function” is based on nineteenth-century penal codes and down plays scientific writing as a source of analysis, Foucault stresses above all the importance of attributing a name to a work so that readers can attribute responsibility to someone for composing it.

Torricelli Evangelista to Mersenne Marin , 13 January 1644, CM, xiii, no. 1245, 12.

As early as November 1639, Descartes had warned Mersenne against making a trip to Italy, though for salubrity rather than intellectual reasons. See Descartes René to Mersenne Marin , 13 November 1639, CM, viii, no. 780, 612–13. Descartes again warned Mersenne of the perils of visiting Italy in October 1642. See Descartes René to Mersenne Marin , 13 October 1642, CM, xi, no. 1136, 301.

Ricci Michelangelo to Torricelli Evangelista , 9 December 1644, CM, xiii, no. 1318, 263.

Torricelli Evangelista to Ricci Michelangelo , 17 December 1644, CM, xiii, no. 1321, 275.

Ricci Michelangelo to Torricelli Evangelista , 24 December 1644, CM, xiii, no. 1323, 279–80: “Il Padre Mersenne è stato da me finora tre volte, prima col Padre Emanuelle Magnani amicissimo mio, poi con un Armeno pur mio amico, et ultimamente assieme col Sigr. Cavalier del Pozzo. Ma quanto è stato facile in onorarmi con le sue visite, altrettanto difficile si rende in trovarlo in Convento per restituirgli la visita, poichè sempre va fuori, cercando virtuosi manoscritti, et altre curiosità. Questa sera mi non trattenuto alla Trinità fino a mezzora, e più di notte, volendogli presentar la lettera di V.S.; ma facendosi troppo tardi, et esso non veniva, mi son resoluto di lasciarla in mano del suddetto Padre Emanuelle, il quale gliela ricapiterà sicura, e complirà per me. Ho stimato bene di far così, acciocchè fosse in tempo di respondere a V.S”.

Ricci Michelangelo to Torricelli Evangelista , 28 January 1645, CM, xiii, no. 1339, 341: “Questo Padre mostra di non saper molta Geometria, ma di aver fatte infinite osservazioni. Ha un trattato meccanico, il quale leggerò per servir V.S. in quel poco, che mi permetterà la mia debolezza d'ingegno, e d'intendenza di lingua franceze”.

Ricci Michelangelo to Torricelli Evangelista , 26 February 1645, CM, xiii, no. 1352, 387.

Ricci Michelangelo to Torricelli Evangelista , 4 February 1645, CM, xiii, no. 1342, 353: “Mi fece vedere il Padre le figure, et li sommari delle proposizioni, e non più”.

Ricci Michelangelo to Torricelli Evangelista , 31 December 1644, CM, xiii, no. 1327, 290.

Torricelli Evangelista to Mersenne Marin , around 17 January 1645, CM, xiii, no. 1334, 324.

On the Latin edition of the Dioptrics, see Mersenne Marin to Torricelli Evangelista , 15 March 1645, CM, xiii, no 1357, 400. On Torricelli and Roberval's work on the lengths of curves, see Mersenne Marin to Torricelli Evangelista , 4 February 1645, CM, xiii, no. 1341, 345.

Torricelli Evangelista to Ricci Michelangelo , 25 February 1645, CM, xiii, no. 1350, 384.

Dear Peter , Mersenne and the learning of the schools (Ithaca, NY and London, 1988), 206.

There are two strands of research that discuss expertise in early modern Europe. The first concerns facility with and application of a specialized body of knowledge. See Ash Eric H. , “Introduction: Expertise and the early modern state”, Osiris, xxv (2010), 1–24. Other essays in the first part of this special issue of Osiris are relevant conceptually. See also Ash Eric H. , Power, knowledge, and expertise in Elizabethan England (Baltimore and London, 2004). It should be noted that this approach underscores expertise in its relevance to state concerns rather than general intellectual affairs. Slightly older literature concerning expertise emphasizes the socio-cultural aspects of individuals and can be seen, for example, in the work of Steven Shapin. See Shapin Steven , A social history of truth: Civility and science in seventeenth-century England (Chicago, 1994); Shapin Steven , “The house of experiment in seventeenth-century England”, Isis, lxxix (1988), 1988–404; Shapin Steven Schaffer Simon , Leviathan and the air pump: Hobbes, Boyle, and the experimental life (Princeton, NJ, 1985).

Inspiration for this idea comes from the Bruno Latour's notion of spokespeople. See Latour Bruno , Science in action: How to follow scientists and engineers through society (Cambridge, MA, 1987), 70–79.

Mersenne Marin to Beeckman Isaac , 1 October 1629, CM, ii, no. 138, 282–3: “De vacuo bene argumentaris. Sive enim vacui dicantur esse pori aeris, aquae, plumbi etc., sive totus locus vacuus inter supremam circumferentiam aeris nostri et sydera, nihil absurdi sequitur. Quod enim philosophi garriunt de rerum omnium necessariâ unione, de accidentium et specierum visibilium in aere propagatione, de impossibilitate motûs in vacuo, etc., aniles mihi videntur fabulae; nihil enim in philosophiâ admitto quam quod imaginationi velut sensile representatur”.

For a classic perspective, see Popkin Richard , The history of Skepticism from Savonarola to Bayle, rev. edn (Oxford, 2003), 112–27. For a discussion of Mersenne's mitigated skepticism specifically with regard to Galileo's Copernican ideas, see Sarasohn Lisa T. , “French reaction to the condemnation of Galileo, 1632–1642”, Catholic historical review, lxxiv (1988), 34–54.

Piecemeal evidence of this comes from two different letters. On 5 June 1647, Theodore Haak notes to Mersenne that Samuel Hartlib has informed Haak of Mersenne forthcoming experiments on the void. See Haak Theodore to Mersenne Marin , 5 June 1647, CM, xv, no. 1632, 248. Additionally it can be inferred in a letter from Jacques le Tenneur to Mersenne on 9 July 1647 that Mersenne had made experiments of the void to draw conclusions about the nature of light. See le Tenneur Jacques to Mersenne Marin , 9 July 1647, CM, xv, no. 1639, 295.

Galilei , Two new sciences, 25–26.

Mersenne Marin to Huygens Constantijn , 26 August 1639, CM, viii, no. 759, 493; Descartes René to Mersenne Marin , 27 August 1639, CM, viii, no. 760, 498–9; Descartes René to Mersenne Marin , 16 October 1639, CM, viii, no. 772, 541; Mersenne Marin to Haak Theodore , 18 December 1639, CM, viii, no. 796, 692; Descartes René to Mersenne Marin , 25 December 1639, CM, viii, no. 797, 701; Daguin to Marin Mersenne, 1639?, CM, viii, no. 801, 733; Marin Mersenne to Theodore Haak, 20 January 1640, CM, ix, no. 812, 39–40. On building sinks to raise water see the entirety of Constantijn Huygens to Marin Mersenne, 1 April 1640, CM, ix, no. 848, 257–60; see also Constantijn Huygens to Marin Mersenne, 3 June 1640, CM, ix, no. 874, especially 379–84.

On Italian experiments concerning the void between Galileo and Torricelli, see Middleton W. E. Knowles , “The place of Torricelli in the history of the barometer”, Isis, liv (1963), 11–28. See also de Waard Cornelis , L'expérience barométrique: Ses antécédents et ses explications; étude historique (Thouars (Deux-Sèvres), France, 1936), 103–11.

This is the hypothesis advanced in Middleton W. E. Knowles , The history of the barometer (Baltimore, 1964), 30–32.

See the entirety of François du Verdus to Marin Mersenne, end of July 1644, CM, xiii, no. 1286, 178–81.

In a letter from Michelangelo Ricci to Evangelista Torricelli, there is a discussion about Mersenne not being able to afford high quality glasses for void experiments in Italy because of travel costs. See Ricci Michelangelo to Torricelli Evangelista , 5 March 1645, CM, xiii, no. 1353, 390.

As early as November 1645, Mersenne seriously began inquiring into reconstructing the Torricellian experiment. See Deschamps Théodore to Mersenne Marin , 1 November 1645, CM, xiii, no. 1397, 506–7. Some time after this, probably in the following year, Mersenne again tried to replicate the experiment with Pierre Chanut, the French ambassador to Sweden. See Petit Pierre to Chanut Pierre , 19–26 November 1646, CM, xiv, no. 1563, 645.

See the entirety of Petit Pierre to Chanut Pierre , 19–26 November 1646, CM, xiv, no. 1563, 645–54. An excellent synthesis on bringing the vacuum from Italy to France that expands upon this issue is Jones Matthew L. , “Writing and sentiment: Blaise Pascal, the vacuum, and the Pensées“, Studies in history and philosophy of science, xxxii (2001), 2001–81, focus on 141–3.

Descartes Besides , who is discussed in the text, the only consistent objector to the void writing to Mersenne at this time was a fellow Minim, Gabriel Thibaut.

This can be inferred from de Roberval Gilles to Desnoyers Pierre , 20 September 1647, CM, xv, 430, 433.

Baliani Giovanni Battista to Mersenne Marin , 16 July 1647, CM, xv, no. 1642, 308.

Desnoyers Pierre to Mersenne Marin , 24 July 1647, CM, xv, no. 1645, 319.

Mersenne Marin to Hevelius Johannes , 25 October 1647, CM, xv, no. 1693, 507–8.

Mersenne Marin to Rivet André , 4 November 1647, CM, xv, no. 1696, 518.

Baliani apparently awaited Pascal's treatise. See Baliani Giovanni Battista to Mersenne Marin , 4 January 1648, CM, xvi, no. 1726, 5–6. On the receipt of both books, see Baliani Giovanni Battista to Mersenne Marin , 8 January 1648, CM, xvi, no. 1730, 21.

Pascal Blaise to Périer Florin , 15 November 1647, CM, xv, no. 1702, 544.

See, for example, Descartes René to Mersenne Marin , 5 December 1638, CM, viii, no. 710, 230–31; Descartes René to Mersenne Marin , 16 October 1639, CM, viii, no. 772, 540; Descartes René to Mersenne Marin , 11 June 1640, CM, ix, no. 878, 395; René Descartes to Marin Mersenne, 30 July 1640, CM, ix, no. 899, 525.

Descartes René to Mersenne Marin , 13 December 1647, CM, xv, no. 1713, 571–2: “Ie m'estonne de ce que vous auez gardé quatre ans cette experience, ainsi que le dit M. Pascal, sans que vous m'en ayez iamais rien mandé, ny que vous ayez commencé a la faire auant cet esté”.

Descartes René to Mersenne Marin , 4 April 1648, CM, xvi, no. 1775, 206–7.

Mersenne Marin to Hevelius Johannes , 20 January 1648, CM, xvi, no. 1738, 72.

le Tenneur Jacques to Mersenne Marin , 9 July 1647, CM, xv, no. 1639, 296; Baliani Giovanni Battista to Mersenne Marin , 31 October 1647, CM, xv, no. 1694, 511–12.

Mersenne Marin to Huygens Constantijn , 17 April 1648, CM, xvi, no. 1781, 230; Huygens Christiaan to Mersenne Marin , 20 April 1648, CM, xvi, no. 1784, 241; Baliani Giovanni Battista to Mersenne Marin , 21 April 1648, CM, xvi, no. 1785, 242; Mersenne Marin to Huygens Christiaan , 2 May 1648, CM, xvi, no. 1793, 291; Huygens Constantijn to Mersenne Marin , 3 May 1648, CM, xvi, no. 1795, 296; Baliani Giovanni Battista to Mersenne Marin , 11 May 1648, CM, xvi, no. 1799, 309; Desnoyers Pierre to Mersenne Marin , 21 May 1648, CM, xvi, no. 1802, 318; Mersenne Marin to Hevelius Johannes , 1 June 1648, CM, xvi, no. 1806, 337.

Mersenne Marin to Huygens Constantijn , 4 January 1648, CM, xvi, no. 1727, 11.

Hobbes Thomas to Mersenne Marin , 17 February 1648, CM, xvi, no. 1748, 109–10; Hobbes Thomas to Mersenne Marin , 25 May 1648, CM, xvi, no. 1805, 334.

Mersenne Marin to Louis Henri de Montmor Habert , 23 April 1648, CM, xvi, no. 1787, 256–7.

Mersenne Marin to Rivet André , 9 May 1648, CM, xvi, no. 1798, 306–7: “Je ne sache icy rien de nouueau sinon le bruit que fait le vuide pretendu dans des tuyaux de verre par le moyen du , dont vous auez assez ouy parler et qui commence de produire quantité de liures pour et contre, car pour Naple rapatriée à son Roy et la prise de M. de Guyse a Gayeste, ie ne doute pas qu'il n'y ayt longtemps que vous le sachiez ou l'auez preiugé.” Italics my emphasis.

Mersenne Marin to Hevelius Johannes , 1 March 1648, CM, xvi, no. 1755, 140.

Huygens Constantijn to Mersenne Marin , 12 September 1646, CM, xiv, no. 1508, 451. For more on communication tactics and self promotion of Christiaan Huygens and his father, see Stoffele Bram , “Christiaan Huygens — A family affair: Fashioning a family in early modern court culture” (Master's thesis, Utrecht University, 2006), 66–73. The idea of showcasing child prodigies was not unique in the Huygens family. For another example, see Mazzotti Massimo , “Maria Gaetana Agnesi: Mathematics and the making of the Catholic Enlightenment”, Isis, xcii (2001), 657–83.

See the entirety of Christiaan Huygens to Constantijn Huygens, brother, 3 September 1646, CM, xiv, no. 1505, 434–6. A copy of this letter was sent to Mersenne; this was the copied letter discussed in the preceding footnote.

Mersenne Marin to Huygens Christiaan , 8 January 1647, CM, xv, no. 1583, 32.

Mersenne Marin to Descartes René , 25 December 1639, CM, viii, no. 797, 697; Mersenne Marin to Pell John , 7 March 1640, CM, ix, no. 835, 184.

Huygens Constantijn to Descartes René , 8 March 1640, CM, ix, no. 836, 186. Descartes received the work a few weeks later. See Descartes René to Mersenne Marin , 1 April 1640, CM, ix, no. 849, 263.

Deschamps Théodore to Mersenne Marin , August or September 1643, CM, xii, no. 1213, 311.

Shapin Steven , The scientific life: A moral history of a late modern vocation (Chicago, 2008), 209–304; Rabinow Paul , Making PCR: A story of biotechnology (Chicago, 1997).

Benkler Yochai , The wealth of networks: How social production transforms markets and freedom (New Haven, CT and London, 2006), especially 35–90.

See Sassen Saskia , Territory, authority, rights: From medieval to global assemblages, updated edn (Princeton, NJ and Oxford, 2006), 328–77.

Theoretical implications abound. Most explicit is Alain Viala's work on a public emerging in the mid-seventeenth century around specific literary genres. Viala, however, does not speak to the class of scientific literature in his work. Though they did not refer to themselves as a mathematical public, the term “public” appears in Mersenne's correspondence. See Viala Alain , Naissance de l'écrivain (Paris, 1985), 123–51. A science-oriented paradigm highlighting struggles for legitimacy in a field of research is Bourdieu Pierre , “The specificity of the scientific field and the social conditions of the progress of reason”, trans. by Nice Richard , in Biagioli Mario (ed.), The science studies reader (New York and London, 1999), 31–50. Additionally, the sociologist Gary Alan Fine recently has urged scholars to look at webs of local interactions as a medium through which larger swaths of society and its institutions function. See Fine Gary Alan , “The sociology of the local: Action and its publics”, Sociological theory, xxviii (2010), 2010–76. Broader theoretical influences are Jürgen Habermas and Benedict Andersen. Habermas sees the rise of news and intelligencing in the seventeenth century preceding the emergence of a public sphere in the century after, though my notion differs from Habermas's in that the community I am discussing is one that is generally restricted to mathematics rather than an entire social class. Additionally, unlike the rational-critical debates challenging state authority that are central to Habermas's public sphere, Mersenne's community was in part subjected to government regulations. See Habermas Jürgen , The structural transformation of the public sphere: An inquiry into a category of bourgeois society, trans. by Burger Thomas (Cambridge, MA, 1991), especially 14–26. Similar notions between seventeenth-century vernacular print and capitalism as a precursor to communities are found in Benedict Andersen's work. See Andersen Benedict , Imagined communities: Reflections on the origin and spread of nationalism, rev. edn (London, 2006), 37–46. Andersen, however, emphasizes the emergence of large, national communities in the nineteenth century rather than specialized early modern intellectual communities.

Literature on seventeenth-century Jesuit science is vast. For the most focused cultural studies, see Heilbron John L. , Elements of early modern physics (Berkeley, 1982); Dear, Discipline and experience.