In 1654, Antoine Gombaud, Chevalier de Méré, approached Blaise Pascal with a question about the throw of dice and drew his attention to the problem of points, which had been around for 250 years or more in the Italian “abbaco” literature. A correspondence ensued between Pascal and Pierre de Fermat which is widely regarded as marking the birth of probability calculus. While historians of probability have rightfully focused on Pascal and Fermat, they have generally ignored Gombaud’s part, portraying him only as a gambler, sometimes an avid one. Through a careful examination of Gombaud’s life and philosophy, it is argued here that his role was more important than has usually been attributed to him. In addition, a review of the historical background to the problem of points shows that gambling was not as central to the early development of probability theory as has often been assumed.
References
Bellhouse, D. R. and Fillion, N. (2015). Le Her and other problems in probability discussed by Bernoulli, Montmort and Waldegrave. Statist. Sci. 30 26–39. MR3317752 10.1214/14-STS469Bellhouse, D. R. and Fillion, N. (2015). Le Her and other problems in probability discussed by Bernoulli, Montmort and Waldegrave. Statist. Sci. 30 26–39. MR3317752 10.1214/14-STS469
Bernoulli, J. (1690). Quæstiones nonnullæ de usuris, cum solutione problematis de sorte alearum, propositi in Ephem. Gall. A. 1685, Art. 25. Acta Erud. 9 219–223.Bernoulli, J. (1690). Quæstiones nonnullæ de usuris, cum solutione problematis de sorte alearum, propositi in Ephem. Gall. A. 1685, Art. 25. Acta Erud. 9 219–223.
Bernoulli, J. (2006). The Art of Conjecturing: Together with “Letter to a Friend on Sets in Court Tennis.” Johns Hopkins Univ. Press, Baltimore, MD. Translated from the Latin and with an introduction and notes by Edith Dudley Sylla. MR2195221Bernoulli, J. (2006). The Art of Conjecturing: Together with “Letter to a Friend on Sets in Court Tennis.” Johns Hopkins Univ. Press, Baltimore, MD. Translated from the Latin and with an introduction and notes by Edith Dudley Sylla. MR2195221
Boyer, A. (1702). Dictionnaire royal, françois et anglois. Le françois tiré des dictionnaires de Richelet, Furetiere, Tachard, de l’Academie françoise, & des remarques de Vaugelas, Menage & Bouhours. Divisé en deux parties. Adrian Moetjens, The Hague, The Netherlands.Boyer, A. (1702). Dictionnaire royal, françois et anglois. Le françois tiré des dictionnaires de Richelet, Furetiere, Tachard, de l’Academie françoise, & des remarques de Vaugelas, Menage & Bouhours. Divisé en deux parties. Adrian Moetjens, The Hague, The Netherlands.
Cardano, G. (1539). Practica arithmetica et mensurandi singularis. Milan. Reprinted 1966 in Hieronymus Cardanus Omnia Opera: Faksimile-Neudruck der Ausgabe Lyon 1663 mit einer Einleitung von August Buck 4. Friedrich Frommann Verlag, Stuttgart-Bad Cannstatt.Cardano, G. (1539). Practica arithmetica et mensurandi singularis. Milan. Reprinted 1966 in Hieronymus Cardanus Omnia Opera: Faksimile-Neudruck der Ausgabe Lyon 1663 mit einer Einleitung von August Buck 4. Friedrich Frommann Verlag, Stuttgart-Bad Cannstatt.
David, F. N. (1962). Gods, Games and Gambling: The Origins and History of Probability and Statistical Ideas from the Earliest Times to the Newtonian Era. Hafner, New York. MR1638639David, F. N. (1962). Gods, Games and Gambling: The Origins and History of Probability and Statistical Ideas from the Earliest Times to the Newtonian Era. Hafner, New York. MR1638639
de Coste, H. (1649). La vie du R. P. Marin Mersenne: Theologien, philosophe et mathematicien de l’Ordre des Peres Minimes. Sebastien & Gabriel Cramoisy, Paris.de Coste, H. (1649). La vie du R. P. Marin Mersenne: Theologien, philosophe et mathematicien de l’Ordre des Peres Minimes. Sebastien & Gabriel Cramoisy, Paris.
Edwards, A. W. F. (1982). Pascal and the problem of points. Int. Stat. Rev. 50 259–266. MR0693220 10.2307/1402496Edwards, A. W. F. (1982). Pascal and the problem of points. Int. Stat. Rev. 50 259–266. MR0693220 10.2307/1402496
Franci, R. (2002). Una soluzione esatta del problema delle parti in un manoscritto della prima metà del Quattrocento. Boll. Stor. Sci. Mat. 22 253–265.Franci, R. (2002). Una soluzione esatta del problema delle parti in un manoscritto della prima metà del Quattrocento. Boll. Stor. Sci. Mat. 22 253–265.
Gassendi, P. (1976). The reality of infinite void according to Aristotle. In The Concepts of Space and Time: Their Structure and Their Development (M. Čapek, ed.). 91–95. Springer, Dordrecht. MR0462420Gassendi, P. (1976). The reality of infinite void according to Aristotle. In The Concepts of Space and Time: Their Structure and Their Development (M. Čapek, ed.). 91–95. Springer, Dordrecht. MR0462420
Gombaud, A. (1930). Œuvres complètes du Chevalier de Méré: Texte établi et présenté par Charles-H. Boudhors. Tomes 1–3 (F. Roches, ed.). Les Belles Lettres, Paris.Gombaud, A. (1930). Œuvres complètes du Chevalier de Méré: Texte établi et présenté par Charles-H. Boudhors. Tomes 1–3 (F. Roches, ed.). Les Belles Lettres, Paris.
Grubbs, H. A. (1932). Damien Mitton (1618–1690): Bourgeois honnête homme. Princeton Univ. Press, Princeton, NJ. Reprinted 1965 by Kraus Reprint Corporation, New York.Grubbs, H. A. (1932). Damien Mitton (1618–1690): Bourgeois honnête homme. Princeton Univ. Press, Princeton, NJ. Reprinted 1965 by Kraus Reprint Corporation, New York.
Hald, A. (1990). A History of Probability and Statistics and Their Applications Before 1750. Wiley, New York. MR1029276 10.1002/0471725161Hald, A. (1990). A History of Probability and Statistics and Their Applications Before 1750. Wiley, New York. MR1029276 10.1002/0471725161
Huygens, C. (1657). De ratiociniis in ludo aleæ. In Exercitationum mathematicarum in libri quinque (F. van Schooten, ed.) 517–534. Elsevier, Leiden, The Netherlands.Huygens, C. (1657). De ratiociniis in ludo aleæ. In Exercitationum mathematicarum in libri quinque (F. van Schooten, ed.) 517–534. Elsevier, Leiden, The Netherlands.
Kendall, M. G. (1956). Studies in the history of probability and statistics. II. The beginnings of a probability calculus. Biometrika 43 1–14 (2 plates). MR0076678 10.2307/2333573Kendall, M. G. (1956). Studies in the history of probability and statistics. II. The beginnings of a probability calculus. Biometrika 43 1–14 (2 plates). MR0076678 10.2307/2333573
Malet, A. (1996). From indivisibles to infinitesimals: Studies on seventeenth century mathematizations of infinitely small quantities. Departament de Filosofia (BeIlaterra), Universitat Autónoma de Barcelona, Barcelona. MR1658963Malet, A. (1996). From indivisibles to infinitesimals: Studies on seventeenth century mathematizations of infinitely small quantities. Departament de Filosofia (BeIlaterra), Universitat Autónoma de Barcelona, Barcelona. MR1658963
Montucla, J.-É. (1960). Histoire des mathématiques. Librairie scientifique et technique Albert Blanchard, Paris. 4 tomes, nouveau tirage augmenté d’un avant-propos par M. Ch. Naux. MR0124168Montucla, J.-É. (1960). Histoire des mathématiques. Librairie scientifique et technique Albert Blanchard, Paris. 4 tomes, nouveau tirage augmenté d’un avant-propos par M. Ch. Naux. MR0124168
Peterson, M. A. (1997). The geometry of Piero della Francesca. Math. Intelligencer 19 33–40. MR1475147 10.1007/BF03025346Peterson, M. A. (1997). The geometry of Piero della Francesca. Math. Intelligencer 19 33–40. MR1475147 10.1007/BF03025346
Peverone, G. F. (1558). Due brevi e facili trattati, il primo d’arithmetica, l’altro di geometria: Ne i quali si contengono alcune cose nuove piaceuoli è utili, si à gentilhuomini come artegiani. Per Gio di Tournes, Lyon.Peverone, G. F. (1558). Due brevi e facili trattati, il primo d’arithmetica, l’altro di geometria: Ne i quali si contengono alcune cose nuove piaceuoli è utili, si à gentilhuomini come artegiani. Per Gio di Tournes, Lyon.
Pisano, L. (2002). Fibonacci’s liber abaci. Sources and Studies in the History of Mathematics and Physical Sciences. Springer, New York. A translation into modern English of Leonardo Pisano’s book of calculation, translated from the Latin and with an introduction, notes and bibliography by L. E. Sigler. MR1923794Pisano, L. (2002). Fibonacci’s liber abaci. Sources and Studies in the History of Mathematics and Physical Sciences. Springer, New York. A translation into modern English of Leonardo Pisano’s book of calculation, translated from the Latin and with an introduction, notes and bibliography by L. E. Sigler. MR1923794
Rigatelli, L. T. (1985). Il problema dell parti in manoscritti del XIV e XV secolo. In Mathemata: Festscrift für Helmuth Gericke (M. Folkerts and U. Lindgren, eds.). Steiner, Wisebaden, Germany. MR0799739Rigatelli, L. T. (1985). Il problema dell parti in manoscritti del XIV e XV secolo. In Mathemata: Festscrift für Helmuth Gericke (M. Folkerts and U. Lindgren, eds.). Steiner, Wisebaden, Germany. MR0799739
Sanchez, C. (2014). Les livres de jeux aux XVIIe et XVIIIe siècles: Une typologie des lecteurs-joueurs. Mémoire de master, Université Lumière Lyon 2, Lyon, France.Sanchez, C. (2014). Les livres de jeux aux XVIIe et XVIIIe siècles: Une typologie des lecteurs-joueurs. Mémoire de master, Université Lumière Lyon 2, Lyon, France.
Schneider, I. (1988). The marketplace and games of chance in the fifteenth and sixteenth centuries. In Mathematics from Manuscript to Print, 1300–1600 (Oxford, 1984) (C. Hay, ed.). Oxford Sci. Publ. 220–235. Oxford Univ. Press, New York. MR0961299Schneider, I. (1988). The marketplace and games of chance in the fifteenth and sixteenth centuries. In Mathematics from Manuscript to Print, 1300–1600 (Oxford, 1984) (C. Hay, ed.). Oxford Sci. Publ. 220–235. Oxford Univ. Press, New York. MR0961299
Smith, D. E. (1970). Rara Arithmetica. A Catalogue of the Arithmetics Written Before the Year MDCI with a Description of Those in the Library of George Arthur Plimpton of New York. Chelsea Publishing Co., New York. Fourth edition, including A. De Morgan’s Arithmetical books. MR0284307Smith, D. E. (1970). Rara Arithmetica. A Catalogue of the Arithmetics Written Before the Year MDCI with a Description of Those in the Library of George Arthur Plimpton of New York. Chelsea Publishing Co., New York. Fourth edition, including A. De Morgan’s Arithmetical books. MR0284307
Steinmetz, A. (1870). The gaming table: Its votaries and victims. In All Times and Countries, Especially in England and in France 1. Tinsley Brothers, London.Steinmetz, A. (1870). The gaming table: Its votaries and victims. In All Times and Countries, Especially in England and in France 1. Tinsley Brothers, London.
Taillé, J.-P. and Foisseau, R. (2012). Le Chevalier de Méré: Un gentilhomme poitevin, cultivé, précieux et parfois arrogant. Mon Petit Éditeur, Paris.Taillé, J.-P. and Foisseau, R. (2012). Le Chevalier de Méré: Un gentilhomme poitevin, cultivé, précieux et parfois arrogant. Mon Petit Éditeur, Paris.
Van Egmond, W. (1981). Practical Mathematics in the Italian Renaissance: A Catalog of Italian Abbacus Manuscripts and Printed Books to 1600. Editrice Giunti Barbèra, Firenze.Van Egmond, W. (1981). Practical Mathematics in the Italian Renaissance: A Catalog of Italian Abbacus Manuscripts and Printed Books to 1600. Editrice Giunti Barbèra, Firenze.
