Agnes Scott College

F. N. David, D.Sc.

Games, Gods and Gambling: The origins and history of probability and statistical ideas from the earliest times to the Newtonian era
Charles Griffin Co. Ltd., London, 1962
(Reprinted Dover Publications, 1998)

Cover Page


Todhunter on the "History of Probability" has been and always will be the major work of reference in this subject. He is rarely wrong, always explicit, and has obviously read widely through all available literature. That he stops early in time (with Laplace) and thus does not treat the interesting developments of the nineteenth century is hardly his fault, since he wrote his book in 1864-65 and would have been collecting his material for some years before this. From the point of view of the development of ideas he does not start soon enough. He notes the mathematical arguments fairly and with precision, but this is like embarking on a river when it has become of respectable size, and paying no attention to the multitude of small streams and tributaries of which it is the united outcome.

The idea that one might speculate about the development of the random element through references in literature of all kinds—classical, archaeological, biographical, poetical and fictional—is one which came to me as a student some thirty years ago. since then, as friends and colleagues learnt of my interest, the number of references to which my attention has been drawn has increased rapidly, each year filling many notebooks. It is too much to hope that this list of references can ever be completed, but it is, I think, fair to say that many of the most significant have been made known to me. And from these references I have tried to supplement Todhunter on the early development of ideas about chance and to fill in a certain amount of the background of ideas and controversies which attended the creation of the mathematical theory of probability.

Writers on the history of science, and in particular on the history of a branch of mathematics, tend to fall into one of two categories: they either write severely on the subject-material and leave the men who created it as wooden puppets, or they tell us interesting (and often apocryphal) stories about personalities, with no real attempt to place their achievements. Thus Todhunter will rarely be read for pleasure, although always for profit, by anyone interested in probability theory, while the potted biographies, always read for pleasure, convey little to us which profits our understanding of theory. I have tried, probably without success, to steer a middle way between the Scylla of Todhunter and the Charybdis of the story-teller. The man creates the mathematical theorem, but the events of a man's life create the man, and the three are indissoluble. Thus I would hold, for example, that it is not enough to remark on and wonder at de Moivre's analytic genius, but that one should also realise that poverty was his spur, that much of his work might not have been achieved had he been sure of a post which would have brought him some leisure and about which he wrote so longingly to John Bernoulli.

Wherever possible I have gone back to the original documents to check mathematical developments; in the same way, I have tried to check the stories told about great men. The similarity between so many of these latter induces a profound scepticism about all of them, even when told autobiographically, and I have tried to indicate this scepticism in the text. I have tried, not invariably with success, never to express an opinion without at least adequate information of the relative facts. The documentation of one's opinions naturally grows easier as the millennium advances, although the upheaval of the French Revolution led to much of value being mislaid. The lack of information about de Moivre can only be described as startling.

Table of Contents

  1. The development of the random event
  2. Divination
  3. The probable
  4. Early beginnings
  5. Tartaglia and Cardano
  6. Cardano and Liber de Ludo Aleae
  7. Galileo
  8. Fermat and Pascal
  9. The arithmetic triangle and correspondence between Fermat and Pascal
  10. Bills of Mortality
  11. Christianus Huygens
  12. Wallis, Newton and Pepys
  13. James Bernoulli and Ars Conjectandi
  14. Pierre-Rémond de Montmort and The Essai d'Analyse
  15. Abraham de Moivre and The Doctrine of Chances
  1. Buckley's Memorable Arithmetic, Translated by Jean Edmiston
  2. Galileo's Sopra le Scoperte dei Dadi, Translated by E. H. Thorne
  3. Brother Hilarion de Coste's Life of Father Marin Mersenne, Translated by Maxine Merrington
  4. Letters between Fermat and Pascal and Carcavi, Translated from Oeuvres de Fermat by Maxine Merrington
  5. From The Doctrine of Chances by A. de Moivre