Abraham De Moivre. Setting the Stage for Classical Probability and its Applications

Author(s): 
David R. Bellhouse
Publisher: 
CRC Press
Year: 
2011
ISBN: 
9781568813493
Short description: 

In the first four chapters, the book deals about the De Moivre’s life in a Huguenot family at France, and then how he got established at London by political or religious concerns (both the same at that time). And the next ten chapters hinges on the three most important books written by De Moivre, which are “De Mensura Sortis”, “Doctrine of Chances” and “Miscellanea Analytica”, all about some probability problems based mainly on currently games of cards and dices. Also his short book “Annuities upon Lives” is extensively commented.

MSC main category: 
01 History and biography
MSC category: 
01A05, 01A45, 01A50
Other MSC categories: 
01A85
Review: 

This kind of books use to treat a twofold item as they tale the mathematician’s life and also the mathematical history through the developments made by the mathematician himself. But I would say this book even serves a fourfold purpose because the author gives a deeper insight into De Moivre’s reasons that inspired him during his life, so becoming an essay upon the history of mathematics, and he also covers some mathematicians' lives akin to De Moivre, showing us the typical environment of what is nowadays known as the “Republic of Letters”.

The book hinges on the three most important books written by De Moivre, which are “De Mensura Sortis”, “Doctrine of Chances” and “Miscellanea Analytica”, all about some probability problems based mainly on currently games of cards and dices. About the way they are explain let me use the author own words on pg. 74: “The details of the mathematics in De Mensura Sortis, some quite intricate, have been described fully elsewhere. [the author cites Schneider I. (1968) Der Mathematiker Abraham de Moivre. Archive for History of Exact Sciences 5: 177-317; and Hald A. (1990) A History of Probability and Statistics and Their Applications before 1750. New York: Wiley] Consequently, the focus of the remainder of this chapter, as well as the rest of the book, is to give the flavour of the mathematics and how it fits with the general message that De Moivre tried to convey”. With this aim, the author turn to analyze the division of stakes problem, the problem of the pool with its many variants, the gambler’s ruin problem, the duration of the play problem, some card games as “Basset”, “Pharaoh”, “Piquet”, etc, and also some dice games.

The author also uses the review of the De Moivre’s book “Annuities upon Lives” to show at least a moderate influence of the mathematician upon the price of life annuities in the marketplace during the first half of the eighteen century, contrary to some historian comments. And so, explains the current types of annuities upon land, the more usual, and upon one, two or up to three lives, all with several cases of payment to the heir.

Ultimately, the reader will discover the strong personality of De Moivre, who quarrelled to anyone who neglects him the merits of his work, as with Cheyne, Montmort, or Simpson among others, but who keeps his friendship tied during his long life, as with Newton, Halley, and others.

Reviewer: 
José L. Guijarro
Affiliation: 
Universidad Complutense Madrid

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