Abraham de Moivre: Setting the stage for classical probability and its applications by David R Bellhouse

Abraham de Moivre: Setting the stage for classical probability and its applications by David R Bellhouse

This erudite book is an interesting biography of Abraham De Moivre (1667-1754), the London mathematician who wrote extensively on probability and life annuities, and made some important discoveries. It gives details of his contacts with other mathematicians, especially Newton, Halley, Montmort and members of the Bernoulli family, showing how each of them tried to claim priority in discovering the solution of various probability questions, including problems relating to the division of the stakes in games that were discontinued prematurely, based on the players' chances of ultimate success at that time.

One of the book's strong points is the author's considerable research into the details of De Moivre's life and connections, viewed against a contemporary background. Many sources have been used, some of them previously untapped.

One of the sections that held particular appeal to me was a

detailed explanation of an allegorical engraving that appeared in Montmort's book of 1708, depicting Montmort superseding the god Mercury in the outcomes of dice games. Not to be outdone, de Moivre included a different allegorical engraving in his Doctrine of Chances, 1718, showing his own mathematical results dominating fickle fortune or fate.

The book discusses the impact of De Moivre's Annuities upon Lives, the first edition of which appeared in 1725, and produces evidence suggesting that it probably generated work for him as an annuity consultant, including the valuation of reversions and leases on lives.

The book also explains the various probability questions that the mathematicians tackled, and outlines the approaches that were adopted to find solutions. Much of this ground has been covered previously by Isaac Todhunter, but Bellhouse adds his own comments, including a suggestion that Todhunter's criticism of a paper published by Francis Robartes [or Roberts] in 1693 was unfair.

This book is a 'must read' for anyone who is interested in the emergence of probability theory in the first half of the 18th century.

Reviewed by Chris Lewin