519: The Unfinished Game by Keith Devlin

by Gerard

519.2: Devlin, Keith. The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter that Made the World Modern. New York: Basic Books, 2008. 181 pp. ISBN 978-0-465-00910-7.

Before you can understand science, you have to have a basic working relationship with mathematics, so books on mathematics are placed at the beginning of the 500s (in the 510s to be exact). Since new and exciting mathematical breakthroughs are made every day, this division keeps getting more and more packed with interesting subsections, but section 519 is reserved for probability and applied mathematics.

In 1654, Blaise Pascal, the precocious son of a French tax collector, sent famous mathematician Pierre de Fermat a letter with a proposed solution to an old but still lingering problem. The problem goes thusly:

Suppose two people are playing consecutive rounds of a game of chance. There is an agreed upon number of rounds a player has to win in order to take the pot. For each round, they each pay into the pot equally. At some point in the game, they are interrupted and the pot has to be divided. Without knowing the current “score”, how do you divide the pot fairly?

This was known as “the problem of the points” in Pascal’s day. The exchange of letters between Pascal and Fermat started the development of mathematics into the realm of probabilities and applied statistics.

Keith Devlin’s Unfinished Game uses these letters as a springboard to showcase the history of applied statistics. From John Graunt to the Bernoulli family to Gauss and Bayes, he explores the implications of the letters’ solutions. Interestingly enough, no one had thought to use mathematics to make prediction about human population or games of chance before.

The book is succinctly written, and can easily be knocked out in an afternoon. There’s a bit of jumping around in history, and Devlin tries competently to weave together the threads of discovery. There are some digressions, however, that he gets carried away with (most notably, the bit about DNA and prosecutorial fallacies), but overall, the book does a decent job of explaining statistical history. It’s hard to fathom that a single set of letters marked the starting point of both the modern insurance racket and mathematical epidemiology.