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The Mathematics and the Liberal Arts pages are intended to be a resource for student research projects and for teachers interested in using the history of mathematics in their courses. Many pages focus on ethnomathematics and in the connections between mathematics and other disciplines. The notes in these pages are intended as much to evoke ideas as to indicate what the books and articles are about. They are not intended as reviews. However, some items have been reviewed in Mathematical Reviews, published by The American Mathematical Society. When the mathematical review (MR) number and reviewer are known to the author of these pages, they are given as part of the bibliographic citation. Subscribing institutions can access the more recent MR reviews online through MathSciNet.
Dahlke, Richard; Fakler, Robert A. and Morash, Ronald P. A sketch of the history of probability theory. Math. Ed. 5 (1989), no. 4, 218--232. (Reviewer: William J. Adams.) SC: 01A99 (60-03), MR: 91i:01148.
Focuses on the history of probability theory, but also touches on the development of statistics. Considers one ancient root of probability theory to be the gambling with astrogali. Mentions the related ancient Egyptian game "Hounds and Hackals", of c. 3500 BC. Discusses the table of frequencies of tosses of 3 die in De Vetula, and Cardano's and Galileo's explanations of the probabilities of such events. Galileo's telescope led him to consider some of the theory of errors, and he arrived, in effect, at some of the features of the normal probability distribution. (It is interesting that later on, Gauss refined some of his own work in statistics to rediscover the planetoid Ceres.) Discusses the "division of stakes" problem and its solution by Pascal and Fermat. The first book actually published on games of chance was written by Huygens. In addition, as the author explains, "Huygens was the first to use probability in studying vital statistics of humans. He used John Graunt's (London) now famous book displaying vital statistics to construct a mortality curve and to define the notions of mean and probable duration of life. Shortly thereafter, probability theory was being applied to annuities." The article continues through the beginning of the 1900s. Much of this later material is of course beyond the scope of these pages. Closely related topics: Probability, Statistics, Gambling, De Vetula, Girolamo Cardano, Galileo Galilei, Astronomy, Blaise Pascal, Pierre de Fermat, and Christiaan Huygens.