Thomas Bayes, a Presbyterian minister, expressed a method of inductive inference in a precise and quantitative form, which lead to the development of Bayesian statistics, or Bayesian inference. His stature as a mathematician is based on only two short mathematical papers, both of which were published posthumously by the Royal Society of London. The first paper demonstrates what may be the first recognition of asymptotic behavior by series expansions. The second and far more important paper addresses a problem with continuing application in most areas of human endeavor. In this paper, Bayes discusses the estimation of future occurrences of an event, given knowledge of the history of the event--that it has occurred a number of times and failed a number of times. This work continues to spawn mathematical research, and provides the foundations for Bayesian statistical estimation, used today on such diverse problems as electoral polling or estimating...