Modern Probability as Part of Mathematics
Overview
Probability theory developed into a branch of abstract mathematics during the first 30 years of the twentieth century. Until the late nineteenth century probabilities were treated mostly in context, be it as the probability of testimony or arguments, of survival or death, of making errors in measurement, or in statistical mechanics. This is the era of classical probability. It was rife with paradoxes and had a low mathematical status. In the early twentieth century various efforts weremade to develop a probability theory that was independent of applications and possessed a provably consistent structure. The theory that found near universal acceptance tied probability theory to measure theory. The Russian mathematician Andrei Kolmogorov (1903-1987) gave in 1933 a definitive axiomatic formulation of measure theoretic probability. Probability is now defined as a measure over an algebra of subsets of an abstract space, the space of elementary events.
Background
Probability theory as mathematics goes back to the 1650s when Blaise Pascal (1623-1662) solved a problem about the fair division of an interrupted game of chance. At that time the expression "calculus of chances" was used. Soon afterwards a connection was made with the art of conjecture, an analysis of "probable arguments," in which the conclusion is not conclusively, but only partially, established by the premises.
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