Probability

The mathematical study of chance. Its founding episode is a correspondence in the summer of 1654 between Blaise Pascal and Pierre de Fermat, prompted by gambling questions already partly studied by Cardano, Pacioli and Tartaglia, most famously the problem of points, how to divide the stake of an interrupted game fairly between two players given the score at the point of interruption. Fermat solved it by enumerating every possible way the game could still be played out; Pascal introduced what became the notion of expected value; together they could not extend their solution cleanly to three or more players, but their letters are traditionally credited as laying the foundation of probability theory. The subject waited until 1933 for a fully rigorous axiomatic footing, when Andrey Kolmogorov placed it within measure theory using three axioms comparable, in his own description, to Euclid's treatment of geometry: that a probability is never negative, that the probability of every possible outcome together is one, and that the probabilities of mutually exclusive outcomes add.