Definition
The Pascal-Fermat correspondence refers to a series of letters exchanged in the summer of 1654 between the French mathematicians Blaise Pascal and Pierre de Fermat about gambling problems posed by the Chevalier de Mere. Their key puzzle was the problem of points: how should the pot be divided when a game of chance is interrupted before it is finished?
Their solutions, arriving at the same answer through different methods (Pascal via recursion and his arithmetic triangle, Fermat via enumeration of remaining outcomes), are widely regarded as the founding moment of probability theory.
Why it matters
How it works
In the problem of points, two players agree to play until one wins a fixed number of rounds. If the game is interrupted, how should the pot be split? Pascal and Fermat's insight was that the split should depend not on the rounds already won but on the probability each player would have eventually won had play continued. They computed those probabilities by enumerating remaining outcomes (Fermat) or by recursion on a single round (Pascal), arriving at the same fair division.
From this seed grew the whole of classical probability — Bernoulli, de Moivre, Laplace each extended the framework, until probability matured into the rigorous discipline it is today.