Definition
The history of probability spans four centuries. It begins with the 1654 correspondence between Pascal and Fermat over a gambling puzzle, matures through Jacob Bernoulli's law of large numbers (1713), Bayes' posthumous theorem (1763), and Laplace's monumental treatise (1812), and reaches its modern form in Kolmogorov's 1933 axiomatisation.
The arc is one from puzzle-solving to philosophy to axiomatic mathematics, and finally to a tool that pervades nearly every quantitative discipline of the 21st century.
Why it matters
How it works
The history can be read as alternating waves of expansion and consolidation. Pascal and Fermat formalised gambling games. Bernoulli and de Moivre extended the theory to long-run frequencies. Bayes and Laplace introduced inverse probability — reasoning from data to causes. The 19th century absorbed probability into statistics, error theory, and statistical mechanics. The 20th century, with Kolmogorov, rebuilt the entire edifice on a measure-theoretic foundation, then watched as computing power and the rise of machine learning sent probability flooding into every corner of modern life.