Probability is a mathematical theory of random events and random variables. It even extends to random functions of time (stochastic processes). Probability models occur in almost all areas of science: biology (genetics, epidemiology), economics (financial markets), physics (diffusion, theories of molecular matter), and so on, and it is essential for many statistical techniques. Relatively simple probability principles lead to astonishing results. One that has been famous for centuries is the Gaussian or normal curve (the bell-shaped curve). It is an almost universal solution to problems involving independence or weak dependence. Are there similar universal principles for strong dependence? Can these principles be applied to random functions of space? Or even to quantum fields and the structure of elementary particles? Such questions are at the forefront of current research.

Several of the people active in probability are also involved with mathematical biology, mathematical physics, or mathematical economics.