The area of probability and stochastic processes is the study of randomness. This study is both a fundamental way of viewing the world and increasingly a core branch of mathematics. Probability was central in a number of recent Fields Medal awards.
Probability is a theoretical and abstract subject in mathematics which is also highly applied. Stochastic processes add dynamics to random changes to study evolutions of random systems in time and/or space. Since a great number of phenomena can be best modeled or understood by probabilistic means, probability and stochastic processes provide indispensable tools for applied modeling in a number of fields such as statistical physics, financial mathematics, mathematical biology, data science, machine learning, computational methods, Bayesian statistics, graph theory, and dynamical systems.