Classical mathematics, grounded in axiomatic geometry and number theory reaching back to the era of Euclid and Pythagoras, is intellectually and historically intertwined with the worldview of classical physics. A picture of the universe at one instant of time would, in a world governed by classical physics, contain all past and future as consequence. Thus it is no surprise that the laws of classical physics, with its essentially static worldview, can be expressed in the language of classical mathematics. This worldview was replaced in the early 20th century by the far more mysterious picture expressed by quantum physics.
Uncertainty, a notion deeply understood in human culture and but left entirely out of the classical mathematical framework, took center stage in the quantum view of the universe. Even aside from quantum theory, the role of random phenomena became more and more recognized through the development of statistical physics. The ideas and tools of probability theory became central to the description and analysis of a wide variety of phenomena, including those studied in economics, finance, social sciences, biology, medicine, and computational methods. A field where the core ideas for understanding uncertainty were given mathematical form by the Bernoullis, Gauss and others, saw its mathematical foundations built by Kolmogorov and Hausdorff in the 20th century.
Today probability theory is a vast field of diverse activities of many different intellectual flavors, growing both from questions of intrinsic interest and through its essential role in the analysis of real-world phenomena.
Probability @ LSU 