The rise of stochasticity in physics

In the last 175 years, the physical understanding of nature has seen a revolutionary change. Until about 1850, Newton's theory and the mechanical world view derived from it provided the dominant view of the physical world, later supplemented by Maxwell's theory of the electromagnetic field. That approach was entirely deterministic and free of probabilistic concepts. In contrast to that conceptual edifice, today many fields of physics are governed by probabilistic concepts. Statistical mechanics in its classical or quantum version and random-matrix theory are obvious examples. Quantum mechanics is an intrinsically statistical theory. Classical chaos and its quantum manifestations also require a stochastic approach. The paper describes how a combination of discoveries and conceptual problems undermined the mechanical world view, led to novel concepts, and shaped the modern understanding of physics.