In these lectures, we explore how mathematics evolved from describing a predictable mechanical universe to understanding adaptive, self-organising, and interconnected systems. Beginning with mechanical philosophy and Newtonian determinism, the lecture traces the emergence of cybernetics, information theory, and complexity science through ideas of feedback, entropy, and emergence. Drawing on diverse examples ranging from autonomous machines to hyperuniform structures and generative AI, the lecture reflects on evolving mathematical worldviews for understanding complex organisation across natural, technological, and social systems.