Chaos theory explores how small changes in initial conditions can lead to vastly different outcomes, exemplified by weather forecasting. It focuses on deterministic systems rather than random effects, characterized by a positive Lyapunov exponent indicating exponential divergence. This theory is significant both mathematically and philosophically, as it illustrates how complex phenomena can arise from simple rules. The discussion highlights that chaos theory has become mainstream, with recommendations for accessible literature, such as Gleick's book, to better understand its concepts. Overall, chaos theory provides valuable insights into the unpredictability of certain systems.