Chaos Theory: Mathematics, Philosophy, and the Limits of Predictability

This article provides a comprehensive introduction to chaos theory, examining its mathematical foundations and philosophical implications. Beginning with Edward Lorenz's historical discovery of sensitivity to initial conditions, the text guides the reader through key concepts such as the butterfly effect, strange attractors, and fractals. The authors explain how nonlinear dynamical systems challenge traditional determinism, setting impassable limits to predictability in complex systems. Beyond theory, the publication points to practical applications in meteorology, cardiology, and economics, where bifurcation cascades and numerical modeling allow for a better understanding of the reality around us. This is a profound reflection on the order hidden within chaos and the limits of human cognition in the face of adaptive systems.