This talk explores a mathematical approach to understanding intelligence by focusing on adaptive cycles and nonlocal interactions, particularly in systems affected by damage. We begin with an introduction to nonlocal analysis—mathematics that considers influences beyond immediate neighbors—and how this approach provides insights into damage in materials, such as the propagation of corrosion. We will explore how to extend this idea to intelligent systems—both natural and artificial. Continuing our discussion on intelligence, we will consider a Koopman Operator approach to identifying adaptive cycles, aiming to capture the homeostasis seen in ecological and biological systems. Through frequency analysis and Koopman operators, we’ll explore how systems can learn and adapt to changing conditions by capturing natural rhythms and cycles. This presentation is designed to be accessible to undergraduate audiences, inviting an interdisciplinary discussion on applications spanning neuroscience and mathematical biology.