Neuromorphic computing seeks to replicate the remarkable efficiency, flexibility, and adaptability of the human brain in artificial systems. Unlike conventional digital approaches, which suffer from the Von Neumann bottleneck and depend on massive computational and energy resources, neuromorphic systems exploit brain-inspired principles of computation to achieve orders of magnitude greater energy efficiency. By drawing on insights from a wide range of disciplines -- including artificial intelligence, physics, chemistry, biology, neuroscience, cognitive science and materials science -- neuromorphic computing promises to deliver intelligent systems that are sustainable, transparent, and widely accessible. A central challenge, however, is to identify a unifying theoretical framework capable of bridging these diverse disciplines. We argue that dynamical systems theory provides such a foundation. Rooted in differential calculus, it offers a principled language for modeling inference, learning, and control in both natural and artificial substrates. Within this framework, noise can be harnessed as a resource for learning, while differential genetic programming enables the discovery of dynamical systems that implement adaptive behaviors. Embracing this perspective paves the way toward emergent neuromorphic intelligence, where intelligent behavior arises from the dynamics of physical substrates, advancing both the science and sustainability of AI.