Achieving genuine (human-level) artificial general intelligence (AGI) is one of the major goals of computer science, engineering, psychology, and mathematics. In this article, we critically reexamine the relation between natural intelligence and artificial intelligence at a fairly general theoretical level. After identifying four major structural themes in natural intelligence, we move to the issue of AGI implementation through physical computing machines. Motivated by Penrose’s G¨ddelian argument refuting the thesis of AGI realizability via Turing machines, we formulate several theses on the noncomputable essence of AGI systems and suggest that infinitary noncomputability might constitute a viable path toward future AGI implementations, especially if coupled with nonlocality and a non-classical probabilistic structure such as the quantum case. A theoretical mathematical framework for non-Markovian stochastic dynamic systems is then presented and illustrated by describing multiagent AGI assemblages comprised of interconnected dynamic agents. We envision that such networked dynamical assemblages might be powered by noncomputable physics or arranged in an infinitary structure.