This survey article stems from the preparatory lecture on mathematical logic delivered at SETSS 2024 and a series of lectures over recent years on mathematical logic, human-cyber-physical systems, and artificial intelligence to diverse audiences. The thematic points we seek to reiterate include the following: This discussion highlights how fundamental problems in logic, mathematics, and computing emerged, and how the search for solutions has shaped modern computer science and technology. We argue that together with philosophical implications of Gödel incompleteness theorems, the fixed and unchanging languages of formal logical systems, along with the closure of provable theorems under implications relative to axioms, reveal the incompleteness of logical expression and reasoning when compared to human intuition, perception, and consciousness. These may all be fundamental factors distinguishing human intelligence from machine intelligence (i.e., artificial intelligence).