Mathematics, Continuity, Discreteness, and Artificial Intelligence: Logical Differences, Advantages, and Weaknesses

This paper examines the logical differences between continuous and discrete mathematical reasoning and their implications for physics and artificial intelligence. It argues that the historical dominance of continuous models reflects human cognitive and sensory constraints rather than necessities of nature. By contrasting constructive and non-constructive reasoning—particularly proof by contradiction—the paper analyzes why discrete, finite logic aligns naturally with artificial intelligence while continuous mathematics introduces idealized structures that exceed finite execution. Young’s double-slit experiment is reinterpreted as a consequence of continuity assumptions rather than evidence of intrinsic wave behavior. Two appendices further explore the role of human sensory bias in the development of electromagnetic theory and the limitations of contradiction-based reasoning in open domains such as law. The work positions artificial intelligence as a tool for exposing hidden assumptions and restoring constructive clarity in foundational reasoning.