The UMA Monad Theory: A Number-Theoretic Philosophy on Emptiness and Infinity

This thesis aims to redefine the very existence of emptiness and infinity by reimagining the origin of numbers in addition and multiplication—not as static symbols such as "0" or "1," but as a multi-layered cosmic model in which the law of conservation of energy functions dynamically, while also exploring the possibility of defining division by zero. This work serves as a sketch of number-theoretic philosophy, acting as a preliminary stage to rigorous mathematical proof. In this model, following Leibniz, the "Monad" is established as the smallest unit of existence. By reinterpreting "0" not as a mere singularity but as an "exit" for dimensions, this paper discusses the necessity of an absolute zero point---the "Universal Mapping Absolute (UMA) Monad"---which integrates addition and multiplication without contradiction. (This has the potential to provide fundamental meaning to the limits of physics and the origins of noncommutative geometry.)