👉 Self-math, or self-referential mathematics, is a branch that explores mathematical concepts and structures through their own language and axioms, often leading to intriguing and counterintuitive results. It involves defining mathematical objects and operations within a system that mirrors the system it studies, creating a loop where statements about the system itself can be made. For example, Gödel's incompleteness theorems are a classic self-math result, demonstrating that any sufficiently powerful mathematical system cannot be both complete and consistent. This means there will always be true statements within the system that cannot be proven from its own axioms. Self-math also includes self-referential paradoxes, like the Liar Paradox ("This statement is false"), which challenge our understanding of truth and logic. These explorations not only deepen our comprehension of mathematics but also have profound implications for philosophy and computer science.
