👉 Mathematical Undecidability (Und) is a concept in mathematical logic that refers to the existence of statements within certain formal systems that cannot be proven true or false using the system's axioms and rules of inference. This means that for some statements, no algorithm can determine their truth value within the system, highlighting fundamental limits in what can be proven or disproven. The most famous example is Gödel's Incompleteness Theorem, which shows that in any consistent formal system capable of expressing basic arithmetic, there are true statements that cannot be proven within the system. This has profound implications for mathematics, philosophy, and computer science, indicating that there are inherent boundaries to formal reasoning and proof.
