Gödel's Theorem

Gödel's Incompleteness Theorem states that in any sufficiently complex formal system—like mathematics—there are true statements that cannot be proven within that system. Essentially, no matter how you structure your set of rules and axioms, some truths will always lie beyond formal proof, highlighting inherent limitations in the pursuit of complete mathematical certainty. This reveals that mathematical systems are fundamentally incomplete: they cannot verify all truths purely through their own rules.