Gödel

Kurt Gödel was a brilliant logician who proved that in any sufficiently powerful system of mathematics, there are true statements that cannot be proven within that system. This means that no matter how advanced our mathematical rules are, some truths are fundamentally unprovable inside the system, revealing inherent limitations in formal mathematical structures. His results, known as Gödel's incompleteness theorems, showed that mathematics is inherently incomplete—there will always be true facts that we cannot prove, emphasizing the limits of formal systems and impacting logic, philosophy, and computer science.