Gödel's Continuum Hypothesis

Gödel's work relates to the Continuum Hypothesis, which addresses the size of infinite sets, specifically the set of real numbers. It asks whether there's a size of infinity between the countable infinity of natural numbers and the uncountable infinity of real numbers. Gödel showed that this hypothesis cannot be disproven using standard set theory (assuming it is consistent). Later, mathematician Paul Cohen proved the opposite—that the hypothesis cannot be proven either. Thus, the Continuum Hypothesis remains independent of common mathematical axioms, meaning its truth or falsehood cannot be determined within the usual framework of mathematics.