Cantor’s Continuum Hypothesis (CH) is famous for its independence from standard set-theoretic axioms. On its face, mathematics appears exact, yet CH raises questions about absolute undecidability and the possibility of persistent disagreement even in mathematics. We survey historical perspectives, Gödel’s incompleteness results, and modern developments, focusing on whether expanding our base of axioms can or should settle CH definitively. Recent theorems—some joint with Hugh Woodin—recast CH as self-referential within this debate, essentially inviting us to let a thousand flowers bloom.