Continuum Hypothesis is Independent of ZFC/Historical Note

Historical Note on Continuum Hypothesis is Independent of ZFC
Between $1938$ and $1940$ (accounts differ), showed that the Continuum Hypothesis (CH) is formally consistent with the axioms of Zermelo-Fraenkel set theory (ZF) with or without the Axiom of Choice (ZFC).

Between $1963$ and $1966$, showed that the negation of both the Continuum Hypothesis and the Generalized Continuum Hypothesis are also consistent with the axioms of ZF and ZFC.

Thus, neither ZF and ZFC are strong enough to settle the question of the Continuum Hypothesis either way.