The Deepest Uncertainty (2013)

The Continuum Hypothesis states that there is no infinite collection of real numbers larger than the collection of natural numbers, but smaller than the collection of all real numbers. Kurt Gödel described a model that satisfies the axioms of set theory, which does not allow for an infinite set to exist whose size is between the natural numbers and the real numbers. Put another way: for there to be a proof of the Continuum Hypothesis, it would have to be true in all models of set theory, which it isn’t.

Source: nautil.us