In 1940 Gödel proved the consistency of the [continuum hypothesis](https://en.wikipedia.org/wiki/Continuum_hypothesis) with the [Zermelo-Fraenkel axioms of set theory](https://en.wikipedia.org/wiki/ZFC), by introducing the [constructible universe](https://en.wikipedia.org/wiki/Constructible_universe) $L$ and subsequently founding the subfield of set theory now known as [inner model theory](https://en.wikipedia.org/wiki/Inner_model_theory). In 1963, Paul Cohen introduced the method of forcing, which he used to show the continuum hypothesis is independent from the Zermelo-Fraenkel axioms, resolving Hilbert's first problem. However, forcing can also be used to give an alternative proof of the consistency of the continuum hypothesis, giving two proofs.