Originally Posted by

**anticorncob28**
I've recently heard that Kurt Gödel and another guy proved that the continuum hypothesis can neither be proven nor disprove under the axioms of set theory, with or without the axiom of choice. Does this mean that the situation is completely hopeless? Is it possible that we can prove/disprove it with new axioms, or a completely different approach altogether? I'm starting to get worried. Perhaps a lot of the unsolved problems in mathematics cannot be solved under assuming whatever is self-evident? I understand that a lot of things are true but unprovable (Gödel's first incompleteness theorem), but most of these statements are self-evident and can be immediately accepted by nearly anybody without proof.