Picard's Great Theorem would be one of my favorite counterintuitive facts: As a holomorphic function approaches an essential singularity, it takes on every pos

Picard's Great Theorem would be one of my favorite counterintuitive facts: As a holomorphic function approaches an essential singularity, it takes on every possible value (except at most one) infinitely often. An astonishing result. https://en.wikipedia.org/wiki/Picard_theorem https://en.wikipedia.org/wiki/Picard_theorem And the nice thing is you can prove this with fairly elementary techniques (e.g. first year complex analysis is all you need).