Many times mathematicians draw proofs about the impossibility of something. As an example, take the Abel–Ruffini theorem, which states no generic formula exists for quintic equations (I know the proof is more contrived that this).
Some "proofs" might be wrong though: maybe a formalism was overlooked... maybe there was a failed axiom. What I want to know is examples of once claimed proofs on the "impossibility" of something, but which later were revealed wrong?