Kurt Godel rather famously claimed to have spotted logical contradictions in the US constitution, which of course is not too controversial on its own (and was probably right given who he is), but presenting this argument in response to questions about the constitution that were given as part of his citizenship test was an insane thing to try no matter how good his logic.

Amazingly he still passed.

Einstein talked him out of presenting it. Recent HN conversation on it: https://news.ycombinator.com/item?id=44812159