Let's just say that if I received $10 every time I read a philosophical misunderstanding of Gödel's theorem, I would be a rich man by now. I've heard many times that it means NO axiomatic system is consistent and complete. Duh. I have also met a philosophy student (who studied mathematical logic as part of the university curriculum) could tell the difference between the Axiom of Choice and the Banach-Tarski Paradox. I've tried for hours to explain a philosophically inclined would-be engineer that 1 is greater or equal to 0. He said it isn't, because it is *greater* than zero, not greater or equal. Duh.
Yet, most of my knowledge that I couldn't have learnt from books came from a maths teacher who is both a serious mathematician and a serious philosopher. Mathematics and philosophy should be inseparable; the fact that they are treated as separate fields shows that we, as a society, understand neither.