I have to disagree. The lesson I have drawn from studying mathematics is that intuition cannot be trusted and that even obvious things must be proven. Or you mu

I have to disagree. The lesson I have drawn from studying mathematics is that intuition cannot be trusted and that even obvious things must be proven. Or you must admit they cannot and convert those things to axioms. Russell's Paradox [0] is a good example of intuition going wrong in the field of set theory. As I recall Zermelo-Frankel (ZFC) set theory eliminated the known paradoxes of naive set theory but it took decades to complete. There are formally undecidable propositions in ZFC but that's different (to me at least) from incorporating outright contradictions.