This question already has an answer here:
- Can you prove anything in philosophy? 12 answers
A proof is some explanation to convincing others that a statement is true (or false in case of a counterexample). As Yuri Manin once wrote: "A proof becomes a proof only after the social act of accepting it as a proof".
Since Mathematics is not comprehensively 'connected' to the nature, I am trying to compare it with another situation: there were many beliefs in history that every body was convinced their truth, it could even be as far as a superstition. But as time passed their validity changed.
My question is: Do we need other type(s) of intelligent creation (like intelligent aliens) for final check whether our proofs are true or not? Or, human mind is enough for checking their truth?
Note - My question is especially focus on non-empirical Mathematics.
EDIT - Also, there have been many mathematical proofs that had very subtle inconsistency detected by smart people; checking Fermat Last Theorem's proof by a colleague of Wiles came up with a subtle mistake is an example; Is it possible that a 'proof' has that type of mistake but not easy enough to 'see' even by nowadays' people for a long long time? any historical story?
PS - migrated from math.SE