TITLE: Is It True that We Can Never Be Sure of Validity of a Mathematical Proof?
QUESTION [8 upvotes]: The reason I ask this is because difficult mathematical proofs are just not plain self-evident. You would need a few years of intensive study before you can get to the point of understanding the topics and the proofs. The problem is that for a difficult math theorem, maybe only a handful of mathematicians have studied and agreed on the validity of the proof. There is a chance, given that the topic is highly esoteric, that there are bugs in the proof that render it invalid. We just don't know. 
This would give us a conundrum; we thought that mathematics is the most secure branch of knowledge, but it isn't; because a lot of the proofs are convoluted and esoteric to the point that only a handful a people who can understand them. So we can never be 100% sure that a proof is always valid.
Am I right?

REPLY [4 votes]: If I understand you correctly, you aren't bringing up the issues raised by Gödel. You are raising the point that since it's always possible a mistake has been made, we can't be sure of the validity of a mathematical proof. There is always the possibility that even our computational examination of a proof is forgetting some facet that renders it untrue. 
One must understand, however, that this is not a flaw in mathematics but an inherent element of reality. Maths does remain the most secure branch of knowledge, except that the way we practically do math may not be as secure as previously imagined. A fair point.