http://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_t...

I would say this is a good thing, as there are also many cases where a 'proof' is later shown to have holes, areas where everyone made an assumption and didn't realize it.

A good example of this involves limits; for many years mathematicians proved a number of interesting results using infinitesimal limits. It was many decades before a mathematician (Riemann? Maybe?) noted that you can't assume that all the limits in an equation approach their number at the same rate.

This was a super smart thing to notice, and junked a huge number of 'proofs' that had all relied unobtrusively on this idea. All that to say, good theoreticians spend a lot of time wondering if an idea makes sense to them or not.