[temujin]

This is oversimplified. In many cases, it is the conjunction of a reasonably strong prior belief and the absence of preexisting "proof" that motivates a scientist (or mathematician) to try to prove something in the first place.

The key is to perform proper Bayesian updates in the face of evidence in either direction; if you do, as long as your prior wasn't totally insane it doesn't really matter where you started.