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.
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.