**Don't be a puss!** (A rejoinder to Skeptic Cat)

On a personal level:
Hmm, guilty until proven innocent or innocent until proven guilty? Demanding 'proof of innocence' frequently in a relationship is incredibly corrosive, not to mention time-consuming and emotionally draining. In fact, I would argue that without trust there is no real relationship. So, proof of what and by whom? And what constitutes a proof (as Alex notes)--news reports, gossip?

In mathematics:
How often does a mathematician confirm the truth of theorems he uses? Don't most wait for apparent inconsistencies or other inadequacies to appear before closely examining a mathematical edifice skeptically? And even then, don't most mathematicians trust the 'authorities' in the field to resolve the problem? 

In some sense, a belief that a good, pragmatic approximation to 'the truth' will out is implicit in people's approaches to most endeavors. (E.g., see Michael Atiyah's comments on Proof in [Advice to a Young Mathematician][1].) So, in the spirit of Euler, Fourier, Riemann, Heaviside, and Ramanujan (some of the most productive personalities in mathematics), don't be a puss, have the courage to forge ahead (albeit not blindly) until your belief is no longer tenable. 

  [1]: http://www.kyxk.net/att.php?p.29.16927.518.pdf