"I remember reading of a competition for a paper on resolution of singularities of surface; Castelnuovo and Enriques were in the committee. Beppo Levi presented his famous paper on the resolution of singularities for surfaces.

Enriques asked him for a couple of examples and was convinced; Castelnuovo was not. The discussion got heated. Enriques exclaimed 'I am ready to cut off my head if this does not work', and Castelnuovo replied 'I don't think that would prove it either.'"

-- Angelo Vistoli, mathoverflow