Another month, another rationality quotes thread. The rules are:
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"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
Of course, if bad proofs lead to heads being cut off, then there would probably be fewer bad proofs. (I take it the point here is not that Castelnuovo had any doubts about whether Enriques was being honest about believing the result or had come to his belief on flimsy grounds (which is usually not something one can take for granted...), but that he understood this and was interested in finding an explicit formal proof of the result.)