What can mathematical fools tell us?

In a fascinating American Scientist piece, Foolproof, author Brian Hayes says "in recent years [mathematical] proof has become a surprisingly contentious topic." Placing himself somewhere in the middle of the mathematics is/is not in a crises, he is nonetheless right - and offers the evidence - when he suggests that "proof is a tool that can also prove you a fool."

Perhaps when it comes to some mathematical proofs, apophasis would make more sense.