Madness is perseverance misapplied. Necessary to discover logical insights, perseverance—when applied to emotions and not moderated by reason—magnifies the emotions into madness. Madness is also in holding the outside world to the standards of certitude satisfied only by the world of one's imagination (e.g., mathematics, literature, music). Madness is the inability to accept ambiguity. The fear of madness is the fear of getting discouraged by the chasm between the desired and the attainable.
Knowledge progresses in two directions. Logic derives new implications of existing axioms. Logic also deduces the existing axioms from more elementary ones---or challenges their appeal. In social matters, axioms are tastes, selected by assessing the appeal of their implications, by introspection, and by analysing the lives of others.
Education consists in alerting individuals to axioms' malleability, in teaching to derive inferences from axioms, and in showing the limit of these inferences by pointing out that even a well-defined language can generate truths unprovable in that language. The existence of unprovable truths invites one to live, not just derive, one's life. If even mathematics must be an experimental science (i.e., computer science), so must be every intellectual pursuit.