Michael Faraday, who had little mathematics and no formal schooling beyond the primary grades, is celebrated as an experimenter who discovered the induction of electricity. He was one of the great founders of modern physics. It is generally acknowledged that Faraday's ignorance of mathematics contributed to his inspiration, that it compelled him to develop a simple, nonmathematical concept when he looked for an explanation of his electrical and magnetic phenomena. Faraday had two qualities that more than made up for his lack of education: fantastic intuition and independence and originality of mind.
-- Marshall McLuhan, The Medium is the Massage
I love this paradox: sometimes ignorance can lead to insight, and even brilliance.
And yet it has to be the right kind of ignorance, doesn't it?