"My education was of the most ordinary description, consisting of little more than the rudiments of reading, writing, and arithmetic at a common day school. My hours out of school were passed at home and in the streets." 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.
Professionalism is environmental. Amateurism is anti-environmental. Professionalism merges the individual into patterns of total environment. Amateurism seeks the development of the total awareness of the individual and the critical awareness of the groundrules of the environment. The groundrules provided by the mass response of his colleagues serve as a pervasive environment of which he is contentedly unaware. The "expert" is the man who stays put.
"There are children playing in the street who could solve some of my top problems in physics, because they have modes of sensory perception that I lost long ago." [Robert Oppenheimer]