Ariadne's Thread: The Role of Mathematics in Physics

Reading Eugene Wigner's essay¹ on the role of mathematics in science, the physics teacher is struck by the sentence: “(Newton's law of planetary motion,) particularly since a second derivative appears in it, is simple only to the mathematician, not to common sense or to non-mathematically-minded freshmen.” The statement is undoubtedly true, but why? Why do freshmen seem to have a harder time with physics than with French, with political science, or, for that matter, with mathematics? What is so difficult about physics? Thinking about this question leads to three observations that bear on the more general problem set forth by Wigner…