Proofs and Applications

This is a quote that lives rent-free in my head, and comes up a lot in discussions I participate in.

From Stein/Barcellos, Calculus and Analytic Geometry, 5E, "To the Instructor", p. xxii (1992):

At the Tulane conference on "Lean and Lively Calculus" in 1986 we heard the engineers say, "Teach the concepts. We'll take care of the applications." Steve Whitaker, in the engineering department at Davis, advised us, "Emphasize proofs, because the ideas that go into the proofs are often the ideas that go into the applications." Oddly, mathematicians suggest that we emphasize applications, and the applied people suggest that we emphasize concepts. We have tried to strike a reasonable balance that gives the instructor flexibility to move in either direction.