do you ever find yourself disappointed and confused when an interesting result follows from an algebraic identity that seems to have come out of nowhere? do arguments that are "so elegant that they conceal what is really going on" leave you longing for more? what if everything you ever wanted came in one fft talk? i'm going to present a short proof of a classical result that follows from an unmotivated algebraic identity. i will then walk through an intuitive, functional analytic, derivation of the theorem introducing and explaining definitions as i go. ideally the long proof of the theorem will completely illustrate the meaning of the short one. the emphasis of the talk will be on introducing interesting ideas in functional analysis in the context of an extended example.