The content of the theorems in the title, one proved 200 years ago (an algebraic surprise) and the other 40 years ago (a topological surprise), will be revealed during the talk.  Both results went contrary to popular opinions at the time.  The proofs we give will be topological, the first involving configuration spaces and the braid group, and the second some stable homotopy theory (for Mona).  If time permits, we might speculate about spiritual connections between the two results.