Ten years ago, G.Bergman asked: "Can one factor the classical adjoint of a generic matrix?"
With G.Leuschke we showed that, yes, sometimes you can. We arrived at this by translating the question into one on morphisms between matrix factorizations of the determinant.
Understanding all such morphisms lead through joint work with Leuschke and van den Bergh to a description of a noncommutative desingularization of determinantal varieties in a characteristic-free way and we are just about to put the finishing touches on this work here at MSRI.
I will desribe the highlights of this journey and mention some resulting, and remaining open questions.