The Deligne Simpson problem (DSP) arises in the classification of linear ODEs in the complex domain, but it is elementary to state: given k conjugacy classes in GL(n,C), determine whether or not there are matrices in these classes with no common invariant subspace and product equal to the identity. Work I did on quiver algebras led to a conjectural answer for the DSP, I proved one direction in 2006 with P. Shaw, and although I announced a proof of the other direction, it never got written up. In this talk I will explain the background to the DSP and discuss recent work with A. Hubery aimed at completing the other direction.