text: abstract
  we show that if the nearly-linear time solvers for laplacian matrices and their generalizations
  can be extended to solve just slightly larger families of linear systems, then they can be used
  to quickly solve all systems of linear equations over the reals. this result can be viewed either
  positively or negatively: either we will develop nearly-linear time algorithms for solving all
  systems of linear equations over the reals, or progress on the families we can solve in nearlylinear time will soon halt.