> Solving a system of sparse linear equations ... is the single most important problem in scientific computing.
I think this is arguable. To be sure, a lot of linear-system solving goes on in science, but you cannot conclude from this that it is the "single most important problem", it's just the one that we happen to know how to solve, and so that's where the compute power goes. It's like looking for your keys under the street light because it's easier to see rather than because it's where you lost your keys. Protein folding and the Navier-Stokes equation are arguably "more important", we just have no idea how to solve those problems.
I think this is arguable. To be sure, a lot of linear-system solving goes on in science, but you cannot conclude from this that it is the "single most important problem", it's just the one that we happen to know how to solve, and so that's where the compute power goes. It's like looking for your keys under the street light because it's easier to see rather than because it's where you lost your keys. Protein folding and the Navier-Stokes equation are arguably "more important", we just have no idea how to solve those problems.