When I read about hardest equations I thought it would be equations of either General Relativity or Quantum Mechanics of complex systems. Both are much more com

When I read about hardest equations I thought it would be equations of either General Relativity or Quantum Mechanics of complex systems. Both are much more complex than Navier-Stokes. For Navier-Stokes we have at least numerical methods that allow to solve the equations in practical time for useful cases. But we still do not know how to model, say, dynamics of a galaxy using General Relativity. Typically such models just assume Newton mechanics with minimal if any relativistic corrections with no proof that one can use such approximations of equations of GR on big scales. Or consider the problem of a possible state of metallic hydrogen. It is just a bunch of protons and electrons mixed together, the simplest possible material. Yet we cannot calculate from the first principles its properties.