C++ author, trainer
It's the way ye tell it.Um, I'm not blaming them for doing PDEs and not homeomorphisms. Someone has to do the gritty and unpleasant work of PDEs so that the more poetic and artistic types can prove theorems in etale cohomology. It's that old Morlock/Eloi divide.
Have you studied the PDE works of Lagrange, Laplace, Euler, Hamilton, Navier-Stokes, Poincare?
PDE doesn't mean what you think it means.