Concrete example: Navier-Stokes. I don't make any claims about the truth of the announcement of the proof. But for the sake of the argument le't just suppose we know now that there is a smooth solution with smooth boundary and initial data which blows out in finite time.
Navier-Stokes is the simplest among evolution problems for continuum media, because it has maximal material symmetry (that's the mathematical meaning of a fluid).
If this is solved then go to a harder one, Coulomb friction. As a real life phenomenon, friction is very interesting to explore and mathematically is much harder than NS.
So it is not like we will ever be left without things to think about.
Oh, you want another? The present AIs are things made of mathematics. I would like to understand as a mathematician how and why they can beat human problem solvers?
Is that because mathematics is in some precise, interesting sense, more "computable" than it seems?