One of the most exciting developments in CMP at present is the theory of topological quantum computation. Particles with knotty statistics, called anyons, can be potentially used to build a fault tolerant quantum computer. And it also seems that materials science and nanotechnology is moving ahead in leaps and bounds.
Now imagine what we could do with a new physical theory, a theory that does not merely assume that the universe is FRW homogeneous and isotropic. After all, it's the matter that is interesting, not the inferred background in which it appears. Imagine a theory where anyon knots live instead in the pure world of categorical logic, where we are no longer constrained by the limitations of analytical geometry.