Statistical Mechanics above all

Quantum field theory (Continuum Limit, Propagators, Feynman diagrams, Renormalization Group, Renormalizable versus non-renomalizable theories, Effective Field Theory, Phase Transitions, Symmetry Breaking, ...) is nothing but statistical mechanics!

I believe, in theoretical physics, we say we understand something if we can reduce it to a quantum stat. mech. problem. That's why we say we don't understand gravity! That's indeed what the goal of quantum gravity is!