Originally Posted By: socratus
.we have merely proven that we do not need it (for computations)..
Lagrangian and Hamilton formalism used in quantum mechanics for description of steady state distribution of energy density (simply because the momentary values of quantum function are experimentally inaccessible for us) is based on Newtonian physics and optics of Victorian era. The derivation of Einstein field equations uses a Newton's gravitational law and constant as well. The concept of geodesics of general relativity has its direct relevance to Hamiltonian flow and Fermat theorem. Feynman's concept of path integrals is just an Huygens-Fermat principle in its integral form. The principles of topology are derived from behavior of soap membranes: the same groups of operations, which are allowed to do with manifolds are allowed to do with soap membranes in vacuum inclusively. The concept of natural numbers and Peano algebra rules are tightly connected with concept of colliding particles, which are countable in this way. The differential and integral calculus is based on gradient driven reality inside of particle field, where only density gradients can be see from sufficient distance. And so on...

If mainstream physicists would be more consequential in understanding of their formalism used, they would recognize easily, approach of contemporary physics is still deeply rooted in classical particle physics.