After Newton, re-formulations progressively allowed solutions to a far greater number of problems. The first was constructed in 1788 by Joseph Louis Lagrange, an Italian - French mathematician. In Lagrangian mechanics the solution uses the path of least action and follows the calculus of variations. William Rowan Hamilton re-formulated Lagrangian mechanics in 1833, resulting in Hamiltonian mechanics. In addition to the solutions of important problems in classical physics, these techniques form the basis for quantum mechanics : Lagrangian methods evolved in to the path integral formulation and the Schrödinger equation builds Hamiltonian mechanics.