Principle of least action
Of all paths a system could take between two fixed events, the one realised in nature is the path for which the action S is stationary.
Definition
First stated by Maupertuis in 1744 and placed on rigorous footing by Euler the same year, the principle of least action is the variational backbone of classical mechanics. It replaces Newton's moment-by-moment force law with a single global optimisation: choose endpoints, define S = ∫ L dt over all smooth paths connecting them, and the physical path is the one at which δS = 0.
The same principle, with different Lagrangians, generates Maxwell's electromagnetism, Einstein's general relativity, and every quantum field theory of the Standard Model. 'Least' is historical — the rigorous condition is stationarity, which for almost every classical problem is in fact a local minimum.
History
Stated by Maupertuis in 1744; rigorously derived by Euler the same year; extended by Lagrange in Mécanique analytique (1788). Hamilton rewrote it in 1834 in a form that survived into quantum mechanics.