The principle of least action is a fundamental framework for physics because classical mechanics emerges from quantum mechanics through the constructive interference of paths near the minimum action.

“This explains how light knows where to go. I mean, it doesn't. It just explores all possible paths, but the past we end up seeing are the ones that interfere constructively. And those are the paths of least action.”

The name principle of least action is technically misleading because the principle actually relies on finding a stationary point, not necessarily a minimum.

“The principle of least action more properly stated should be the principle of stationary action. That the laws of motion come from demanding a stationary point, which is tantamount to this condition of setting a certain derivative to 0 and then getting the Euler-Lagrange equation from that.”