Mathematics
The Euler–Lagrange Equation and the Principle of Least Action
Quick fact
The Euler–Lagrange equation is the mathematical consequence of the principle of least action, and it was derived independently by Leonhard Euler and Joseph-Louis Lagrange in the 1750s. It is so universal that it applies not only to mechanics but also to electromagnetism, general relativity, and even the Standard Model of particle physics.
Why this is interesting
You've been told that nature always chooses the path of least action—but what exactly is 'action,' and why would nature care about a mathematical quantity? The answer, hidden in a simple equation, governs everything from a falling apple to the orbits of planets.