Suppose a particle travels from

point a at time t1 to

point b at time t2. What path does it take?

Joseph Lagrange found that the particle will select the path that minimizes a

quantity called the

action, defined as the

integral along the path of the

kinetic energy minus the

potential energy.

This is completely counter-intuitive, and keeps physics students up very late at night wondering how it could possibly be true.