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.