In 1953 Fermi, Pasta, Ulam, and Tsingou ran one of the first computer simulations: a chain of nonlinear oscillators. They expected energy to spread to all modes (thermalization) — instead it nearly-periodically returns to the initial state. This launched nonlinear dynamics.
Energy in mode 1 (red) should spread to higher modes, but instead recurs. The recurrence time scales as ~ 1/α². This mystery was only explained decades later via solitons and KAM theory.