Isaac Newton first posed the three-body problem in Principia, showing that even the Moon's orbit could not be fully explained by the Sun's and Earth's gravity alone.

Leonhard Euler discovered the first particular solutions by assuming one body has negligible mass (the restricted three-body problem), laying groundwork for lunar theory.

Joseph-Louis Lagrange found five equilibrium points (L1–L5) where a small body can remain stationary relative to two larger bodies. L4 and L5 are stable and host Trojan asteroids.

Henri Poincaré proved that the three-body problem has no general analytic solution and discovered that even simple deterministic systems can exhibit unpredictable behavior — the birth of chaos theory.

Karl Sundman found a convergent infinite series solution valid for all time (except collisions). While mathematically complete, the series converges too slowly for practical computation.

The advent of computers enabled numerical integration methods (Runge-Kutta, symplectic integrators) allowing accurate simulations over limited time spans.

Using variational methods, researchers discovered thousands of new periodic orbits — figure-eight, butterfly, and many other exotic trajectories.

Modern ML techniques learn effective Hamiltonians and discover novel periodic orbits from data, pushing the boundary of what can be predicted in chaotic regimes.