We still don't understand magnetism

Unlike the two-body problem solved by Newton, predicting the motion of three gravitationally interacting bodies has no general analytical solution due to chaotic, dynamic forces. Heinrich Bruns proved it unsolvable in 1887 (8:15), yet attempts to solve it gave us the foundations of modern mathematical physics.

Joseph-Louis Lagrange developed a scalar field approach (2:35) that assigns values to points in space based on mass and distance, creating a landscape where the gravitational field equals the negative gradient. This allowed physicists to add scalars instead of complex vectors.

Five locations where gravitational forces balance to zero, discovered through potential analysis (5:30). These are now used practically for placing spacecraft like the James Webb Space Telescope.

A revolutionary approach to mechanics using kinetic minus potential energy (6:45), plugged into the Euler-Lagrange equation to derive equations of motion without dealing with complex force vectors directly.