> Unlike the two-body problem, the three-body problem has no general closed-form solution,[1] and it is impossible to write a standard equation that gives the exact movements of three bodies orbiting each other in space.
This seems like the opposite of your claim.
A similar claim is that roots of polynomials of degree 5 (and over) have no "general closed form solution" (with, as usual, the implicit qualification: "in terms of functions I'm currently comfortable with because I've seen them a lot"). That doesn't mean it's a difficult problem.
The two problems have in common that they are significantly harder than their smaller versions (two bodies, or degree 4). Historically, people spent a lot of time trying to find solutions for the larger problems in terms of the same functions that can be used to solve the smaller problems (conic sections, radicals). That turned out to not be possible. This is the historical origin of the meme "three body problem is unsolvable".
For polynomial roots, see wikipedia.org/wiki/Elliptic_function.
Not that it's particularly relevant to this discussion but the three body problem is easy. You can solve it numerically on a laptop with insane precision (much more precisely than would be useful for anything) or also write down an analytic solution (which is ugly and useless because it converge s extremely slowly, but still. See wikipedia.org/wiki/Three-body_problem).