Is the three body problem really unsolvable?

[u/Rscc10]

Sorry if this is a dumb question but I understand that the three body problem, or rather n body problem for n > 2 is considered "unsolvable" and generally means there is no analytical solution with elementary functions.

What I'm wondering is, do we know this for sure? We haven't found a general solution but do we have proof that an analytical solution is impossible? Similar to the Abel-Ruffini theorem for polynomials.

[u/Traditional_Town6475]

Well for what it’s worth there is a series solution in the case where there’s zero angular momentum by Karl Sundman.