Popular belief, and This paper, imply that the three-body problem is unsolvable. The authors mention Poincaré's work demonstrating this. However, they don't me

Popular belief, and This paper, imply that the three-body problem is unsolvable. The authors mention Poincaré's work demonstrating this. However, they don't mention Sundman's work in the early 1900's proving that the n-body problem can be solved as a converging power-series. Sundman's solution is correct, but the series converges very slowly and is impractical. Since an analytic solution was found over 100 years ago, why are we still debating whether one exists?