To explain this shortly, a three body, or N body system where n > 2, creates a system of equations where there are more unknown variables than the number of equations. And this creates a problem that cannot be solved "analytically". The equations create a system of differential equations, and they become unsolvable. And the mathematicians say they can solve it through numerical methods, but those are just "approximations" of the system and not the real solutions, and as one of the scientists have described it, it is a "blind" solution and people only resort to numerical if they couldn't find the proper analytical solutions.