On the other hand, physics is filled with problems that are far worse behaved than even large polynomials. 3+ massive bodies interacting under Newtonian gravity

On the other hand, physics is filled with problems that are far worse behaved than even large polynomials. 3+ massive bodies interacting under Newtonian gravity. 2+ massive bodies interacting in General relativity [0], anything in quantum field theory, almost all differential equations you run into outside of a textbook on differential equations. [0] To be far, I'm not actually positive that the 2 body problem in GR is actually computationally harder than massive polynomials, but there is no exact solution to it; and understanding the approximation is definitely harder.