The eternal struggle of mathematicians everywhere! When your co-author suggests using numerical methods because "there's no analytical solution," it's like they've committed a cardinal sin against mathematical purity.
Analytical solutions are the elegant, closed-form expressions that give you the exact answer. Numerical methods? Those are just... approximations. Shudder. It's like being offered a microwave dinner when you were expecting a five-course meal prepared by a Michelin-star chef.
Pure mathematicians would rather spend six months finding an analytical solution than six minutes coding up a numerical approximation. "Sorry, I don't speak wrong" is the perfect response to anyone suggesting we abandon the search for mathematical truth!