A mathematical proof or analytical solution. I understand that analytical solutions only apply for very narrow ranges of problems but... consider writing an ana

A mathematical proof or analytical solution. I understand that analytical solutions only apply for very narrow ranges of problems but... consider writing an analytical solution to a differential equation versus applying a numerical solver. A numerical solution rarely leads to as deep an understanding as an analytical solution or a number of approximations in various limits. I feel like we're in the limit of something analogous to writing numerical solvers and claiming understanding from observing the output.