In mathematics education, sometimes a teacher may stress that mathematics is not all about computations (and this is probably the main reason why so many people think that plane geometry shall not be removed from high school syllabus), but I find it hard to name an application of mathematics in other research disciplines whose end goal isn't to calculate something (a number, a shape, an image, a solution etc.).
What are some applications of mathematics — in other disciplines than mathematics — that don't mean to compute something? Here are some examples that immediately come to mind :
- Arrow's impossibility theorem.
- Euler's Seven Bridge problem, but this is more like a puzzle than a real, serious application, and in some sense it is a computational problem — Euler wanted to compute a Hamiltonian path. It just happened that the path did not exist.
- Category theory in computer science. This is actually hearsay and I don't understand a bit of it. Apparently programmers may learn from the theory how to structure their programs in a more composable way.
Best Answer
Would you count these sculptures by Bathsheba Grossman as non-computational? Maths for the sake of beauty. (Also they include a Klein Bottle Opener!)
A nice but technical example I remember from electronics electronics at university was the proof that a filter which perfectly blocks a particular frequency range but lets everything else through can't exist. The reason is that its response to a step input begins before the step is applied. Though I'm not sure whether to count this one since it does involve working out the step response via a Fourier transform.