I think I know what you are talking about. For example, there is a famous problem called the 4 colour problem. It states that any region that has been decomposed into smaller regions can be coloured with at most 4 colours such that no two adjacent ones has the same color. When mathemations where working (or worked) on this problem they completely changed the problem. Because the original problem was not mathematical enough, I am myself not sure how you even begin to define something like that but that is what they did.Actually, I've noted Mathematicians using this one too. They simply redefine the problem into one they know how to solve.
I know that joke too.Physicists, on the other hand, tend to use "spherical horses," as the joke goes.)