Is finding a solution for a problem in a given context is an attempt to find a solution for the problem in another context?
For example, it seems some of the hardest problems of real analysis were not solved till their solutions were found in the context of geometry.
Update: I think it makes the question more clear if I provide an example. Let's say I want to prove if x+y=x+z, then y=z, where x,y,z $\in F$, where $F$ is a an algebraic field with operation "+". For example for this problem I can think of context where solution exits and that would be the ring of integers. If 1+2=2+1 then I can show 1=1. Now once this solution is found using this context of integers I can now apply this to the original problem in the context of field.
Now what I was asking was that should such a solution exists in some contexts (context as used in example above) for a problem to be solvable.
I do not know the background science behind this but it would be great if references can be introduced so I can get to know the right terminology.