When a proof or concept can be represented by some kind of picture, it becomes quite intuitive, but usually it is not formal. My question is that are there any tools in mathematics, which can formalize this kind of intuition. Any tools that can translate idea such as in analysis into a geometric one, so proof can be done using the techniques of geometry.
The idea comes from usually geometric or topological argument can simplify technical part of the proofs in analysis. I have seen it quite a lot of time. So I wonder is there any tools that are specialized in this task.