Most people think that mathematicians work with numbers, when the truth is far away from that. You are most likely to end up having to work with something that

Most people think that mathematicians work with numbers, when the truth is far away from that. You are most likely to end up having to work with something that cannot be drawn or calculated and is superbly abstract, like some mappings from one theoretical concept to another. Sure, you can draw some "projections" from certain things to other things, or "draw" an analogy to something simpler, but still most of the things are highly abstract and are nowhere "simple" as numbers, or geometric figures or something similar. I think this is true at least in theoretical math research.