Anything that remains abstract (in the sense of not concrete) is hard to think about… I think that mathematicians are those who succeed in figuring out how to think concretely about things that are abstract, so that they aren’t abstract anymore. And I believe that mathematical thinking encompasses the skill of learning to think of an abstract thing concretely, often using multiple representations – this is part of how to think about more things as “things”. So rather than avoiding abstraction, I think it’s important to absorb it, and concretize the abstract… One way to concretize something abstract might be to show an instance of it alongside something that is already concrete.

Oliver Steele, in Bret Victor, “Kill Math”