Hmmm, this seems reasonable, but I personally am extremely annoyed when I ask someone "what is thing x?" and they start by saying "let me give you an example" instead of a general description of the thing first.
Is this because I'm starting to think like a mathematician? Or because I'm conflating a deep, theory-first explanation of a concept with a surface-level summary that is then followed by concrete examples? Or something else?
An example would be helpful (ironically), but I think it's because you already have fluency in many abstract concepts (rooted in a lifetime of concrete application and examples), and in this situation the abstraction is usually much faster to work with, and you're annoyed because the example is effectively a long-winded explanation.
I'm not saying a mature mathematician is wrong to ask for an abstract definition first. For them, that might work well. But it's wrong to conclude from that experience that the abstraction is somehow more primary, or that it could exist in isolation. They've just forgotten the process that got them there.
Is this because I'm starting to think like a mathematician? Or because I'm conflating a deep, theory-first explanation of a concept with a surface-level summary that is then followed by concrete examples? Or something else?