Comment by tkgally

That’s an interesting approach. I don’t think I’ve done that myself, but I can see how it could be helpful.

One positive effect of having studied pure mathematics when young might have been that I became comfortable with thinking in multiple layers of abstraction. In topology and analysis, for example, you have points, then you have sets of points, then you have properties of those sets of points (openness, compactness, discreteness, etc.), then you have functions defining the relations among those sets of points and their properties, then you have sets of functions and the properties of those sets, etc.

I never used mathematical abstraction hierarchies directly in my later life, but having thought in those terms when young might have helped me get my head around multilayered issues in other fields, like the humanities and social sciences.

But a possible negative effect of spending too much time thinking about mathematics when young was overexposure to issues with a limited set of truth values. In mainstream mathematics, if my understanding is correct, every well-formed statement is either true or false (or undecided or undecidable). Spending too much time focusing on true/false dichotomies in my youth might have made it harder for me to get used to the fuzziness of other human endeavors later. I think I eventually did, though.