> This I don't know about. I think math acquires meaning when it contacts reality: like an iota is pointless until there's some circuit that it explains. Abstract math can diverge from that and can become an exercise in playing with symbols for their own sake.

After talking to a mathematician friend I can assure you that contact with reality is not the main goal of abstract math. It is mental constructions that have logical consistency and probably this is not the perfect definition either. It is somewhat of an art which is rendered in the logical mind. However physicists (me) and engineers will align with you.