I have a hypothesis about non-maths people that is that the more removed from maths their actual field is, the more abstract their math interests will skew. E.g. a person who studies sociology might be interested in the more applicable side of statistics but as a stage actor my math interests are as far from applied math as possible.
Possibly! I always got the impression that a lot of people (though of course not everyone) find abstraction intimidating or boring and the general advice is to start from somewhere as tangible as possible, but in maths "looks tangible" doesn't necessarily equate to actual applicability (geometry looks more "tangible" than a lot of stats because it's shapes (I mean past a point the shapes are no longer visualisable but at least you can start from somewhere tangible) but is generally less useful to other sciences, for example). Probably statistics in particular is more interesting to people who use it though!
(That said, these are fellow phd students in science, so most probably do use statistics (& therefore probably know more than me - but may not know topological data analysis so that is a potential topic that would interest them!))















