I hear you, but that feels like more of a physics model vs. engineering heuristic dichotomy rather than math vs. statistics.

(If you haven’t seen it already, the Engineer Guy did a lovely little series of videos about engineering heuristics)

The kind of math I find alluring doesn’t operate in an idealized version of reality; rather, it’s completely divorced from reality, instead living in universes defined solely by mathematical axioms. It’s only incidentally that real-world applications that arise from these investigations (e.g. modern cryptography from the work of centuries of number theory nerds). But to each their own! In general, I prefer the concrete to the abstract, but statistics is an exception.