I think there's a pretty clear distinction between math and science. The former builds theoretical models of what certain axioms and assumptions imply. The latter builds actual models of what we see and measure in the real world.

Advances in math will probably result in advances in science, which in turn will result in advances in engineering (which is probably where the average person sees an actual benefit in their day to day life). But it's not automatic and a lot of the hand wringing by mathematicians about the AI math results include "is this (AI) method of finding proofs actually going to result in as many of those downstream advances as the old fashioned way?"

(I include theoretical CS as a subfield of math - and believe the S in it is a misnomer).