Well if someone wrote an article about the Poincaré conjecture calling it the "crown jewel" of math, and someone else said "actually I consider the primary goal

Well if someone wrote an article about the Poincaré conjecture calling it the "crown jewel" of math, and someone else said "actually I consider the primary goal of math to be in helping build low-cost housing and other practical issues," then they're talking about two different things. Both are math, but to say that the Poincaré conjecture isn't important to math because you use math primarily for different things is misleading.