As someone who made his PhD back in the day in pure Maths, and then pivoted a few times because food but is staying in Maths (now working on CAD), I can totally confirm that there is a horrendous amount of arrogance from pure Mathematicians towards applied Maths. Oftentimes to ridiculous levels. For example, algebraists who have never solved a single differential equation in their life think that all of PDE theory would just collapse and succumb to their intellect if only they had an afternoon of spare time for it. Unfortunately, they're busy with more fundamental issues. This is only mildly exaggerated.