It is remarkable that this people, though unarmed, dares attack an armed foe; the infantry defy the cavalry, and by their activity and courage generally prove victors.
Being able to improvise is the basis for creating all characters and situations, for everything to do with performing, really. And it's good therapy as well.
Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.