The usefulness of mathematics is impossible to ignore. It has become a vital part of medicine and engineering, which provides evidence for or against math’s value to humanity. These are “crude” arguments but are important to address.

Mathematics has vast application in the sciences, and science is useful to humanity, but it’s not generally useful to most people on a daily basis. Ignorance of the chemistry of fire doesn’t stop anyone from cooking a meal. Knowing some basic arithmetic, along with history, geography, and economics, is useful, but math’s main utility depends on what it can do for society as a whole.

Elementary math, up to calculus, is quite useful, but to a mathematician it’s somewhat dull and unaesthetic. The most satisfying challenges in math lie in its more advanced and generally useless parts. This doesn’t mean that mathematicians revel in uselessness, but many appreciate that among the sciences, math is the least liable to be used for destructive purposes.