2 questions often asked, in general, are:
why study humanities (what practical use is this information)?
why study mathematics (what practical use is this information)?
i submit that the answer, to both questions, is the same: to learn how to think. to ability to think clearly, in both an analytic\logical sense, and a naturalistic\linguistic sense, is of indespensable use in ANY endeavor, be it designing torpedos, painting a landscape, writing a government funding request, hunting deer, or making forum posts. too often, people who see the reasonableness of one kind of learning, deride the other. i believe that the mathematician without something of the poet and philosopher in them, is not much of a mathematician, and the poet or philosopher who cannot think logically, is not exemplary in their field, either.
we (humanity as a whole) desperately need both skill sets: we need to be able to form and communicate ideas, and we need to know how to sensibly discern between various ideas for value. two things essential for survival (and we learn this intuitively at an early age) are the ability to imagine things, and the ability to determine things that constrain our imaginings. now, for many people, the expansionist practice of accumulating ideas (having a "bigger bag of tricks") is of obvious value (but why the humanities? does it not stand to reason that we should start our idea acquisition from those whose ideas were considered good enough to keep, over the centuries?).
but mathematics is essentially "reductionist", mathematics is the gentle art of "forgetting stuff that's not relevant". linear algebra is a case in point...what the various entries in our matrices and vectors stand for, is of no help in determining their relationships, and keeping the "link" just slows down the calculations (and doesn't help notation, either). the hope is, of course, that by exposing young 'uns to numbers, they will see that this one example shows the value of such reductive abstraction ('rithmetic is as good a 'larnin' as 'ritin is), but many people get confused by the lesson....and deduce that calculation IS mathematics (odd that no one ever makes a similar mix-up between spelling and reading). that's too bad, as many of the "prettier" examples are only available when you have a large enough mathematical vocabulary to speak of them (just as many great books, or works of art, require understanding how they are put together, to get the most out of them).
what i think is needed, is a more categorical approach to being educated. the case for specialization has been made well, but how much are we missing, because people in different fields don't understand each other (or even try)? a historian with a knowledge of structures, has one more tool to analyze events with; a mathematician with a knowledge of history, has one more structure to add to his tools. the two sides of our nature are not at war: they inform each other, and the person who has access to both will be more successful, no matter what their chosen field.