I was studying discrete mathematics with a book that had mini biographies of the mathematicians that worked on wharever was being explain on that section. And it had one of them, who considered mathematics an art at the same level as painting or sculpting and hated that mathematicians "lower" themselves to do math that were "useful", like nobody expects the same "useful results" from the art department. This guy worked really hard to only research on pure mathematics and the most "useless" branch of it, number theory. Eventually, his work helped build the necessary mathematics background to make encryption a thing, and now the entire society use his research. It's a shame I can't remember the name of the guy.
Idk man I've seen mathematicians at my university shudder at applied math and they were kind of half joking and half not. Not all of the faculty were like that though, some of them had a wide range of interests! My favourite was a wonderful Polish professor named Edward who knew tons of things about not just math but also computer science, physics, and chemistry.
Extended version 1 (legible): http://i.imgur.com/WVGF9.jpg Arranged by complexity: http://i.imgur.com/hDa0P5M.png Extendend version 2: https://i.imgur.com/POrlDF4.png
Math is literally made up. There is no physical basis for math. Math is just another language used to describe things. The universe doesn't care whether there's "2 particles" or "1 particle and another particle" or "1 particle + 1 particle". It doesn't make these distinctions. Math only exists as long as there is an intelligent species which uses it. If there are no intelligent brains capable of using math and with a knowledge that it exists, math stops existing.