Why learn abstract mathematics? What is the point?

I’m a mathematics college lecturer and have an mphil degree in the subject. But I often wonder why I’m learning this senior undergrad level mathematics—analysis, topology, functional analysis, abstract algebra etc. Whatever I learn from my mathematics books is hardly any use to me when I move around in society where I live.

The only use I’m presently making of my mathematics knowledge is to teach this subject to my pupils (those amongst who major in mathematics are likely going to teach it in turn to their pupils). I know that engineers study and utilise mathematics, but the only things they ever get to learn during their degrees are the calculus, linear algebra, differential equations, numerical analysis, and statistics / probability—all at a rather elementary, calculational level. And I also know that computer science students also learn discrete mathematics.

But those who are studying mathematics here are only learning it to get through their degrees and to later teach the subject, most often at secondary school and elementary college level, at schools, colleges, universities, privately run tuition centers, or by going from door to door tutoring.

Apart from this, I find that abstract mathematics has little use at least in my daily life; nor does it get discussed or talked about, unlike literature, politics, economics, etc.

Once on my return home while I was pursuing my mphil, an elderly kinsman, who has had very little schooling himself, inquired of me what I was learning at the university and requested me to teach him some of it too. Now I was really confused how I should communicate to him (a man who doesn’t even know the high school mathematics) concepts like the Hahn Banach Theorem! So I was speechless and he a bit disappointed.

During my interaction with my parents, siblings (one of whom is a civil engineer studying for a PhD at Univ. of Queensland and another is a dentist), or other kinsmen, whatever little bit of mathematics I’ve learnt doesn’t seem to do me any good (apart from the salary I earn of course, but even there it’s often too much of a struggle for me to teach mathematics with my poor eyesight).

I wonder if it’s like this with most (if not all) of the SE community.

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Why learn abstract mathematics ? What is the point ?

$\quad$ A century ago, Hardy argued very passionately about the non-utility of abstract mathematics. Number theory, in particular. He was quite proud of this. Now, guess what branch of knowledge is used today overwhelmingly in telecommunications security ? 🙂 P.S. : Please don’t write a follow up question, asking us about the purpose of information security : Why secure data ? What is the point anyway ?

Can’t that be said about any advanced degree in a topic that’s not directly vocational? Even physicists after a certain point are just expanding society’s collective knowledge about the topic. The only difference between very advanced physics and society’s perception of it, versus very advanced mathematics and society’s perception of it is that physicists have better publicists. Physicists take the time to write pop-physics books to get the public interested in the wonders of the Universe (no doubt to keep their funding haha), but mathematicians don’t do that. With few exceptions, mathematics is sort of insular and the notation used by mathematicians is impossible for the layman to understand (and difficult even for undergraduate BS students at times). Couple that with the way mathematics is taught in schools (i.e. as a rigid recipe for computation without building upon intuition–though I think the common core is fixing that slightly, but even it is meeting HEAVY opposition and is regularly taught by people who themselves don’t have the proper intuition of the subject), and you have end up in our current situation where the layman not only doesn’t understand/know what mathematicians do, but they don’t care.

What’s the point? It’s an intellectual pursuit, and some of the results help other fields. Not everything directly applies to the real world.