Maths is useless. Why would anyone bother? Aside from working out mortgage payments or paying taxes.
And yet, people devote years of their lives in search of esoteric patterns of numbers and ideas. Why would they do this? Wouldn’t society be better off if they worked on curing disease?
One might as well ask, why are we alive? To procreate? To pave everything in sight? Of course not!
We are alive to search for truth and beauty in this world.
Mathematics is, by definition, the search for truth. Literally. Even truth that exists beyond the world that we can touch, see or taste.
In a very real way, mathematics is the art of ideas. Unfortunately, unlike a painting, it is an art that generally requires years of study to appreciate because it has been built layer by layer upon prior mathematics.
The best way to develop an appreciation for mathematics is to start with problems that started the study of mathematics, for example the perfect number problems in the main article.
Abstract mathematics is useless in the way art is useless. They are both simultaneously unnecessary and the reason for our existence.