Besides, the more I think of pure mathematics, the more I see them as an art rather than a simple tool to apprehend the world.
There's some truth to that, even if you ultimately adopt a very applied mindset like I have because there's a certain playfulness that you need to have in math that goes beyond sitting down and just solving problems directly, so even if you just care about applications, you may sometimes be lead to think more about math internally and just be ready to grab something from that that you think might be useful to solve your problems. V.I. Arnold says "there are no applied sciences, only applications of sciences."
I still don't know what the hell he means by that, but I am guessing it could be something like what I am trying to get across now.
I would caution you against coming to conclusions too early on. At a topology conference, I met a grad student, finishing his PhD from Berkeley who said he thought he wanted to be a pure mathematician, but now he's not so sure--after all that time. Why? From my point of view, it's easy to relate to that. In practice, you might find that maybe a lot of pure math that is being done on the cutting edge isn't as "artistic" as we might hope. I'll link you to Baez's very astute post here that addresses this problem
https://golem.ph.utexas.edu/category/2007/04/why_mathematics_is_boring.html
That's part of the reason I quit pure math (the other reason was that I was really an applied mathematician trapped in a pure mathematician's body). I couldn't take it, personally. Baez loves his job as a math professor, even despite these issues, although it's clear that he is bothered by it. He says that math is one of the most exciting things in the world, yet people succeed, against all odds, in making it boring. I'm not sure all of math can be rescued from boring-land, but a lot of it could be.
Another thing is that a lot of what mathematicians seem to be concerned with these days is checking that things are true, rather than understanding why they are true. Take the 4-color theorem. I don't see any artistic value in asserting that "it's true because the computer said so". Doron Zeilberger, champion of computer-based mathematics, would probably call it a "beautiful" proof. I don't really see why he would say that, other than the fact that he loves computers so much, and perhaps it signifies that the theorem is so deep that it defies human comprehension. Can we say that the 4-color theorem is a beautiful theorem? I would actually say yes, but the problem is it's not really that the theorem is beautiful. It's more that the problem (figuring out if you only need 4 colors to color a map) is beautiful. The theorem doesn't add much to that by telling us that it's true, even though we don't know why. The issue goes beyond computers. Very technical proofs that no one understands are similar to computer-based proofs, as far as this goes.
So, I question your idea that it's all a pretty art form--maybe it could be more than it is now, though. Some mathematicians approach it much more like a sporting event where they set certain goals for themselves and the object is not so much to make beautiful things, but to pull off impressive stunts. If you have a more artistic bent, you might be put off by that side of things, and you might find it hard to avoid, if you aren't careful.
Maybe there's value to sporting achievements, though. Maybe they teach us more about to solve really hard problems. For example, the 4-color theorem is always one of my big examples I like to pull out when I talk about this stuff.
Another point is that I think a lot of the artistic value of math actually comes from the connection with applications, particularly physics (read any book by V.I. Arnold for proof of this), so it's not always the case that the art form is separate from apprehending the world. My big gripe about a lot of the math that I learned was the lack of motivation. It turns out that things like symplectic manifolds have a physical motivation. It's beautiful because there's an inspiration for it. If it's just some arbitrary definition that some mathematician pulled out of his butt, I don't find it beautiful. Some things have a purely mathematical motivation, but what annoys me is when the best motivation, coming from physics, is thrown out, in order to keep math more a of a "pure" science that's independent of the physical world and applications. The truth is that, psychologically speaking, the roots are not separate from the real world, even if it is possible to make it formally independent of it.
One thing I find somewhat objectionable about the "art form" point of view is how small an audience you may be talking about, the deeper you get into math. It's sort of like doing paintings that get locked away and only displayed to certain special people who have to work really, really, really, really hard in a sort of treasure hunt to be given their secret location (50 or at best, maybe a few thousand people if you prove a really accessible result). There's just something weird about it. But hey, whatever floats your boat. I'd be the first to say what's popular isn't always what's good, in a lot of ways, but still. This can be alleviated to some degree if we address some of the problems Baez was pointing out. On the other hand, you can always take the point of view that you're an explorer, so it's kind of cool that you are discovering things that no one else knows. Personally, I found it profoundly unsatisfying and anti-climatic when I finally managed to prove something no one else knew. I will admit in retrospect, it's slightly cool that I can look back on it and say that I did it, but it was unbelievably painful to carry out, so it's a fairly small consolation that I'm getting as my reward for all the blood, sweat, and tears that went into it. It doesn't always come cheaply. There was even an article in the AMS notices one time about the psychological dangers of being a mathematician that talked about poor little mathematicians breaking their backs to prove theorems that seem completely trivial in retrospect. So, it takes someone a little crazy or else unbelievably talented to think that the "art form" or the sport is so compelling as to justify the immense amount of effort required. I think Halmos or Hardy or maybe both of them talked about how you have to love math above all else, even your family and so on. Bertrand Russell has a quote that says something to the effect that you have to lose your humanity in order to make a great discovery or something like that. Mathematicians who happen to be more normal human beings can hope that maybe that's not true because it's a fairly hideous thought. If it is true, it casts the "art form" in an even stranger light. These things seem considerably less cold and sinister if the art form has practical consequences that can change the world for the better. All the madness seems worthwhile if it can help us figure out how proteins fold and create new drugs to treat horrible disease and save your grandmother. It's a double-edged sword of course, because maybe it helps the NSA to spy on you, make bigger bombs that blow up children, etc., but on the whole, it has so much potential if used responsibly.
You always have to ask yourself if one day you'll be bothered that you aren't doing something practical. Maybe one day it could hit you, like it hit me. "Hit" isn't really right because it was much more gradual. In light of all the things I've mentioned, this possibility might seem more real to a hopeful student who is in the honey moon phase of their relationship with math and doesn't see all the difficulties ahead.
I really wish someone could make a really strong and clear case, for the practical benefits that result as a spin-off of the art-form/sporting phenomenon that is pure math, so that more pure math students and maybe even profession mathematicians can sleep at night, without feeling so guilty about not contributing much to society. I've even toyed with the idea of writing a book that does just that one day, but I wonder if I'll ever be up to the task.
Finally, although I don't object to people getting their kicks in whatever manner they please, however strange (after all, we have a much bigger labor supply than we need, so it's useful to have some people just make a living by goofing off, so that some of us can get the jobs they would have been doing, instead of being unemployed), at some point, you have to convince people to pay you, which I don't think you can do if you can only say that it's an art form that only pathologically hardworking people are able to appreciate. So, keep in touch with the rest of us, the physicists, the engineers, the computer scientists. Don't distance yourself too much. It can be an art form, but it's got to have those useful spin-offs or it cannot survive. It's not only money but attention and interest from as wide a range of people as possible to help keep the subject alive and keep it from dying, forgotten in some obscure journal or even worse, not even fully written down, as was the case for so much of the intuition and folklore associated with the subject of foliations in the 1980s. Practically speaking, this may even make a difference in getting that grant money. In my branch of topology, if you said "quantum computer", that was sort of a magic phrase in some ways, even if it's only a hope of an application, rather than an actual one.
I caution people who think like me from getting into math because they may be unhappy there due to these problems, but maybe some of them should go, like I tried to for a while and be crazy enough to think they can change some of these things. I'm crazy enough to think maybe I can change some of these things as a hobby, while I find another way to pay the bills and contribute directly to things that affect people's lives in a positive way.
Sorry I have been so long-winded, but I hoped to give you a sense of the dangers involved with falling in love with math as an "art form". I don't mean to imply that it could not work out for you. Whatever makes you happy makes me happy, even if it's pure math. Just be careful. Think really hard about what you're getting yourself into first.