If somebody asked me, who or what I am or wish to be, I wouldn't say I am an artist, or a scientist, or philosopher, not even author, believer, speaker, writer, thinker, teacher, visionary, expert, pundit, none of those labels. Without a moment's hesitation, I would say that I am, for serious, only this:
I have a social studies degree from a respectable university and I'm so far successfully working on acquiring the next one. I have over a decade of experience in a number of arts, publishing as well as performing live for real audiences, even winning competitions. I am also a spiritual person, though with no affection for organized religion. And I don't say that to brag, I do not claim that it is good to do all those things with one's life in general or for anybody in particular. If you enjoy cooking or footbal, building machines or saving lives, or anything else that exists and isn't utterly destructive, do that and be proud of yourselves. Or not, it's up to you.
It is entirely possible that nobody at all cares about what magic really is except me, but it would be a pretty stupid way of being special. The general contemporary idea of magic is that magic equals supernatural nonsense rooted in wishful thinking, devoid of logic or any empirical basis. The trouble with this notion, apart from it being an analytically useless and clearly biased strawman, is that magic is the most important discipline to master for anybody. And it isn't even difficult to understand. At all.
It's right out there in the open - magic is both a science and an art of making wishes come true.
Quite simply, science is a school of magic, art is a school of magic, philosophy is a school of magic, as are all their forms and subcategories. The magic was not only the first way of thinking, it never disappeared and it shall not disappear, as long as there will be sentient creatures wishing for things to happen. Or not happen. Or transform. Or be left as they are. Or anything else a mind can wish for.
Magic includes logic, methods, experience, the whole package. You can assume that simply wanting something is enough, and see how well that works out for you, or maybe you wish to be able to achieve results in a reliable way and choose science. Or you prefer taking what you want and making things come true. It's up to you, all perspectives on life have their benefits and drawbacks. Science only makes its own very clearly defined.
The rules of magic are simple - know yourself and be yourself, know what you want and do what you want. That is the primal magic that can do no wrong. By which I mean truly wrong, universally wrong - you cannot wrong the universe for being who you are, if it is an entity that cares about you/made you/is you. And living the life your way makes sense even for a secular skeptical atheist. Only to deprive yourself and the world of YOU is a universal crime against life and the whole of existence. Most of all you.
At this point the notion of magic thus presented may be subject to ridicule as some pseudo-eastern popular-psychology self-empowering newage crap, but only if you assume nobody can fail. Everyone has magical potential, but an astonishing amount of people fail to tap it, people of all walks of life. Some have power that is consuming them and destroying all in their path, while others aimlessly waste their lives thinking there is nothing they can do to affect anything.
One of the greatest spells of this age is the spell of disenchantment of everyday reality. We can fly, even into outer space, explode celestial bodies, control our instruments remotely, communicate over vast distances, create virtual worlds of our design, but no, there is no magic in it. It's just science of reality. What the scientists forget is that all of those accomplishments started as mere wishes, crazy notions, fiction and fantasy. The fact is that we are so good at magic today that we have already bested most of the fabled wizards from the legends of our past.
Science without magic is when you forget why you are doing the science. An error that can wipe out a civilization. It's when you reduce magic to healing hit points or (only the obviously ridiculous) superstitions, when you declare all magic an escape from reality and a delusion. Truth be told, yes, some magic is lame. Magic can be done wrong too - playing Advanced Dungeons and Dragons, while being an amusing exercise of imagination, is by itself one of the furthest things from real magic. When you prefer to invent a fictional character you identify with rather than living your own life, you're doing magic very, very wrong.
I'm not saying you shouldn't be playing games - you must, if that is what fulfills you. But if you specifically desire to be a mage, then science or art are much better options than AD&D. You want to throw lightning? Read about Tesla. You want to be immortal? Research medical nanotechnology or genetics. You want to be a god? Programming can make you a veritable creator of worlds. And if you wish to master primal magic itself, you can start by studying as many philosophies of life as you can find - all are just as true as they are arbitrary. Find out all there is to want in life and why, how do people make any of that come true, what leads to success and what to failure, what do success and failure even mean from all the seemingly conflicting points of view. Draw a picture of the whole of existence and then find your place in it, which should put you into proper perspective. Not necessarilly flattering, but there is nothing more realistic than transcendental holism. In simple terms, get real by looking at the big picture and getting over yourself. Without losing yourself. Be aware and humble and honest. Unless you wish to become an evil warlock, but I won't help you with that.
Or you can decide that magic is an unrealistic nonsense, thus magically making it so.
It's up to you.