In this world I'm working on, magic is extremely bound by the laws of physics. Magic is explicable through science, and many people study it. The study of magic itself is like studying physics; the study of applied magic is like engineering. I like to think of magic as behaving similar to electromagnetism. Humans emit electromagnetic radiation naturally, but it would be very unnatural if a human suddenly could shoot out a bolt of lightning, or if they could use their bare hands to power a circuit.
In a world like that, where magic is akin to electromagnetism, how would a civilized society react to individuals capable of magical feats? Note that these mages would be incredibly rare--perhaps 1 for every 750,000.
Thought 1: Extremely negative reaction
Society would view this as a threat and eliminate it entirely.
Thought 2: Curiosity
Society, already advanced in studying magic, wishes to learn more and wants to determine if the condition can be induced onto others.
Thought 3: Militaristic
Society finds a means of using their abilities to conduct war and trains them as soldiers.
I can see a lot of possibilities. I want to know: which possibility, of the ones above or otherwise, is the most realistic one to occur, and why?
Murphy in the comments below asked some neat questions, here are my replies:
1: Does magic run in families or is it totally random?
Let's say that it is beyond the scope of genetics. It is not inherited. No single race or ethnicity is more likely than another to have mages appear. Mages may also appear in animals, but the scope of ability is limited based on physical constraints. A cow's magic is different than a human's.
2: Is it a recent thing? Did mages start appearing like X-Men or have they always been?
It is not a recent thing, but it gets more noticeable as time goes on due to ease of communication amongst people. Additionally, since the probably of being born a mage remains the same throughout time, having an increased population means the likelihood of mages appearing also increases over time.
3: Do mages have any historical organization/guild/power base?
I doubt this largely because of how rare it is, though I can see these emerging as time goes on, for reasons stated in 2.
4: Just how powerful are they? World shattering, city shattering or small country village shattering?
This I believe varies greatly depending on the individual. While some mages may only be able to, say, cause light to emerge from their hands, others may very well be capable of devastating offensive tactics. That said, since I do want magic to be at least partially tied down to a scientific study, I wouldn't imagine an individual capable of destroying the world. For cities, it'd likely have to be a small one. Humans have limits, and as such human mages also have limits.