Just because something follows rules doesn't mean science can grasp it.
All human convention - ALL of which is make-believe - follows rules.
Magic in the DA universe abides - very poorly - by a set of rules that are prone to changing.
Science doesn't change. The rules are binding.
Except when they aren't? For centuries, physics operated under Sir Isaac Newton's theories, until, in the '40s, Mr. Albert Einstein said, "Sorry Sir, but you were wrong". The rules changed, as did the theories that allowed those rules to work.
Also - on Thedas - the "educated" mage is a myth. There are only a handful of educated mages - Flemeth, Morrigan, Solas, Zathrian and Avernus (let's forget three of them are psychos and one is a craven survivalist). You can be other things as a mage on Thedas... political (Dorian and Vivienne) - militant (the Saarebas) - a cause-head (Anders).
None of them advanced their research... Dagan, a none mage - was a more educated mage than 95% of all DA mages presented so far.
You are born a mage... education has nothing to do with it. Mastering magic is more akin to a religion (mental discipline, visualization techniques, etc.) on Thedas. It's ridiculous to think you're "born prone to wanting to be educated".
So we are the sum of our birth, and cannot rise above that station? Being born a mage does not prohibit gaining an education. Being able to use magic does not preclude one from being educated, nor does education have anything to do with it at it's core. However, that does not preclude being able to gain knowledge, aka education. Can they be educated in the principles of magic? Yes, and if you've played the mage origin, you'll have seen this at work.
Also - it is pitifully unreproducable and obeys laws from the LEAST scientific place of them all. The Fade. A place of thought, mind, idea. A totally chaotic irrational place that will never bend to the static categorization required for a scientific discipline to form around it.
Except that it's not? A fire mage that has learned to cast a firewall can cast that firewall again. That's a reproducible effect. It can be measured, and it can be relied on to happen. Now, if we're discussing DnD's Wild Mages, you'd have a point, since they never knew exactly what they were going to get. That concept, however, does not exist in Thedas. In fact, it's quite the opposite, barring a respect of your character. A Rift mage will have spells associated with that
school of magic. Note, I bolded school because it drives home a point from earlier in this post: Being born a mage doesn't mean you can't be educated, and that education can indeed include magic, at it's very core.