Magic is not the converse of Reason. Indeed, many branches of Magic are rigorously logical, even mathematical.
At collegia there are two scholae, or viae: the Way of Three and the Way of Four. The Way of Four is the more mathematical, dependent more on formulae and chemicals, but also on astrology and numerology. The Way of Three is more intuitive. Illusionism resides here, and clairvoyance.
Or, perhaps clairvoyance etc. is inborn and cannot be taught. The Way of Three is for something else.
Certain heretics, such as the Bogomils and the Cathars, teach the Way of Two—the Dark and the Light—but educated people understand this is too simplistic. A handful of obscure sects even teach the Way of One, but this is clearly foolishness or worse.
Combinations of Three and Four are potent. This is why Seven is a powerful number, as is twelve. Those are the strongest, for numbers beyond that cannot be said in a single word and are made up of compounds of the purer numbers. Hundred and Thousand have a certain power, but they are mixed, not pure. The same is true for twenty. Some numbers are strong from Roman times: V, X, L, C, D, and M. And special numbers, such as MDCLXVI (1,646). Or MDCXVI because it yields a doubled number, 1616, yet itself has no number repeated.
A newer sect is the Fifth Way, so named for the magic 3-4-5 triangle. They call themselves Pythagoreans, hearkening back to the ancient mathematician. They take the original curriculum and turn it inside out and upside down. Few understand their deliberately obscure writings. They are much concerned with alchemy and the Quintessence.
The Plague of 2100 and especially the persistent attacks by the Drow gave rise to an efflorescence of new magicks and methods. Many were simply old wine in new bottles, but even the most mundane recyclings had a new twist or at least a new focus, while the more creative produced really astonishing works.
At the same time, a contrary trend emerged: a glorification of ancient Rome and Greece, and a longing for a world before magic and monsters. The leading proponents of this rebirth called themselves Humanists, for their emphasis on things Human.
Those who are collegium-trained are scholars. They disdain to work common magic. Typically they enter a House or a noble court. A handful succeed and are fortunate enough to afford their own tower. They become famouse and attract their own followers.
There was a time, from about 1800 to 2100, that the Wild seemed to be tamed, or at least contained and kept at bay. There were enclaves of monsters here and there, but in general there was only petty fighting such as ever delights Men and Dwarves.