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TheArchDruid has an interesting post on them

By "wizard" here I don’t mean your common or garden variety fortune teller or ritual practitioner; we have those in abundance today. The wizard of the early Middle Ages in Europe and the Muslim world, rather, was a freelance intellectual whose main stock in trade was good advice, though admittedly that came well frosted with incantation and prophecy as needed. He had a good working knowledge of astrology, which filled roughly the same role in medieval thought that theoretical physics does today, and an equally solid knowledge of ritual magic, but his training did not begin or end there. According to Picatrix, the compleat wizard in training needed to get a thorough education in agriculture; navigation; political science; military science; grammar, languages, and rhetoric; commerce, all the mathematics known at the time, including arithmetic, geometry, music theory, and astronomy; logic; medicine, including a good knowledge of herbal pharmaceuticals; the natural sciences, including meteorology, mineralogy, botany, and zoology; and Aristotle’s metaphysics: in effect, the sum total of the scientific learning that had survived from the classical world.

Now it may have occurred to my readers that this doesn’t sound like the sort of education you’d get at Hogwarts, and that’s exactly the point. Whether you believe that the movements of the planets foretell events on Earth, as almost everyone did in the Middle Ages, or whether you think astrology is simply a clever anticipation of game theory that gets its results by inserting random factors into strategic decisions to make them unpredictable, you’ll likely recognize that a soothsayer with the sort of background I’ve just sketched out would be well prepared to offer sound advice on most of the questions that might perplex a medieval peasant, merchant, baron or king. Nor, of course, would someone so trained be restricted in his choice of active measures to incantations alone. This is arguably why so many medieval kings and barons had professional sorcerers and soothsayers on staff, despite the fulminations of all the dominant religions of the age, and why wizards less adept at social climbing found a bumper crop of customers lower down the social ladder.

The origins of this profession are, if anything, even more interesting. Pierre Riché’s useful study Education and Culture in the Barbarian West showed in detail how the educational institutions of the late Roman world imploded as their economic and social support systems crumpled beneath them. In Europe – matters were a little more complex in the Muslim world – they were replaced by a monastic system of education that, in its early days, fixated almost entirely on scriptural and theological studies, and by methods of training young aristocrats that fixated even more tightly on the skills of warfare and government. Only among families with a tradition of classical letters did some semblance of the old curriculum stay in use, and Riché notes that while that custom continued, those who learned philosophy, one of the core studies in that curriculum, were widely suspected of dabbling in magic. It’s not too hard to connect the dots and see how a subculture of freelance intellectuals, equipped with unusual knowledge and a willingness to stray well outside the boundaries set by the culture of their time, would have emerged from that context.

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