The Wizards are major characters in Terry Pratchett's Discworld series. Their title is said to be derived from the archaic word "Wys-ars", meaning one who, at bottom, is very wise. In addition, Rincewind once said in Sourcery that the plural of wizard was once war.
Wizard magic is known to be taught at the Unseen University in Ankh-Morpork, Bugarup University in XXXX and Krull University in the secretive nation of Krull, as well as the recently-established Braseneck College in Pseudopolis. It is very much a scholarly study, largely (many believe) to prevent anyone outside the universities realising how easy it really is.
In fact, the older wizards tend not to understand how magic actually works at all, instead relying on centuries of lore to achieve their effects. Younger wizards enthusiastically experiment, pushing back the boundaries of knowledge and making new discoveries about the nature of the universe. They don't understand how magic works either, but have much more exciting words to explain why not. These often invoke images of particle physics (the events of TSOD are brought about by an experimental apparatus to split the "thaum", for example).
Really, wizard magic is telling the universe what you want it to be like, in terms it can't ignore. This is very draining, due to the Law of Conservation of Reality (which states it takes the same effort to do something with magic as it would to do it mundanely). This is why most wizards store magic in a staff (with a knob on the end). The most complicated parts of most spells aren't the effects, but the baffles to ensure the wizard survives. Magic is treated by its practitioners on the Discworld in a similar fashion to how nuclear weaponry is treated in the real world: it does no harm for people to know you've got it, but everyone will be in trouble if it gets used.
An eighth son of an eighth son is automatically a wizard. When a wizard nears death,(on the discworld, all practitioners of magic can foresee their own deaths, as well as seeing the character, Death) he formally passes on his staff to a wizard just born. Any children a wizard has will also be wizards. If wizard himself happens to have an eighth son, this child will be a "wizard squared" or "Sourcerer"; so called because he is a source of magic - a Sourcerer generates his own magic, and can therefore do just about anything with no effort. This is very dangerous, both because absolute power corrupts absolutely, and because it increases background magic levels considerably, which is why a rigid celibacy law for wizards means there are no sourcerers any more (although Sourcery records an exception).
In the earlier Discworld novels, wizards (at least the ones of the Unseen University) are described as belonging to one of the eight orders of wizardry, currently named:
Ymper Trymon
The Ancient and Truly Original Brothers of the Silver Star
The Brotherhood of the Hoodwink (The Hoodwinkers)
The Order of Midnight
The Venerable Council of Seers
The Ancient and Truly Original Sages of the Unbroken Circle
The Sages of the Unknown Shadow
Mrs Widgery's Lodgers
The Last Order (The Other Order)
Despite their names, these orders are not all that ancient, their original names having been muddled by war and time. This is with the exception of Mrs Widgery's Lodgers, who stem from the early days of UU when the Tower of Art was the only building on campus and some students had lodgings elsewhere in Ankh-Morpork. Since the first few books, however, this system has had no visible impact whatsoever, and seems to have been forgotten. This may be something to do with the fact that all of the top wizards in each order were turned to stone in The Light Fantastic.
Wizards are also classified into levels, which once corresponded to actual magical prowess, but now are rather more indicative of political power. This may be a parody of the "character levels" in many role-playing games, and has also become less significant in later books.
The leader of all wizards, according to UU, is the Archchancellor of UU, the first among equals (the equals being the other eight-level wizards). There are a total of eight eight-level wizards, and the number becomes progressively higher as the level decreases. Presumably, as it is far better for those who have the skill to be tutored than to possibly cause horrendous damage to the space-time continuum, there is an unlimited number of first-level wizards. Because of these limitations, it is periodically common to ascend through the ranks by assassinating superiors, but under the assassination-proof Archchancellor Mustrum Ridcully this practice seems to have fallen out of favour, for a time.
People without magical ability are "level zero". It was the opinion of many tutors at the time Rincewind was a student that he had a level that was possibly in minus figures, and that the overall magical potential of humanity would actually increase after his death.
The Bursar: Mathematically gifted yet completely insane keeper of the University's accounts
The Librarian of the Unseen University: an orangutan, due to a freak accident in The Light Fantastic. Does not want to be changed back.
Ponder Stibbons: Chair of Inadvisably Applied Magic and Reader of Invisible Writings. Due to his relative youth, he is arguably the only member of the UU staff who actually does any work.
Rincewind: The UU's Egregious Professor of Cruel and Unusual Geography, and, by his own admission, a complete coward.
Alberto Malich: Founder of the Unseen University, now butler to Death.
Bill Rincewind: Archchancellor of Bugarup University on Fourecks. May be related to the above Rincewind; if so he seems to have been very fortunate in his genetics.
Mr. Sideney: A member of Teatime's gang who break into the Tooth Fairy's castle in Hogfather.
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