'Wizard' is actually a derogatory term for rogue Sorcerers - those considered too rebellious or dangerous to be schooled in the art of magic - which gives a certain amount of insight into the nature of the Wizard in Diablo III.
The female Wizard in Diablo III originally hails from the island Xiansai (which is located to the far North and has a culture which is similar to that of our Asia). Being young and highly rebellious, she was forced to travel from school to school in the hopes that she could be disciplined. Despite being highly talented (her skills surpassed the most elite of mages), she was constantly found learning dangerous and forbidden magic; not content to merely master the elements, she began to learn the Arcane and possesses the ability to bend time and reality.
Eventually, she was caught in the Ancient Repositories - the place where the most dangerous magic is housed. Valthek, a talented and well-respected mage caught her and confronted her. In the ensuing fight, the Wizard was able to overcome Valthek's magic and fled the city so that she could practice her new skills without opposition.
Female Wizard art.
Abd al-Hazir writes about a Wizard in his seventh journal entry:
"Owing to my lack of tolerance for those who would use magic towards their own nefarious ends, many have assumed that I am averse to the practice of the magical arts on a philosophical level. Nothing could be farther from the truth. My quarrel is with those sorcerers who dismiss the ancient traditions and teachings – teachings that have been honed over millennia in order to preserve respect for authority and the rule of law.
Recently the youth of Caldeum have fallen prey to the overblown stories of just such a delinquent wizard. That is correct: I used the uncouth term Wizard, not Sorcerer. It seems that even the title of a civilized magic wielder is too restrictive for this young upstart. Through my contacts at the Yshari Sanctum of the mage clans, I am one of the few who actually know the truth behind the rumors now sweeping our streets regarding this hellion who flaunts her magic irresponsibly.
This wizard was sent here to spend her formative years under the tutelage of the best mages in the world. Well, it seems they neglected to teach our wizard manners on her native island of Xiansai, for she was a rude and uncooperative student from the very beginning. Originally under the guidance of the Zann Esu mage clan, she was eventually handed over to the Vizjerei in the hopes that their strict and unbending discipline would break her anarchic spirit. Yet even the esteemed Vizjerei instructors were unable to rein her in. She was continually being caught seeking out dangerous and forbidden magics, heedless of the consequences to herself or anyone around her.
Although there is no truth to the tales that she actually ventured into the infamous Bitter Depths below the Sanctum, she was caught in the Ancient Repositories, where the most dangerous incantations are housed for the safety of the public. When confronted by the great Vizjerei mage Valthek and demanded to account for herself, she brazenly attacked him rather than face the punishment merited by her acts. Exaggerated stories of the battle are already being inflated to mythic proportions by the more rebellious of our city's youth, but suffice it to say that she did not actually best Yshari's most powerful mage in single, honorable combat. The details of the encounter remain unclear, as Valthek has yet to regain consciousness, but it has been verified by reliable sources that she relied on trickery and deceit to bring the great man low. I have also been assured that the extensive property damage was chiefly the result of Valthek's magical prowess, not the upstart wizard's. As to where she is now, no one rightly knows, for she fled the city immediately after the encounter.
It is not my goal to alarm, but I find this situation disturbing. We now have a rebellious wizard, young and inexperienced, wandering the world, dabbling in powerful magics she does not understand. Those wiser than you or I determined long ago that certain schools of magic were too dangerous and forbade their practice. It is those magics that this wizard seems determined to explore – magics centered on manipulating the primal forces from which reality is constructed. Imagine, a headstrong nineteen-year-old youth, able to warp time itself to her will! The thought is truly terrifying. It is my honest hope that this self-styled wizard chooses never to return to Caldeum."