A three-minute mage referred to a mage with a talent spec that combined the Presence of Mind and Arcane Power abilities with a powerful burst damage spell, usually Pyroblast. This designation got its name from the fact that Arcane Power and Presence of Mind have 3 minute cooldowns. Since Cataclysm, to get Pyroblast you have to choose the Fire tree at level 10, and before being allowed to spend points in Arcane to get Presence of Mind and Arcane Power you have to get the 31-point talent Living Bomb. Since you won't have enough talent points to even get to Presence of Mind, let alone Arcane Power, the Cataclysm actually killed this spec.