Magic by the Numbers

Master of the Five Magics follows Alodar, a young man from a fallen noble house trying to win the hand of a queen by proving himself in a hard-magic system built from five distinct, strictly rule-bound disciplines — thaumaturgy, alchemy, magic, sorcery, and wizardry — each with its own price and its own limits. Lyndon Hardy's original trilogy, continuing through Secret of the Sixth Magic and Riddle of the Seven Realms, has Alodar master each discipline in turn, before a later book, decades on, adds a fourth-generation story (The Archimage's Fourth Daughter) to the same magic-numbers conceit.