A subject taken by some students at Hogwarts is Arithmancy.
Throughout the Harry Potter series, we don't seem to be given much information as to what arithmancy actually is.
For example, Defence Against the Dark Arts involves spells and techniques to battle dark creatures/wizards, History of Magic is... supposed to be history of magic (but under Professor Binn's tutorship is mostly just goblin rebellions), Muggle Studies is the study of Muggles, Transfiguration is turning one object into another, Divination is trying to see into the future and Astronomy is studying the sky, stars and constellations and what they mean.
What actually is arithmancy?
Is it just Muggle mathematics, or is it a complicated business used in spell creation (a theme often seen in fanfiction), or...?