Arithmancy

Arithmancy is a magical discipline that studies the magical properties of numbers, including (but not limited to) predicting the future with numbers and numerology. Those who practiced Arithmancy were called Arithmancers.

Arithmancy was an elective subject offered from the third year on at Hogwarts School of Witchcraft and Wizardry, the homework assignments of which included writing essays that required the consultation and/or composition of complex number charts.

Notable Arithmancers

 * Bridget Wenlock - the archetypal example; she was a the celebrated witch who first discovered the magical properties of the number seven in the 13th century.
 * Septima Vector - Taught Arithmancy and Advanced Arithmancy Studies at Hogwarts School of Witchcraft and Wizardry for at least six years (possibly more).
 * Hermione Granger - famous high-ranking official in the Department of Magical Law Enforcement who strongly contributed to Voldemort's downfall and translated the Tales of Beedle the Bard into English from runic.
 * Percy Weasley
 * William Weasley
 * Bartemius Crouch Jr. - Death Eater who made Lord Voldemort's second rising possible.

Arithmantic texts

 * Numerology and Grammatica, a third year textbook at Hogwarts.
 * New Theory of Numerology, which Harry Potter gave to Hermione Granger for Christmas in 1995.

Etymology
Arithmancer and Arithmancy come from the Greek αριθμός (arithmos), meaning "number", and μαντεία (manteia), meaning "divination". Hence "Arithmancy" literally means "number divination", which is fitting.

Behind the scenes

 * In reality, Arithmancy is the study of the magical properties of numbers. However, this would include numerology, which reconciles both JK's statement about the definition of Arithmancy and the fact that known Arithmancers like Bridget Wenlock have only been known to study things other than this.
 * Hermione has expressed open contempt for the subject of Divination, yet has also proclaimed that Arithmancy (in which numerology is prominent) is her favourite subject. Whilst this may seem contradictory at first, it should be remembered that Arithmancy applies much more rigorous and mathematical approaches to predicting the future (which the scientifically-inclined Hermione would respond to), unlike Divination, which she detested as it seemed to be "a lot of guesswork".

Appearences

 * Harry Potter and the Philosopher's Stone (video game)
 * Harry Potter and the Chamber of Secrets (video game)
 * Harry Potter and the Prisoner of Azkaban
 * Harry Potter and the Order of the Phoenix
 * Wizard of the Month

Notes and references
Harry Potter and the Goblet of Fire (only mentioned)