Arithmomancy refers to an ancient Greek divination technique through numbers. The term is composed of words ἀριϑμός arithmós (number) and μαντεία manteía (divination). A certain value was assigned to each letter. In fights, for example, it was predicted which of the opponents would win, i.e. the fighter whose name had the higher value.
This technique was also very common in Mesopotamia.
In the Harry Potter books, the alternate spelling arithmancy is used.