Since Arithmetician was name dropped as a profession out there, I've been trying to imagine what exactly it does and what it would look like within the setting. Primarily, I'm wondering how it would differentiate from Eorzea's own "math mages", i.e. Arcanists.

I imagine there might be similarities in the same way that geomancy and astromancy have similarities, or Eastern vs. Western summoning, but since I know almost nothing about math and have never played the Tactics games, I'm a bit stumped.

So, in a nutshell: theoretically speaking, exactly what does an Arithmetician do to manipulate aether to cast spells?