Job: Arithmetician
Branching Class: Any mage
Secondary Class: Any mage
3rd Class for skill pulls: Any mage
Role: DPS or Healer

Some abilities:

Sum - Creates a small circular field. While you are inside the field, increases your spell potency by 5% for each party member and enemy inside the field. Lasts 20s. 120s recast.
Difference - Creates a large circular field. Deals damage over time to all enemies inside the field at 60 Potency, but potency is reduced by 15 for each party member inside. Lasts 15s. 40s recast.
Redistribute - Single target spells damage nearby enemies instead, and AoE damage spells damage the target instead at increased potency. (Undecided recast)