This is based off the job from Final Fantasy Tactics.

An arithmetician is someone who casts magic through a complicated, yet powerful means of doing so. Most wouldn't go down this path, as it seems unorthodox, and hard to wrap around, but those who do can gain great power with their talents.

Weaker Numbers

Starting when you pick this subclass, you gain access to what is called "weaker numbers". These numbers are called this for their lack of usefulness in arithmetic based casting.

When you cast a damaging spell, you can choose to use a prime number. If the number rolled for damage is a prime number, you can add one more damage dice to the total, but if it isn't prime, you fail the casting of the spell.

The amount of damage dice this adds increases to 2 at 5th level, 3 at 11th level, and 4 at 17th level.

Enemy's Numbers

At 2nd level, when you cast a spell with a range of touch, you can instead make it a restricted range of sight. If you target a creature you can see, you can choose from exp or level, then a number out of 3 and 5.

If a creature meets the exp or level that is a multiple of the number you chose, then you can target that creature with your spell. If it is a damaging spell, then if any of your allies within a 30 feet radius of you meet the requirements set, they are also affected by the spell.

Calculations

Beginning at 6th level, whenever you take a long rest, you can think of numbers ahead of time in your sleep. You can roll one d6 and one d4, and subtract the number rolled on the d6 by the one rolled on the d4. You gain an extra spell slot equal to the number you get, unless it is zero or lower.

At 11th level, the d6 becomes 2d4, and at 17th level the d4 becomes a d2.

Advanced Numbers

Starting at 10th level, you have gained access to "advanced numbers". When you use weaker numbers, you can now choose from multiples of 3 or 5, along with prime numbers. Also, when you use enemy's numbers, you can use a multiple of 2 or 4, as well as use health instead of exp or level.

Soulbind

At 14th level, you now gain the power to bind your life force to an opposing foe, through the calculations you make. When you are about to be hit (but before you take damage), you can use your reaction to roll a 3d6. You can use 2 of those d6 to multiply together, and if the resulting number is a multiple of the damage you have taken or higher, the attacking creature takes the same damage as you do.