An Arithmancer is a wizard who had specialized in the field of Arithmancy, or the study of the magical property of numbers.  Arithmancy Wizards are wizards who understand how to manipulate the mathematical side of The Weave, and use it to influence others and create destruction.

Mathmatical Divination

Beginning when you select this school at 2nd level, The gold and time you must spend to copy a divination or evocation spell into your spellbook is reduced by 25%

Numerology

Starting at 2nd level when you choose this school, you learn to calculate the magic numbers surrounding the date of the new day. When you finish a long rest, roll a d12 a number of times equal to your proficiency bonus. Consult on the table below to find your pool of Numerology Dice.  Once per turn you can add these dice to any attack roll, saving throw, or ability check made by you or a creature that you can see.

Each Numerology Dice can be used only once. When you finish a long rest, you lose any unused calculated rolls.

 

D12 Roll	Numerology Dice
1	-1
2	-1
3	-3
4	-4
5	-5
6	-6
7	1
8	2
9	3
10	4
11	5
12	6

Calculated Strike

Starting at 6th level, you add your Intelligence modifier to the damage you deal with any wizard cantrip.

 

The Agrippan method

Starting at 10th level, you understand the numbers that compose a person.  From their name, birthday, height and beyond, you understand the magic behind the numbers that makes up this person.  As such, when talking to them you can tap in to your own personal numbers and adjust them to better attune yourself to talking with them.  You have advantage on Charisma based skill checks against one non-hostile creature of your choice that you can see or hear for 1 minute.  The creature does not know about this affect, and is unaware of any magic at play.

 

You can do this a number of times equal to 1+ your Charisma Modifier per Long Rest.

The Chaldean System

Starting at 14th level, you understand the mathematics involved in casting spells, and learn the ability to manipulate it.  When you finish a long rest, you receive a number of Enhancement points equal to 1 + your Intelligence Modifier.  When you cast a spell that deals damage, you expend points to change the dice that are rolled for the spells damage.

You can spend an enhancement point to increase or decrease the dice size by one size per point spend.  When you decrease the dice size, for each size you go down, increase the number of dice rolled by 3.  If the dice size increases, keep the same number of dice rolled.  You can go up to a dice size of a d12 or down to a d4.

If the spell has a duration other than instantaneous, the damage is only changed on the first time the damage occurs.

If the spell deals multiple types of damage, such as meteor swarm, only one type of damage can be enhanced.

You lose any unused enhancement points when you finish a long rest.