School of Arithmetic

The School of Arithmetic focuses on the fundamental ordering of the universe from the micro to the macro in mundane numbers beneath the incandescent veneer of the arcane sciences. A simple understanding of how altering a value or the scale of a physical force affects the fabric of reality allows a crafty Wizard to apply functions of their own design upon the variables within the weave which can be distilled into numbers.

Reusable Proof

2nd Level School of Arithmetic Feature

Beginning when you select this school at 2nd level, the time you must spend to copy a spell into your spellbook is halved when the spell text describes a geometric shape for the effect.

Sacred Geometry

2nd Level School of Arithmetic Feature

 The collection of secrets known as the Sacred Geometry is often ignored as scientific quackery or religious myth, but you have tapped into the knowledge of how the weave resonates in patterns and can alter the shape of the material plane itself when extracted from the unseen ether. You may optionally reshape your area of effect spells in the following ways:

• Any sphere or cylinder may have its radius increased by 5 ft by reducing its height by 10 ft. It must retain a height greater than 0.
• Any cube may double in length or width by halving the other.
• Any line spell with a 5 ft width may turn into a cone of half the length. For example, a 60 ft line turns into a 30 ft cone.
• Any cone spell may turn into a line with double the length. For example, a 30 ft cone turns into a 60 ft line.

Quick Division

6th Level School of Arithmetic Feature

Thinking quickly and practicing your division when danger is at hand may ensure that you or an ally is left with a remainder. You may use your reaction to roll either a d4, a d6, or a d8 to alter an amount of incoming damage for yourself or one ally within 30 ft. On a roll greater than 1, if the damage amount is divisible by the number rolled, then divide it before it is dealt. On a 1, if the damage amount is a prime number, then it is reduced to 0. In any other case, simply subtract the number rolled from the incoming damage before it is dealt.

Simple Addition

10th Level School of Arithmetic Feature

Sometimes returning to the basics yields results that you were not ready for as a novice. You may add your Intelligence modifier to the damage of cantrips. In addition, when you cast a ranged cantrip, you may expend a spell slot to target additional creatures with the cantrip. For each spell level, you may target 1 additional creature, requiring a separate attack roll or saving throw for each. You cannot target the same creature more than once with a single casting of your cantrip.

5th Postulate

14th Level School of Arithmetic Feature

You've disproven what everyone believes about straight lines. You see the curve of the Weave, and you can trace an unexpected path. You may ignore line of sight restrictions for spells targeting a creature behind total cover. If the creature is not invisible and has not taken the hide action, then your spell affects them as if you can see them clearly. If the creature is invisible or hiding, you may still cast the spell, and they are affected if they have remained in their last known location, such as when they only have 1 spot in which to hide behind a tree.

You may use this feature a number of times equal to your Intelligence modifier and regain all expended uses when taking a long rest.