School of Arithmancy

The School of Arithmancy is a discipline within the arcane arts that merges magic with the power of mathematics. Arithmancers believe that the universe is a complex equation, and by understanding the fundamental principles of numbers, geometry, and patterns, they can manipulate reality itself. Wizards who study Arithmancy use mathematical precision to enhance their spells, solve problems, and predict outcomes with uncanny accuracy.

Mathematical Precision

2nd-level Arithmancy feature

Beginning when you select this school at 2nd level, your understanding of numbers and patterns allows you to cast spells with greater accuracy. When you cast a spell that requires an attack roll, you can choose to roll with advantage. You can use this feature a number of times equal to your proficiency bonus. You regain all expended uses when you finish a long rest.

In addition, when you make an Intelligence (Arcana) check to understand a magical effect or solve a puzzle, you have advantage on the ability check.

Geometric Reconfiguration

6th-level Arithmancy feature

At 6th level, your understanding of geometry allows you to adjust the shape and area of your spells with precision. When you cast a spell that creates an area of effect, you can use your Geometric Reconfiguration feature to alter the shape of that area in one of the following ways:

Line to Cone. Convert a line with a length into a cone of half the line's length.
Cone to Line. Convert a cone into a line that extends twice as far as the cone’s length.
Sphere to Cubes. Convert a sphere into two cubes, each with sides equal to half the diameter of the sphere.
Increase Size. Increase the radius, length, or width of the spell's area by up to 10 feet.
Decrease Size. Reduce the radius, length, or width of the spell's area by up to 10 feet.

You can use this feature a number of times equal to your Intelligence modifier (minimum of once). You regain all expended uses when you finish a long rest.

Prime Factorization

10th-level Arithmancy feature

At 10th level, you can identify and exploit the weaknesses in any arcane or physical structure using prime numbers. When you cast a spell that deals damage, you can designate one creature or object affected by the spell to become vulnerable to that spell's damage type for the duration of the spell. If the target is immune, it instead becomes resistant; if it is resistant, it loses that resistance.

Once you use this feature, you can’t use it again until you finish a short or long rest.

Law of Equivalence

14th-level Arithmancy feature

At 14th level, your mastery of mathematical balance allows you to create a protective equation that equalizes damage and effects. When you are hit by an attack or affected by a harmful spell, you can use your reaction to activate the Law of Equivalence.

Balancing the Equation. The damage you take from the attack or spell is reduced by half the damage. The attacker takes damage equal to the amount reduced.

Parallel Effect. If the attack has a harmful effect, you can apply that effect to a creature within 30 feet of you as well, using your spell save DC.

You can use each of these abilities once, after which you can’t use them again until you finish a long rest.