School of Mathemagics (HB)

You search for the logical concepts behind the arcane in mathematics and numbers and use this knowledge to manipulate the spells you cast from the most basic building blocks up.

Arcane Algebra

When you transcribe a spell, you can choose to either double the time spent transcribing and half the cost or double the cost to half the transcription time.

Basic Arithmagical Theorems

Starting at 2nd level, spending years sharping your knowledge of basic numerical properties has allowed you to apply them in practice and alter the core of spells and other magical effects in many unthinkable ways.

You choose to focus on an arithmagical property, which is detailed under “Arithmagical Properties” below. Many properties enhance your magic in some way. You can apply only one property per turn.

When you gain certain wizard levels (6th, 10th, and 14th level), you choose one additional property to focus on. You may also change one of your focus properties to another property you know whenever you finish a long rest.

If a property has prerequisites, you must meet them to learn it. You can learn the property at the same time that you meet its prerequisites. A level prerequisite refers to your level in this class.

Additionally, when you gain a level in this class, you can choose one of the properties you currently focus on and replace it with another property, including one that you could learn at that level.

You can't use this feature more than twice until you finish a long rest. You can use this feature 3 times between long rests starting at the 5th level, and 4 times between long rests starting at the 17th level.

If you roll initiative and have no uses remaining, you regain one use of it.

Associative Magic

Prerequisite: 8th level
When you or an ally you can see within 30 ft of you is targeted by a spell, as a reaction, you can swap the space of you or your ally with another creature (including you), assuming that creature is also willing and is within 30 ft of you.

Alternatively, you can force a creature that you can see within 30 ft of you to make a Constitution saving throw. If the creature is unwilling or hostile to you, it makes this save with advantage. On a failed save, you or your ally and the creature may swap each other's space.

In either case, the swapped creature now becomes the new target of the spell that triggers your reaction.

Commutative Magic

Prerequisite: 4th level
While you are concentrating on a Spell, you can use your Action to move the effect to another point or target within 30 ft. of it. The new point or target must be legal for the Spell. Any spell effects end immediately on targets and places that are no longer targeted by the Spell.

Distributive Magic

When you cast a spell that affects you or other creatures that you can see, you may choose a number of creatures equal to your Intelligence modifier. The chosen creatures automatically succeed on their saving throws against the spell, and they take no damage if they would normally take half damage on a successful save.

Identity Magic

Prerequisite: 16th level
When you cast a spell that targets a creature and it has resistance or immunity to your spell effect or damage, you may choose to ignore resistance and treat immunity as resistance. Creatures that have resistance to a certain effect of the spell make the saving throw against it with advantage.

Inverse Magic

Prerequisite: 12th level
Whenever you successfully counter a spell with Counterspell, you can choose to turn the original spell on its caster instead of ending it. The spell uses the slot level, spell save DC, spell attack bonus, and spellcasting ability of the original caster, but is otherwise treated as if you cast the spell centered on it.

Zero Magic

When you cast a spell that forces a creature to make a saving throw and it succeeds or suffers no effects, you may regain a spell slot of half the level (round down; minimum of once) of the spell slot that was expended to cast that spell. If the spell affects multiple creatures, all creatures must succeed on their saving throws or suffer no effects for you to benefit from this feature.

Advanced Geomagical Theorems

Starting at 6th level, when you cast a spell or cantrip, you may also choose to manipulate the spell you cast that has an area of effect radius in the following ways:

• Line: When the spell you cast hits an object or a creature, you can make it bounce off once (following laws of physics), potentially affects more than one target.
• Cone:
  • If the Spell deals damage, creatures at the thin end of the cone have advantage on the saving throw against it, but the number of damage dice is double.
  • If the Spell deals no damage, creatures on the broad end of the cone have disadvantage on their saving throw against it.
• Cube:
  • If the Spell forces the creature(s) to make a Dexterity saving throw, Large or larger creatures make the save with disadvantage; Small or smaller creatures make the save with advantage.
  • If the Spell forces the creature(s) to make a Strength saving throw, Large or larger creatures make the save with advantage; Small or smaller creatures make the save with disadvantage.
• Sphere: You may choose to trade off between the area of effect (the radius), the damage, and the spell duration. If the area of effect is involved in the equation, you must quarter the value of one of the factors in the equation for the trade-off to be valid. For example, if applicable, you may:
  
  • Double the duration and quarter the radius (e.g. Sleep at 1st level lasts for 2 minutes if the area of effect is a 5-foot-radius sphere)
  • Double the radius and quarter the damage dice (e.g. Fireball at 3rd level does 2d6 fire damage on each creature in a 40-foot-radius sphere)
  • Double the damage dice and half the duration (e.g. Cloudkill at 5th level does 10d8 poison damage for 5 minutes)
• Cylinder: Each creature that moves no more than half its speed during the round makes the save with advantage; otherwise, it makes the save with disadvantage.

You can use this feature twice. You regain all expended uses when you finish a long rest. You can use this feature 3 times between long rests starting at 10th level.

Universal Theory

Starting at 14th level, you are able to use your intellect and knowledge of the basic working of the world to succeed in most of your tasks. When you make a roll that uses Wisdom or Charisma, you can use your Intelligence instead. You can use this feature a number of times equal to your Intelligence modifier (a minimum of once). You regain all expended uses when you finish a long rest.

Additionally, whenever you fail a saving throw on a magical effect that charms or frightens you, as a reaction, you can try explaining the logical workings of the effect to yourself, which immediately lets you reroll the save. You may also extend this benefit to your allies if they are within 10 ft of you and they must be able to see or hear you.