Oath of Numeracy (5.5e)

In hidden alcoves, caves, and under cover of dark... Ancient Mathematicians practiced the numeric arts in secret. In their formulas, they believed that they were looking at the very essence of creation. Knights of the Oath of Numeracy continue the works of these great Mathematicians, using their faith in and knowledge of the great numerical arts to defend creation, extend the limits of human knowledge, and impart the knowledge of mathematics on the common man.

Tenets of Numeracy:

The tenets of the Oath of Numeracy focus on two things - preserving the beautiful universe that gives us the imperfect system known as Mathematics, and teaching this system to others. 

Protect this Beautiful System: Mathematics is the imperfect way that us mortals comprehend the perfect system that is creation. You must work to protect that system from harm.

Enlighten Others: Mathematics can be used to improve countless lives - but only if the masses knows how to use it. You must share your knowledge of Maths with any creature who wishes to become enlightened with this knowledge, and you must strive to find worthy students. 

Seek Further Knowledge: The knowledge mortals hold is incomplete. You must always be willing to learn more, and share it with others once you have achieved this knowledge. 

Oath Spells and Casting

Oath of Numeracy paladins can use their deeper understanding of Maths and the universe around them to twist the inherent magic around them into spells. However, doing so is a process that requires years of study, and intelligence.

This study ensures that you always have certain spells ready; when you reach a Paladin level specified in the Oath of Numeracy Spells table, you thereafter always have the listed spells prepared.

Oath of Numeracy Spells

Paladin Level	Spells
3	Absorb Elements, Longstrider
5	Enhance Ability, Enlarge/Reduce
9	Haste, Protection from Energy
13	Confusion, Death Ward
17	Passwall, Telekinesis

 

As well, when you take this subclass at level 3, your Spellcasting Ability becomes Intelligence.

Spell Save DC = 8 + your proficiency bonus + your Intelligence modifier

Spell Attack Modifier = your proficiency bonus + your Intelligence modifier

Extension Question

 As a bonus action, you can expend one use of your Channel Divinity to force a difficult Maths question into the mind of a creature you can see within 31.4 feet of you. The creature has a minute to complete this Maths question, during which time they have disadvantage on Concentration saves. At the end of each of it's turns, it may make an Intelligence Saving Throw, with disadvantage if they have less intelligence than you. They may also use an action to make this saving throw without disadvantage. On a success, they solve the question, and the effect ends.

While the creature has this question in their mind, your melee weapon attacks deal an extra  psychic damage for each time the creature has failed the saving throw. (x is a random number between 0 and 17).

 

You can only have this effect active on one creature at a time.

 

Calculated Strikes

Starting at level 3, when making a melee weapon attack while wearing medium or heavy armor, you can use your Intelligence modifier, instead of Strength or Dexterity modifier, for the attack and damage rolls.

 

At level 6, you use your Intelligence Modifier instead of your Charisma Modifier for Aura of Protection.

Additionally, at level 11, the damage of your Radiant Strikes feature is replaced by  psychic damage, where x is a random number between 0 and 17. 

The Law of Large Numbers and Probability

Starting at 7th level, the calculus of the universe starts to alter around you, reflecting theoretical probabilities instead of experimental.

Once per round, you may warp reality when a creature in your Aura of Protection makes a D20 Test. After they roll the dice, but before the result of the roll is disclosed, you can replace the number rolled with a 10. (Creatures with Legendary Resistance instead have their roll replaced with a 19, as their average performance is much higher.) You can use this feature a number of times equal to half of your Proficiency Bonus, regaining all expended uses on a Long Rest. 

 

Inverse Operations

Starting at level 15, when a creature hits you with an attack, you may use your reaction to gain AC equal to your Proficiency Bonus, potentially turning the hit into a miss. This bonus lasts until the end of your next turn. Additionally, subtract your proficiency bonus from all attacks you make until the end of your next turn. When a creature hits you with a melee attack during this time, reduce the damage taken by 2d4 and deal that much damage as psychic damage to the attacker. 

Alternatively, when you miss a creature with an attack, you may add your proficiency bonus an additional time to your attack rolls until the start of your next turn, potentially turning the miss into a hit. You also deal damage from your Divine Strike an additional time. Additionally, subtract your proficiency bonus from your AC until the start of your next turn.

You cannot be under both effects of Inverse Operations at the same time, and cannot use Inverse Operations while already under it's effect. You can use this ability a number of times equal to your proficiency bonus, gaining back all expended uses on a Short Rest.

Having your π and Eulering it too.

At level 20, you have unlocked the ability to use your mathematical knowledge to extend the range of your effects, and enhance your own physical prowess.

As a bonus action, enter a perfect state of mathematical focus. For the next minute, you gain the following benefits.
-When you take the attack action, you may make a number of attacks equal to Euler's Number, rounded to the nearest whole number. (3)

- Add π (rounded down, so also 3) to any Ability Check, Saving Throw, or Attack Roll creatures of your choice in your Aura of Protection make.