The mathemagician combines an unparalleled understanding on mathematical concepts and theorems with an intuitive view on arcane magic, enabling her to augment her spells in new and often startling ways. By applying their knowledge of mathematics to arcane formula, a mathemagician is able to quantify and define the often nebulous powers which wizards typically control. By doing so, she reduces what some would call mystical power into an understandable (if complex) equation; one that can be manipulated, altered, and controlled.Though most mathemagicians are gnomes, any race with the appropriate mathematical and magical inclination is able to take up the mantle of the mathemagician. Elves are a notable exception, however, viewing the synthesis of mathematics to magic as tantamount to defiling a precious gift with ‘elaborate gnomish nonsense.’ Most mathemagicians are wizards, since the study of mathematics and wizardry are similar disciplines. Few sorcerers become mathemagicians, primarily due to lack of patience with mathematics or by the boredom caused by the somewhat repetitious calculations that are the bread and butter of the mathemagician.
Hit Dice: d4
Requirements
In order to qualify to become a Mathemagician, a character must meet the following criteria.
Skills: Knowledge (mathematics) 8 ranks, Spellcraft 8 ranks.Feats: Skill Focus (Knowledge (mathematics))
Spellcasting: Ability to cast 2nd level arcane spells.
Class Skills
The Mathemagician’s class skills (and the key ability for each skill) are Concentration (Con), Craft (Int), Decipher Script (Int), Knowledge (all) (Int), Profession (Wis), Search (Int), and Spellcraft (Int). See Chapter 4 of the Player’s Handbook for skill descriptions.
Skill Points at Each Level: 2 + Int modifier.
Class Level Base Attack Bonus Fort Save Ref Save Will Save Special Spellcasting 1 +0 +0 +0 +2 Arithmetic - 2 +1 +0 +0 +3 Magical Theorem +1 caster level 3 +1 +1 +1 +3 Magical Theorem +1 caster level 4 +2 +1 +1 +4 Magical Theorem +1 caster level 5 +2 +1 +1 +4 Magical Theorem +1 caster level 6 +3 +2 +2 +5 Magical Theorem +1 caster level 7 +3 +2 +2 +5 Magical Theorem +1 caster level 8 +4 +2 +2 +6 Magical Theorem +1 caster level 9 +4 +3 +3 +6 Magical Theorem +1 caster level 10 +5 +3 +3 +7 Magical Theorem +1 caster level
Class Features
All of the following are class features of the Mathemagician prestige class.
Weapon and Armor Proficiency: A mathemagician gains no new weapon or armor proficiency.
Spellcasting: A mathemagician continues training with magic. Thus, at 2nd level and every level thereafter, the character gains new spells per day and spells known as if she had also gained a level in whatever arcane spellcasting class she belonged to prior to adding this prestige class. She does not, however, gain any other benefit a character of that level would have gained (improved familiar abilities, metamagic or item creation feats, etc).Arithmetic (Ex): A mathemagician is able to do addition, subtraction, multiplication, division, exponents, roots, and the like almost instantly. She gains the ability to solve any mathematical problem as a free action. In addition, her analytical mind quickly accesses situations, allowing her to act while others are still debating the appropriate courses of action. The mathemagician may add her Intelligence modifier to her initiative rolls.
Magical Theorem (Su): Each time this ability is gained, the mathemagician learns how to apply one type of mathematics to her spells. Magical theorems are divided into seven disciplines (Algebra, Geometry, Calculus, Matrix Algebra, Complex Analysis, Topology, and Statistics). The first magical theorem in each discipline may be learned by any mathemagician, but subsequent theorems may only be learned once the preceding theorems in the discipline have been mastered.
AlgebraI) Subtraction: The mathemagician simply subtracts energy from the sum total of what is required to alter her spells. When applying a metamagic feat to a spell she casts, she subtracts one from the spell level increase the metamagic feat imposes upon the spell.II) Addition: The mathematician adds additional energy to her spells, rendering them more effective. She adds one to each dice of variable numbers in the spell’s description. Thus, a spell that deals 4d6 damage deals 4d6+4 damage when cast by a mathemagician with this theorem, and a spell that stuns a creature for 2d4 rounds now stuns the creature for 2d4+2 rounds.
III) Equation: By mastering algebra, the Mathemagician gains the ability to link two creatures together in an equation. As a standard action, she may designate two creatures, who each receive a Will saving throw (DC 10 + the mathemagician’s class level + her Intelligence modifier). If both creatures fail their saving throw, they are linked together for one round per class level the mathemagician possesses. If one of the linked creatures takes damage, loses hit points, heals damage, or suffers a status effect (such as becoming sickened or petrified), the other creature is affected as well, suffering the same effects, taking the same amount of damage, or healing the same amount of hit points. If one of the linked creatures dies, the remaining creature must immediately succeed at a Fortitude save against this ability’s DC or gain two negative levels. If one of the creatures is immune to a form of damage or a status effect, both creatures are immune.
GeometryI) Euclidian Geometry: The Mathemagician gains a better understanding of distances and spacial relations. She adds five feet per class level to the range of each of her spells.II) Riemann Geometry: The mathemagician’s understanding of Riemann Geometry is such that she is able to curve her spells around obstacles. When casting any spell requiring a ranged touch attack, the Mathemagician can ignore any benefit the target gains from cover, and never risks harming an ally in melee or grappling with a target.
III) Lobachevskian Geometry: The mathemagician understands the curvature of the multiverse and can warp it, allowing her to reach her target from safety. She may cast any of her “Touch” range spells as if they had a range of “Close,” though doing so requires a ranged touch attack rather than a melee touch attack.
CalculusI) Limits: The Mathemagician can simplify otherwise complex spells by creating a function with a set limit which she can calculate as a free action. This allows her to maintain concentration on a single spell as a free action. While concentrating on a spell in this manner, the mathemagician may take other actions, including casting spells, as normal.Matrix AlgebraII) Integrals: The mathemagician can integrate her spells, making them more cohesive and difficult to break down. The DC to dispel a mathemagician’s spells increases by +4.
III) Derivatives: The mathemagician can differentiate her spells, allowing them to function in non-continuous units of time. After a spell is cast, the mathemagician can choose to differentiate her spell as a move action, causing the spell to become suspended. She may recall her spell as a move action, at which point it continues from the point at which it had been differentiated. The mathemagician may differentiate each spell only once.
I) Matrix: The Mathemagician is able to create a matrix, allowing the mathemagician to include or exclude creatures from the spell’s effects. When casting a spell, she may designate up to one creature per class level to be affected by the matrix. These creatures are either affected by the spell to the exclusion of any other creatures within the spell’s area, or are excluded from the spell’s effects completely, as determined by the mathemagician. If the mathemagician places a spell which normally only affects a single target within a matrix, its energies are strained, granting each creature within the matrix gains a +2 bonus to its saving throw for every creature within the matrix.Complex AnalysisII) Determinant: By linking her spell to another spell within a matrix, the mathemagician is able to nullify the second spell as it is being cast. She gains the ability to attempt to counterspell an opponent’s spell as an immediate action, as if she had readied an action to counter that spell on her last turn. The mathemagician must still identify and attempt to counter the spell as normal.
III) Codeterminant: The Mathemagician is able to entrench spells she counters within a matrix of her own creation, reflecting spells she counters through the use of her determinant theorem back at their caster. The caster is treated as if he were the original target of the redirected spell.
I) Imaginary Spell: The Mathemagician masters the use of imaginary numbers, weaving them into her spells. Once per day, after she casts a spell, she may declare that spell to have been an imaginary spell. The mathemagician does not lose memory of the cast spell, and any spell slot she used to cast that spell is not expended.TopologyII) Imaginary Self: As her knowledge of complex analysis increases, the mathemagician realizes that she may not exist. She may become incorporeal for up to 1 round per class level each day. She may become incorporeal on a number of different occasions during any single day, as long as the total number of rounds spent incorporeal does not exceed her class level.
III) Imaginary Opponent: The Mathemagician realizes that her opponent may be imaginary as well, and is able to force him into an imaginary state. As a standard action, she may target any opponent within 60 feet of herself, who must then attempt a Will saving throw. On a failure, the opponent becomes imaginary for one minute per class level she possesses. Creatures the opponent interacts with are allowed a Will saving throw (10 + half the creature’s Hit Dice + its Charisma modifier) to disbelieve the creature’s existence each time they interact with the creature. On a successful disbelief of the imaginary creature, those who disbelieved it treat it as an illusion, essentially becoming immune to most anything the creature attempts to do.
I) Manifolds: The Mathemagician can create complex figures by combining copies of similar figures. When determining the area of any shapable spell, the mathemagician increases her caster level by one half (+50%).StatisticsII) Homomorphism: The mathemagician learns how to transform variables from one set to another set while still preserving the values of the original. She may alter any area-affecting spell she casts so that it affects an area different from its normal area, as selected from the following list: Cylinder (10-foot radius, 30 feet high), Cone (40 feet long), Cubes (four 10-foot cubes), or a sphere (20-foot radius spread). The spell works otherwise normally in all respects.
III) Knot Theory: The Mathemagician understand mathematical knots, allowing her to twist, tangle, and shape her area effect spells. The mathemagician can alter any of her area effect spells so that they exclude any square or squares within their area of effect, as determined by her. She may change which squares are affected by a continuous spell as a free action on her turn.
I) Advantaged Mean: The Mathemagician learns to skew the law of averages, and may take 11 on any action on which she would normally be able to take 10. In addition, she may choose to take 11 on caster level checks, including dispel magic checks and checks made to overcome spell resistance.II) Advantaged Mode: Whenever the mathemagician casts a spell with variable effects, she may choose to take the advantaged average on each dice, as shown on the chart below, instead of rolling.
Die Advantaged Average d3 2 d4 3 d6 4 d8 5 d10 6 d12 7 III) Outliers: The Mathemagician learns that occasional values are created which exist beyond the accepted ranged of results, and manipulates such values to her benefit. Once per day per class level, the mathemagician gains +20 on a single skill check or caster level check she makes.
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