The Mathemagickal Manual

25th dawn, Thermidore, 4855
For scholarly purposes, Amadore X. Raywalker
Clyburn Town, Summit Publishing House
==Preface==
Modern Aquila is ever-changing in values, composition, and inhabitants, and you're unlikely to find a societal circle where this is more evident than in the intellectual one. In the last couple of years of peacetime, especially in the many Realms of Dreiton in which I project most of my readers to dwell, there has been a clear boom in the amount of young men and women attending our institutions of higher education. With the blessing of Dantalion, they march proudly through the doors, ancient or modern, of schools ranging from the world-renowned University of Dreiton to our own Mt. Clyburn College. Their areas of study are anything and everything from linguistics and government to the booming fields of mathematics and physics. On that latter intellectual sect we base the information in this article.
While this new proclivity for the sciences and humanities is deep and widespread, even more widespread are two age-old tendencies of man: those toward battle and magic. Today's world, while continuing to pull away from the whims of unknown forces and deities, remains mostly rural and filled with subsistence living and danger. These two phenomena - increasing intellectualization and the lingering, widespread dangers of the unknown - have shaped the rise of a new kind of warrior.
They are the Mathemagicians, who hone and employ intricate mixtures of pure mathematics, statistics, and physics to tap into the arcane and manipulate the world as we know. While they are unable to go toe-to-toe in epic clashes as a bulky knight would or summon great columns of dark lightning as a sorcerer would, their unique insight into the world and its invisible code make them both fearsome opponents and a desirable occupation for those with a scholarly inclination.
==The Mathemagician==
===Overview===
The mathemagician (less commonly referred to as the arithmancers), being a quantitative take on the Old Ways, are classified first and foremost into the magical half of Aquilan warrior classes. The common thread is most visible in their physical and mental stats; mathemagicians enjoy monstrous intellect and often strong agilities and luck, but lack sorely in strength and endurance. Immediately, then, they find a home in battles with less of a physical toll. However, their similarities with the bulk of their mage compatriots sharply diverge from there. Whereas other practitioners of the arcane focus on harnessing destructive black magics, conjuring deadly beasts and demigods, or impressive feats of healing, these arithmancers work and cast a slyer type of magic. The specifics of their functions and incantations vary along two branches, but in general the "spells" vary from feats as mundane as spoofing the amperage of a redstone circuit to those as unimaginable as changing the strength of the ground's pull on a falling body. All mathemagicians possess the Libra ability, which allows them to research foes' profiles from afar and gain the upper hand in battle through an intellectual third eye. 
*Weapon: Textbooks, calculators, astrolabes, sextants
*Armor: Light armor, robes
*Additional Equipment: Watches, scopes
*Signature ability: Libra (Uncover enemies' stats, attack patterns, and weaknesses through scholarly insight.)
*Strength: 25
*Endurance: 40
*Intelligence: 90
*Agility: 70
*Luck: 60
*Magic: Arithmetic, minimal white
*Patron cities: Kokomo, Denshire, Krak
*Patron god: Dantalion, Keeper of Precepts
===Subclasses (Branches)===
While all arithmancers share the common traits listed above, at a certain point in their class development after years of practice, each must choose to follow one of two separate branches replete with mutually exclusive and powerful skills. The current makeup of mathemagicians, as found by a survey of numerous Adventurers' Guilds throughout the world, is ~55% statisticians and ~45% physicists, implying a roughly even preference for two equally intriguing, competent and powerful subclasses. Both branches share the middle ground of attacks empirically based on their atmosphere. The following sections will explain their unique traits as well as some abilities exclusive to either branch.
====Statistician====
Statisticians can be summed up as the "cunning calculators" of all job classes. Using enchanted textbooks and calculators, they analyze the numerical makeup of the atmosphere and bodies around them and tap into them to manipulate any target's physical or mental composition, as well as the stability of a battlefield. Nowhere is the forte of statisticians more visible than in the field of probability and battle statistics. With an input value, target, and correct incantation, a statistician may easily bless his party to increase their luck (earning them, for example, more item drops in battle or heightened evasion), strength (self-explanatory, I hope), and other stats, while conversely doing the opposite of that to their foes. 
They may also manipulate the quantitative laws of the local atmosphere to apply certain ailments like drowsiness or weakness to enemies based on attributes as mundane as the opponent's height. Any statistician worth their salt, however, knows the First Law of Numerical Sacrifice: more stringent inputs yield more powerful effects. For example, using an opponent's name will apply a status effect for less time than inputting their weight. Beyond numerical manipulation, statisticians are also gamblers among the classes, and have exclusive access to a trove of chance-based magicks that may, for example, either kill an opponent or grow a flower on their head. More numerically, a certain gambling attack may deal damage equivalent to any number from 0 to the target's max HP. Some final gimmicky attacks may swap a target's HP with their MP, or deal damage proportional to the target's wealth. The limit of a statistician exists only where their mind stops imagining and the pages of their textbooks stop turning.
All statistician abilities use the Nil element, meaning they are borderline impossible to resist elementally.
=====Sample Abilities:=====
*Luck of the Draw: Increases the average luck of user's party by random quantity between minus 50% and plus 100%.
*Debilitating Field: Decreases the strength, endurance, and intelligence of an area of enemies by some quanitity q. q=\ln((MP)^ 2)+ \frac{MP}{25}. More MP spent yields a greater decrease. Efficacy can be reduced by powerful foes.
*Empowering Field: Increases the strength, endurance, and intelligence of the user's party by some quantity r. r is equal to a seventh of the user's intelligence stat.
*Random Double: Deal damage to one foe equivalent to 2 ^ n, where n is some random number from 5 to 15. The median is 10, but a high luck from the user makes a higher n more likely.
*Tides of Time: Deal wildly oscillating damage to an area of foes given by |\frac {t}{3}sin(t ^ 9)|, where t is the amount of seconds elapsed that day. Generally more effective as midnight approaches.
*Punisher: Deal damage equivalent to the product of the target's two highest stats. For example, a target whose highest attributes are a strength of 48 and an endurance of 46 will receive 48 x 46 = 2208 damage. Maximum damage is consequentially 10000 (100 x 100). Weakens slightly with each repeated use on the same target.
*Chaos Calculator: Deal random damage to one opponent ranging from 0 to their Max HP. Weakens slightly with each repeated use on the same target. Some powerful enemies may resist, but never nullify, this incredible spell.
====Physicist====
Physicists eschew the debatably nerdy floating textbooks and magical calculators for portable and mystifying astrolabe tablets and sextants that hint at their more geometric and tangible manipulations of the world around them. Rather than play with subtle and unseen numerical laws, physicists use arithmancy to manipulate forces like gravity and electricity, compress and expand objects, change perceptions and functions of time in small regions, hijack machinery, and much more. For example, even a novice physicist could change the strength of Aquila's pull on a body in a small region, causing a potential target to stumble and wobble temporarily. A more experienced one could decelerate time around their foe, crippling them as they struggle to catch up with the physicist and his allies. One could even create a localized singularity that entraps all foes who step within it through an unthinkable mathemagical force.
The ability to bend force and matter, and therefore test the laws of reality, are where physicists excel. They may constrict foes' movement or cripple it as they please, and then let loose with a barrage of mathemagicks that shrink their target, make it weightless, carbonize it with internally coursing electricity, among many more. Around machinery, especially, physicists can combine the mechanical and magical, and use some psychokinetic power to move heavy objects - or their own targets - over some distances as they please. The way of the physicist is to analyze their environment and enemies and quickly devise an empirical situation to defeat them, by means including distance, time, mass, and countless others.
Like those of statisticians, most Physicist spells use the Nil element - however, they have higher variety with a theoretically infinite arsenal of fire and electricity mathemagicks.
===== Sample Abilities: =====
* Degenerator: Generate a collapsing force field around a foe that squashes them out of existence. Likelihood of success depends on intelligence. Useless on various powerful foes.
* Accelerator: Speed up time in a local region around one ally, allowing them to perceive and act considerably quicker. Limited duration dependent on intelligence.
* Attractor/Repellent: Strengthen or weaken a target's pull to the ground, hobbling their movement and in some cases allowing them to fly away or be unable to move entirely. More powerful foes may resist. Limits on the magnitude of change in field strength depend on intelligence.
* Fleeting Ripple: Generate a perfectly circular atmosphere around the caster that deals damage to all enemies caught within, with the option of more damage being dealt either near the circumference or the center.
* Micro-Singularity: Generate a small tear in space that gradually absorbs and damages all enemies in a certain radius. Force of absorption depends on MP input. The singularity may be destroyed by another mage to generate a large and powerful spherical magic blast.
* Living Bomb: Turn a target into a ticking time bomb that explodes in a fireball. Time until detonation can be set, and more time yields a larger and more potent burst.
* Free Energy: Spike the heat and electricity within a living target to cause massive internal damage proportional to MP spent. More powerful enemies may resist, but never nullify, this advanced spell.
=== Notable Arithmancers ===
* I. G. Strode
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