Article 16: Mathemagics
Both in MSF High and the galaxy outside, the casting of magic spells is as much an art as it is a science. Because it is both, there are various means that can be undertaken to complete the casting of any given spell which range from purely improvised to completely mechanical. While those with a strong force of will can benefit most from leaning to cast through that willpower, understanding the basic mathematics behind magic can still bolster their casting abilities even further. At its base, the primary difference between math and science is provability. A mathematic system is one that cannot be disputed--1 plus 1 will always equal 2, as this is inherent to the definitions of one, plus, and two. While science requires observation to support its ever-changing theories, any math can be logically proven. addition, subtraction, multiplication and division will always function the same regardless of what sort of beings create them in whatever dimension they may reside in. Some conversion may be required, but these conversions will always apply, making math a universal language and therefore one of the most reliable ways to express magical manipulations.
The most basic use of mathematics in spellcasting is the mixing, subtracting, and multiplication of different elemental forces. Many of these are logically basic--adding fire and water elements can make a spell that creates a blistering, obscuring cloud of steam--while other permutations may be more conceptual in nature. Most mages understand that the complex hand motions they tend to draw in the air while casting aren't directly what invokes a spell--rather, it is a representation of how their willpower enforces itself the fundamental forces around them, and the pursuit of understanding the specific geometries behind this has led to the segregation of the ten distinct elements. The most potent users of mathemagics, however, are MSF High's own nerds. While they are more commonly known for their incredibly accurate cosplay outfits and eclectic collections, many at first glance mistake their spellcasting abilities for common magery, when this is anything but the case. While they possess their own near-encyclopedic knowledge of magic, much of this is actually about how other facets draw magic forth. This is because of a principle of magic known as elemental vacuums. Basically, when you cast a spell of a particular element in an area, tuned elemental power is drawn from the area, leaving a temporary vacuum through which the opposite element can more easily be drawn. Nerds take advantage of these power vacuums, drawing up opposed elemental energy to easily cast a spell. This makes their casting simple and cheap for them, but it stunts their versatility as they can only cast a spell of the opposite element of the spell most recently cast around them. Some of the smarter students who specialize in particular elements build up resistances against their opposed element as a counter to Nerd tactics, while others create or purchase scientist devices that can quickly cast the most inexpensive spells of the element whose opposite they are most resistant towards. Luckily for MSF High's nerds, their opposite-casting ability is not the only mathemagical trick up their sleeve. Using precise manipulations of the same sorts of power field along with their own knowledge of potential spells and the ability to identify what spell is being cast based on subtle cues the caster gives off, they can push needed energies away from a caster, preventing them from casting spells completely or causing them to have no effects in specific portions of the battlefield. It is for this reason that a Nerd studies spell geometries, as altering the trajectory of a fireball by just a couple degrees can prevent it from hitting them or their friends.
Nerds aren't the only casters that prefer to have a wealth of mathematical knowledge assisting their magical casting. Demomages engineer spells that go off with precise timing directly into their ammunition. The Elemental League's Calculator mages sway the balance of elements in a much more obvious and field-affecting way than MSF High's nerds. Angelic Protectorate Callers utilize atmospheric refraction and orbital mechanics when making their barrage calls. Legion's Terraformers must understand geometry and geography's co-mingling to create structurally sound alterations of the land. It's also said that some Watchers can use mathemagics to predict likely outcomes of the happenings around them.
The conflation of the manipulation of magical energies and mathamatics is also prevalent in different types of magical engineering. Professor Riley's "blue tech", which he back-engineered from pure magical symbols, show just how thin the line is between science and magic, and MSF High's Scientists can replicate this or any of a number of other mahoutech engineering principles to create their own devices. This is not at all exclusive to MSF High, either. The most well-known piece of mahoutech engineering is the BioWarp Engine, which mechanically casts a number of relativity-altering spells using stored magical energy. Most modern starships use these same principles to power their conventional drives, their shields, and weapons systems as well. Many militaries use smaller-scale mahoutech equipment, and all of them are built on the same scientific and magical fundamentals.
Of course, the most direct application of mathematics for magic is the understanding of physics. Regardless of how you cast your spells, knowing how gravity, wind, and drag will affect your spells' trajectories will improve your combat effectiveness, while understanding principles such as thermal expansion or the function of magnetic fields can help you apply the most effective spells at the best times. Most of us can't do complex trigonometry quickly enough to apply it instantly for a spellcasting boost, but it's not a possibility that should be discounted. In summation, any knowledge of math will help you when casting magic, and some of it is so intrinsically linked that you may be doing math without realizing it every time you cast a spell.
