Magic is any physical phenomenon that happens as a result of using tongues. Tongues are essentially mental recitations of various formulas that constitute physical reality. Acquiring tongues is essentially an intensive academic pursuit. Similar to how it's inconceivable to be able to fully learn every single human language, most magic users will stick to one school of magic and a handful of dependable spells. Because of the volatile and dangerous nature of tongues, magic users lives are strictly regulated by the state. Magic is essentially used only for military purposes, and anyone that uses or studies magic outside of a military setting are marked for execution. The only limit of magic is the users own brain power. Even a simple fire spell is a complicated formula that would take most people years to learn. Considering the universal nature of tongues, no one has to be particularly gifted in order to learn them. They just have to have an affinity for academics and the resolve to enter into what is essentially a lifetime of servitude to the state. There are really only two main schools of magic, but each have numerous specialized branches. The School of Thaumaturgy focuses on magic that effects biology. Thaumaturgists tend to focus on healing magic, but can also learn offensive spells such as poison and petrification. Thaumaturgy is particularly challenging because the user must have an in depth knowledge of not only physics but human biology as well. Evokers focus their power on the environment around them and tend to learn offensive nature spells, but can also effect sound and light to make them more stealthy.

TL;DR Magic is thinking about a math problem where the numbers are basically the building blocks of reality, and you can do pretty much anything although the greater the effect the more complicated the arithmetic.