### Writing and the Field of Mathematics

Mathematics can be considered as the exploration of universal truths through abstract concepts we can understand objectively and completely. The common perception is, of course, “solving problems with numbers,” which is still very correct! The formal study of mathematics generalizes from this (and often continues generalizing ad nauseam).

Math can be divided into two encompassing, but certainly not disjoint, fields: pure and applied mathematics, which can concisely be described as “the study of math for the sake of studying math” and “the study of math for its use in other fields.” Each of these contains many subfields (again, not mutually exclusive!) that distinguish themselves mainly by the types of problems they seek to solve and the tools they use to solve them.

What distinguishes math from other fields most prominently is its reliance on a binary of truth and falsehood. What this means is, for a given set of axioms (“things we accept, always”), any statement with a solid logical foundation is either always true or not always true (i.e., false). This, and that idea of the “solid logical foundation,” is precisely what most writing in mathematics is based on.

Writing in mathematics most often manifests itself as **proofs**.