Supplementary mathematics/Branches of mathematics

Mathematics covers various types and depth of subjects throughout history, and only by sorting and categorizing all these subjects in mathematical branches can they be understood and collected in one place. Several models emerged to categorize these issues and although there are commonalities between these models, each one is different from the others due to their purpose.

Traditionally, mathematics is divided into pure (the study of mathematics for its inherent beauty) and applied (the study of mathematics for its application in real-world problems). But this general division was not always clear and many subjects were first founded by pure mathematics only to find its applications later. Major divisions such as discrete mathematics, computational mathematics , etc. have emerged recently.

An ideal taxonomy would allow new branches to be added to previous knowledge, making surprising improvements and being able to accommodate unexpected connections between branches to previous classifications. For example, Langlands' program found unexpected connections between previously considered unrelated fields, such as connections between Galva groups, Riemannian procedures , and number theory.