All math notation was created by mathematicians who wanted to quickly represent something, either to: - better see the structure of the problem; or - reduce t

All math notation was created by mathematicians who wanted to quickly represent something, either to: - better see the structure of the problem; or - reduce the amount of ink they need to write the problem Very similar to how programmers use functions, in fact. To this end, mathematicians in different fields have different notation, and often this notation overlaps with different meaning. Think how Chinese and Japanese have overlapping characters with different meanings. As others have stated, there is no "one true notation" -- all notation is basically a DSL for that math field. Instead, choose a topic you are interested in, find an introductory text, and start reading. They will almost certainly explain the notation. Unfortunately, even within a field, notation can vary, but once you have a grasp of one you will probably grasp the rest quick enough. I will mention, though, that some notation is "mostly" universal. Integrals, partial derivatives, and more that I can't recall right now all use basically the same notation everywhere, since they underlie a lot of other math fields.