> especially when different fields seem to use the same symbols to meant totally different things That is the problem: there are by far too few letters and sym

> especially when different fields seem to use the same symbols to meant totally different things That is the problem: there are by far too few letters and symbols to describe all the objects used in modern mathematics. You need to reuse symbols, and therefore any paper must declare the symbols they use. Sometimes they are even forced to use the same symbol for different things, so you need to have some experience in the field to understand which is the correct reading each time. The symbol declaration can be done explicitly (by stating the fact, usually at the beginning or in a dedicated section; some books also have a table of notations with references to definitions) or implicitly, when the paper is targeted to scholars that are most probably already familiar with that notation. The latter is probably not very friendly to newcomers, but in most cases if you do not know what implicitly defined objects are, then you probably cannot understand the paper anyway. In short, there are very few "short ways" into mathematics. If you want to understand things, you have to spend time and study them.