I don't know a lot of upper-level math. However, I am of the impression that there are a handful of generally agreed upon formal definitions for mathematical terms and objects (to a similar degree that the definitions of English-language words can be roughly agreed upon). I have not, however, ever come across a (formal) dictionary of math. Some searching lead me to an encyclopedia that describes many upper-level maths, a layman's (from OED) non-formal description of terms, and little else.
Often, I need to rely on Wikipedia (or topic-specific textbooks) for formal definitions, which is quite strange. Are there any compilations of standard formal definitions and notation? It seems like such a compilation would be extremely useful. If none such exists, why not?* If it does, why have I never, as an 4th-year undergrad, heard of it? I'd think that the practicality of such a thing would move professors to at least mention it at some point. Especially from a pedagogical perspective, having access to the definitions of math seems very valuable (the number of times I've relied on Wikipedia for definitions is astounding).
*Based on my layman's understanding of Gödel's Incompleteness Theorem, there may be issues of systemasticity, but these shouldn't contradict the practical utility of such a compendium.