On the other hand, I hate it when people take this mentality to the extreme and withhold the mathematical definition and insist on only using examples or "simpl

On the other hand, I hate it when people take this mentality to the extreme and withhold the mathematical definition and insist on only using examples or "simplified" definitions. It's similar with language learning. Sometimes I just want to see the grammar rule (there often is one, at least to a very good approximation), but the teacher has this didactic philosophy that I wouldn't be able to "handle the truth" or something. If there is an adequate definition provide it. It's similar with computer science papers as well. On the one hand, a free-text description of an algorithm or a simplified pseudocode is helpful to get the gist, but very often I also need to see the actual unambiguous code to see exactly how it is and to check if I understood it right because no description covers all the corner cases. Both are important, practical examples but also the abstract definition (if one exists to a good approximation).