I have come to appreciate the mathematical approach of definition first then examples after. I used to prefer examples first, but examples can cloud the concept

I have come to appreciate the mathematical approach of definition first then examples after. I used to prefer examples first, but examples can cloud the concept and conflate their importance. Definitions (what you call abstractions) get at the heart of the matter, and staring at it for a while is actually the fast route. Baby Rudin, for instance, is entirely unapologetic and thus is one of my favorite math books. The book is mathematical in the way it treats mathematics.