Perhaps a better way to think about it is that often when reading these sorts of articles, you realize that there's a name, and likely a corresponding rigorous

Perhaps a better way to think about it is that often when reading these sorts of articles, you realize that there's a name, and likely a corresponding rigorous definition and theory, for some concept which you had already understood intuitively. Once you've made that realization, you start to see the pattern yourself in other areas that you hadn't before, and to understand it more deeply.