When I call GPT-4 intelligent I use the word in the same sense as if I met a very smart person (smarter than me), and interacted with them for some time. It's as simple as that.
My interactions with GPT-4 include quite a wide range of questions: "how to talk to my kid in this specific situation", "what could have happened if Germany had won WW2", "what does this code do", "here's an idea for a research paper, let's brainstorm the details and implementation". I can also discuss with it anything that's been written in this thread and I'm sure it would provide intelligent responses (I haven't, btw).
When you say "intelligent", what do you mean exactly?
What might help is describing what specific interactions give you the impression that GPT-4 is intelligent?