You don't think you're creative while programming? I believe it's more art than math / analytical at times, that is if you're doing OOP. Can't say about functional or system's programming though that sounds like there's not much room for creativity as abstraction is hard from what I've experienced.
No I don't think creativity is linked to the act of programming. I do think creatively when thinking about product and design. Programming is about being a critically thinking pragmatist.