I am a pianist that went throught this. The first time I wrote something of my own "taste" was when I was 15. A couple of somewhat important guys told me "We can't wait until you are 18."
This is the only field in which I had this kind of luck. (I am about 30 now and I can write a song within about three days that I would be happy with. A more recent one was when I took an Estonian poem by Johan Liiv and set it to music. I can sing the words, know their meaning, wrote the song accordingly, but I don't speak Estonian.)
My other interests had no such kind of luck. I am still aweful at soccer, but better than other people who started off as rugby players. My MSc was the first time I discovered/invented mathematics and I still am looking for my taste, though I know what it is (self-dual frameworks). I can program the way I think in mathematics, but I am not an accomplished programmer. All of this takes a lot of time, but the recognition along the way is important–especially that one song that I could write at an early age–but then again, I started playing piano when I was, indeed, a six-year-old.