I guess your definition of "interesting" shifts as you mature. I bet I had a load of interesting ideas when I was 14 that I would no longer find interesting now, 10 years later.

I think a lot of the ideas I had as a teenager were basically things I discovered independently, usually in awkward or incomplete incarnations, but would have been "obvious" to someone more educated and older. Or if not obvious, at least fairly easy to research or look up. (linear algebra particularly stands out as one of those things that, had I known it, I would have saved myself weeks of effort)

I wonder whether I'd be better at what I do now if I'd had access to the internet earlier (thus skipped a load of "unnecessary" hard work) or later. (thus developed my capacity for independent thought further) Given my acute case of "programmer's block" right now I'm leaning towards the latter. :-/