Can anyone give me a nudge on how to research given that I only know basic mathematics (Through calculus and below) but the mathematics that I do know, I know very well.

I'm not expecting to publish or anything like that, I just want to research something that a school would find intriguing and also to try my hand at the heart of mathematics.

To me it just seems like every problem that I can try my hands on is too basic and boring or that every problem in my reach has been solved (but of course it isn't much like every song has not been written) and I just want a nudge in the right direction or an idea on what to 'research'

Thanks!