[for high school students] surely I'm not talking about real research, but I just want to know if you try to solve advanced (physics or maths) problems or if you dedicate some time to study things that are not taught at class. And by "study" I don't mean HSW or popular science books (don't get me wrong, I'm not despising those sources of knowledge!!). If yes, how did you started? which topics do you explore? I found this Gerard 't Hooft website (http://www.staff.science.uu.nl/~hooft101/theorist.html), but it's too much stuff and I'm going to university soon. I just want to get in a topic so I can... speculate... practice... have fun!