I have been thinking about doing my 'high school project' in mathematics and I would like to do some original research. So my question is: Which areas of mathematics would be most suited for me? Having in mind that I'm still in high school, although I have taken some (fundamental) math courses at my local university. And could you give an example of how a research question could be framed. :) Areas that fascinates me: Foundations of mathematics: Proof theory, set theory, mathematical logic. Sub question: Could a high schooler do original research in say proof theory? To mod: I put the thread here because I'm mostly interested in hearing about the foundations of mathematics (but all suggestions are of course very welcome), but if you think that it belongs elsewhere; please move it.