TITLE: How can a high schooler get more involved in mathematics?
QUESTION [26 upvotes]: For a high school student interested in majoring in math and learning more about math, what kinds of mathematical research can a student in high school get involved in? How can a high school student get involved? If a high school student does conduct research, what mathematical journals would be willing to publish their work? Also, what other ways are there for a high schooler to get involved in more complex mathematics?

REPLY [2 votes]: I agree with the responses above that one way to be more involved is to learn more through reading to get an idea of what are some cutting edge problems and math today. Math Stackexchange is a good site, but it can be quite tough for a high school student. 
Is Research Possible for a High School Student? 
However, I would think otherwise to the point that there isn't much opportunities for original Math research for high school students. Even though it is true that with less prior knowledge equipped, there is much less scope for research. However, fields such as combinatorics are usually more of understanding and reasoning and can be done even by a high-schooler! But of course you need to be ready to put in much hard work and time commitment to read through tons of papers across topics and fields sometimes because Math is simply so interconnected!
The Research Process: 
To conduct a research, the most important phase is the inspiration. You do so by looking up some not so "hot" topics or math topics/problems that are not so much worked on. If you are lucky, you can find a problem to work on! :) This is always the hardest but most essential step of research. Then think through the ideas or approaches you can make to solve the problem. If you have any teachers or mentors to consult, you can do so by sharing your problems, initial researches and original ideas to the problem, and get their feedback. Here your research journey begins! :) If you still cannot managed to solve the problem in the end, at least you get this idea already at the back of your brain and perhaps one day with more knowledge and techniques at hand, you can return to the problem and solve it.