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Jan 29 at 13:04 comment added Stephan Kolassa Regarding "go to school": some universities even allow bright and under-challenged high school (or equivalent) students to attend introductory lectures. An acquaintance of mine attended Analysis I & II at the local university while in 10th grade. If this is at all possible, this would enormously benefit your skills in mathematical exposition and in how to write a proof. (There may even be graph theory lectures you might be able to enroll in.)
Jan 28 at 20:27 vote accept Saksham Sethi
Jan 28 at 20:28
Jan 28 at 19:29 comment added Sam Nead Yes, reading a few books is a nice way to learn. After that, the only way to "know which open problems in this field are accessible", is to try thinking about a few of them. If you are interested in writing papers quickly, you might start with a few which are less research focused. Finally, some people work better alone, some work better with a friend or two, and some work better in a large group. So you could try the various ways and see what works for you. Of course, there is the issue of finding other people to talk maths with. Try college... or the internet!
Jan 28 at 17:38 comment added Saksham Sethi Thank you so much for the response. I believe that I would need to read introductory textbooks in Graph Theory to get a solid foundation. However, after this, how do I know which open problems in this field are accessible for me? I am willing to spend one or two years working on a problem, but I don't wish to spend an enormous amount of time for my first paper.
Jan 28 at 8:50 history answered Sam Nead CC BY-SA 4.0