One year ago I decided to myself to write my own scientific work in number theory, graph theory or combinatorics. I tried to find the teacher and theme during this year, but unfortunately I didn't find anyone who want to begin to work with me , because of I'm too young. So decide to write it alone. My question is: what do you think , which theme is the best to begin in scientific work?
Actually I want to hear an advice from someone , who work in this directions or who began there.
If you don't know which theme you should work in, you shouldn't be deciding that yet. Take more classes in all subjects, and see which one appeals to you.
To write a scientific paper on any topic, you need to do some work that nobody has done before you. The only way to do that is to know all (or most of) the work that was done in that specific field, and the only way to do that is to study that field for a long time.
All fields of math are beautiful in their own way, but they all need a lot of work before you can even start thinking of what you can contribute to them.