[inimino]

It is absolutely doable, the question is whether you have the combination of time and skills to make meaningful progress in whatever direction you choose in whatever time you have. Probably start with a review of recent literature (i.e. notable work on arxiv in last year or two) and see if you can replicate something that's already been done, then go from there. This lets you realistically assess your abilities before trying to do something that may be turn out to be more of a PhD thesis level of work. Try to find a mentor in your school or local area to help you out.