TITLE: How do you check that your mathematical research topic is original?
QUESTION [35 upvotes]: Sorry if this question is not well-suited here, but I thought research in mathematics can be identified from other science field, so I wanted to ask to mathematicians. 
I am just starting graduate study in mathematics (and my bachelor was in other field) so I have no research experience in mathematics. Recently I came up with a problem by myself, and thought it was interesting so devoted some time to draw the results. Now I have some results, but I am not sure this is already studied somewhere by someone. I tried to lookup some possible keywords in Google Scholar, but have nothing. 
I am sure for more mature mathematicians they already know their fields of study and recent trends of the research, so it won't be a difficult problem to know this is original or not. But if you come up with some idea that are not seems to belong to any field, how do you know your result is original or not trivial result?
Thank you in advance!

REPLY [2 votes]: It's not that hard nowadays to do a fairly exhaustive literature search to make sure something hasn't been done before.  This is a skill which can take a bit of time to develop but will help and saves a lot of time in the long run, especially if you do not have someone you can show the result to.  This will also help you to be independent, something which is starting to become increasingly important in academia (especially in mathematics).
Now with Google, Arxiv and many other tools which people in the past did not have access to it is much easier to check if something has already been done, although these checks are usually not foolproof. After a while you will probably also develop intuition for what is already a 'reasonably obvious' idea. 
For example, a few weeks ago it occurred me that it would be nice to construct a quantum mechanical system whose Berry phase was a BPS t'Hooft-Polyakov monopole.  It wasn't too hard to do some digging around and find that this had already been done: I encourage you to learn how to do this effectively if you do not already know how.
Edit: See this paper by Tao et al. where they investigate in great detail whether or not a result they have found in linear algebra is new or not and if not, exactly what is the history of the discovery.  In Figure 1, they provide a very detailed tree of all the citations and previous mentions/studies of the result.  Tao does not work directly in the field of linear algebra and his 3 co-authors are neutrino physicists, so how could they possibly have found this out except by doing some digging and deep searching around?  OK, the graph might have been crowdsourced, but I doubt everyone contributing to it was exactly an expert.