I learn math on my own. And I sometimes end up generalizing theorems. I do not claim that these generalizations are ground-breaking. However, I feel these generalizations are not entirely obvious at first-sight.
Could I publish a paper on such a generalization?
Making this more relevant to the community at large, how do you know when your "new" ideas are paper-worthy? Should one pursue research directed only by external trends? As in, if I were to publish a paper, should I only look for current areas of research in order to conduct research that would be relevant to academia today?