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?
Answer
Complementary to Suresh's and Peter's more comprehensive answers that you should definitely take into account: (+1 to both)
Use ArXiv; ie. publish it yourself. Go ahead and write your findings down and put them in public. This will be a good exercise as :
- you will be covered for plagiarism etc. and you 'll be also able to refer other people's attention to it. It will be immensely easier to attract people attention to something tangible than just referring to "some idea you think it is great". As Torvalds said : "Talk is cheap. Show me the code." (or Maths in your case).
- people you do not know, can actually find you; or even cite you for that matter. I know a lot of people who regularly read ArXiv papers to keep up to speed with the bleeding edge of stuff. You might be lucky and really get some attention from people that actually care for your work.
- you will see for yourself if what you wrote can be formulated in a research paper and it doesn't come across as some ''back of the envelope'' calculations. You might even identify where feedback from a collaborator would be helpful.
If you think you are up to something good, put it up there. Worse case scenario: nobody bothers and you never know if you were right or wrong.
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