TITLE: How does one know that a theorem is strong enough to publish?
QUESTION [13 upvotes]: Question. How does one know that a theorem is strong enough to publish?

Basically, I have laid out a framework in which many theorems may be proven. I'm only 18 and therefore lack knowledge of whether this framework and the theorems sprouting from it are trivial along with the theorems. What is a good indicator that work is good enough to be published?
An example of a theorem I have proved is;
Given a (non-constant) meromorphic function $f$ there exists at least one continuous loop over the extended complex plane, $\varphi$, such that $f\varphi :\mathbb{R}\rightarrow \mathbb{R}$ (bijective).

REPLY [9 votes]: At your age, there is no reason to worry about publications.  In fact, it is extremely rare for people to publish anything worthwhile before graduate school.  This includes top-rate people (Fields medalists, etc.).  Publications play essentially no role in either college admissions or graduate school admissions.
One reason for this is that the areas of math which are accessible to high school students (or even undergraduates) have been mined extensively over the last 300 years.  There are a few exceptions, but you won't discover them without extensive guidance from someone who is experienced.  And even then, any papers which result will likely be of little importance.  I know a number of people who wrote papers when they were undergraduates which they are now a little ashamed to include on their CV's!
This is a long-winded way of saying that without looking at it, I can can be 99.999% sure that your theorem is either 1. false, 2. trivial, or 3. known.  But you shouldn't feel discouraged by this.  Your goal in this part of your life is to learn as much math as you can.  Certainly try your hand at proving things if you get some ideas.  But it's not a good use of your time to worry about publishing things -- there will be plenty of time for that later.  Just have fun and take the time to enjoy math!