What Sort of Discovery Warrants Writing a Paper I am a high school student who is deeply passionate about mathematics and I have written many different mathematical proofs. I was wondering what sort of discovery warrants writing a mathematical paper for publication. Does the amount of content matter, or the significance of the discovery? Any advice you can give would be appreciated. I just don't know where to start.
 A: In any field (well, at least in math and physics, the two fields I am interested in) one of the skills acquired over time by a serious researcher is a feel for what problems are open, what problems are interesting enough to be published, who is currently working on what, and so forth.  In general, one doesn't have this fell until at least the second year of grad school. 
The knowledge is acquired by reading journal papers and discussions with professors.  Until you have reached upper-level undergraduate work at the least, you might not have the sophistication to appreciate and follow the journal papers you can get your hands on.  That is why this feel does not often come early.
That said, there are (in Math, but not so much in phsyics) journals that are of high quality yet are more accessible to the younger set.  There are some journals published by the MAA; Journal of Recreational Mathematics has some papers that don't require a Ph. D. to understand, Mathematical Intelligencer is excellent.  If you read the latter, for example, and think your work is on par with the articles you find there, by all means format your work in the way those articles appear (there will be style guides for each journal) and send it in.  Unless you have some really super result, you will have to spend the time to worry about formatting, air-tight proofs, and saying things in good English.   Try to find a journal (perhaps an electronic journal if necessary) that does not demand page charges; those are more common today than in the past.
Also, you might do well by asking on a site like this or MathOverflow qestions like
"I have proven that $\zeta(3)$ is transcendental; is this a known result and is it important enough to publish if it isn't?" 
Some really solid mathematicians visit here, and somebody like Robert Israel may well give you a solid answer to such a question.
Last piece of advice:  If you have attacked a question that is known to be "hard" and think you have solved it, chances are that there is a flaw in your work.  If you can collaborate with somebody capable of finding such flaws, it is worth it.
