Why do my professors ignore my work? I'm a high-school student finishing in December and about to pursue a career in mathematics.
In my free time, I like to ''research'' hard problems and come up with unique proofs or combine already-established proofs to come up with a beautiful solution. As a high-school student, I am obviously not researching anything of importance, but I am solving IMO (Mathematical olympiad) problems in unique ways  and such, constructing beautiful reasoning behind them spanning several pages. I take great pride in my work (even though it is trivial to real mathematicians) and I would love some feedback...However, when I send my work to my professors and teachers, I always get ignored completely. I never receive anything back, even if I remind them. This is making me doubt myself and my abilities.
What on earth could be the reason for this? Do teachers loathe it when students put extra work on them like that? If so, why won't they tell me?
 A: I don't know which country you are from, but in the US, I doubt many HS math teachers would be able to solve math olympiad problems or would need to expend a lot of work to do so. Keep in mind their point of view and pressures.
If you feel that your work is truly unique and worthy of consideration, you may want to write up your proofs and post them on the General Math ArXiv site, where mathematicians can review your work and provide comments. Note that if you are not proving anything new, but just solving problems (albeit hard ones), then don't expect a ton of responses. Most researchers are quite focused on their work or work related to theirs, and don't have time to review problem solutions (especailly if they are already swamped with reviewing their PhD candidates work and assisting with class grading). 
In general, I wouldn't take it personally. You said "your" professors...so I assume you have person-to-person contact with them..why don't you drop by after class and ask if they would be willing to meet to discuss (as opposed to just sending them something). They may not feel that the problems you work on are within their area of expertise.
