Techy233

I am not saying you have an inflated ego. Actually, I haven't read most of the posts in this thread. But if you have not taken analysis (I'm not talking about calculus, (including multivariate, DE, etc)) how do you know that your work is original? There is so much math out there. Without first being exposed to differential geometry, real analysis, topology, - essentially, post-UG math you can't make such huge claims. At the very least, extraordinary claims require extraordinary evidence. And finally, as you well know, many identical concepts in math can be expressed in many different ways.

OTOH, if some of the claims I read above are completely accurate, you should be getting a MacArthur Genius Grant by the time you're 18 :O

mathboy98

Ayush--It's terrific that you are interested in mathematics. The thing is that no matter how brilliant you are, a lot of math is just about sitting down and learning for huge stretches. Until one has spent several years sitting down *inside* a university like Caltech, it is hard to know what is considered "deep" in the mathematical world. Even when folks apply to graduate school in math, professors (who've said so themselves) have scoffed when students mention precisely what problems they want to work on in graduate school. There is simply no substitute to experience in deciding things like that, and so really no matter how brilliant, a student is best off waiting until later to make claims of discovery within the field. A large part of research (of course coming from someone with humble background only) really is figuring out what are the right things to think about.

So making claims of discovery of another field of math at the high school age would probably make a professor quite skeptical of the student's attitude. Some of the absolute best mathematicians alive today (and mark my words, I have this specifically from them) agree that it is best to spend one's undergraduate years just learning good things...and frankly given their brilliance, one might even expect them to advocate a much more aggressive, hurried approach to learning math and getting into research. Try your hand at solving some toy hard problems, and it'll tell you something about yourself, but it doesn't make sense in some ways to try to do things like discover new fields until one is past the grad school stage. Enjoy what you're doing, but it is not yet the time to report all the new findings you've made. In particular, you should save those thoughts for a professor, out of interest and curiosity, and not post it on an admissions forum.