If one student writes the influential paper in mathematics

I’m a high school student and wrote the paper in mathematics about partial differential equation based on my ability of learning math so quickly by myself. I requested for the evaluation of it to my math teacher, and she said it’ll be a much better choice that I visit to professor’s office in the department of mathematics.

Actually, I want to enroll some of great Ivy League schools such as Caltech or Princeton, but my GPA is low. About 2.5 (unweighted maybe).
Because of the terrible depressions and anxiety disorder, and I cured myself with studying psychology and did some treatments of auto hypnosis, and meditation.
Now I’m getting much better. and have studied really really really hard and so quickly. Even there are some of math books I can recite. The studying and paper writing also have done since my suffering from disorder ended and cured.

But the problem is all about my last low GPA in disorder years.
Caltech admission page once said that they will evaluate the students into many point of views such as his talents even though he got the low GPA. I don’t know if they’re sweet talking or not.

So do I have any possibility to get into Caltech, if I request for the discussion with a great professor from Caltech and show my talent through the paper?
I also have the psychological reason for my low GPA. Nowadays I’m thinking of whole new kind of mathematical structure and operators for improving Mathematical Psychology(the idea of it was totally from my disorder years).

One of my scheme is that I had a great score in practice SAT from the internet many times, and it looked easy.
I have a confidence with it (the high score).
but my GPA is always bothering me…

  1. Can I get into Caltech do you think? (High SAT, Low GPA, Special achievements)
  2. What's the accepted students' case with Low GPA, Low SAT/ACT ? (There were some of green dots on the datebase)

Talk to your guidance counselor. I would say no chance at all. Those green dots are under-represented minorities, legacies and athletes.

A college that’s highly competitive for its enrolled students, where nearly every single student is highly prepared, is going to see academic weakness as a problem for an applicant. Grades reflect learning levels and focus. They’ll wonder if you can keep up. It’s not about a side achievement only at what interests you, did capture your attention.

Agree with the above.
–I don’t see you having a realstic chance of getting into the schools on your list with a 2.5 GPA as an unhooked applicant.
–The transcript, including GPA is an important part of the application review.
–I can’t imagine college professors will be interested in reading an unpublished npaper written by a HS student. (If the paper has been published in a peer reviewed journal you should include that on your application but that doesn’t seem to be the case).
–Mental health issues are usually considersd red flags to college admissions officers.
–It is fine to apply to a couple of reach schools but be realistic in your expectation and be sure to seek out match and safety schools that appear affordable and that you would be happy to attend based on your actual academic stats.

Seems like the paper you wrote is more of an article and not peer reviewed research on a new original topic. Unfortunately I don’t think that will help

Hopefully with your improved health and grades some universities will appreciate your potential. If you do well in college, you can more realistically set your sites on a top program for graduate school but not for undergrad.

Are you familiar with Google Scholar? Your subject line describes your paper as influential but in academia one way this is measured is the number of cites on Google Scholar.

I’ll be honest. It’s extremely rare that a high school student can write an original paper in pure math, let alone “influential”. But there are quite a few smart self-taught people who think they’ve made a contribution to math or other sciences when in fact their ideas either contain glaring errors or have been known for hundreds of years. I would advise you to get a thorough education in a good state school with a strong math department (there are plenty), work with professors and then consider a graduate school based on your achievements during the college years.

Also your English writing ability sounds like English is not your first language. While that may be OK for Caltech, it may not really be easy for you to write a convincing essay. Please have an English teacher correct your written English on your college essays. Find matches for your GPA. Still apply to Caltech, but just don’t focus much on it.