At this point, there’s nothing you can research and finish on your own that’s going to be considered research. Professors are years ahead of you and you need to learn from them. NO peer-reviewed journal will publish a paper from a minor without a reputable first author.
So what do you suggest? How do I find a professor in math / theoretical physics willing to work with me?
@HopefullyTiger It’s not that hard. If you just reach out to professors and talk to them about what you’ve done, then sometimes they’ll agree. It might not work out on first try, but someone is bound to agree to work with you. Look at nearby universities in your country and ask if you could do research with them. Sell yourself a bit- speak about what courses would be relevant and ask if they know anyone that would be willing to mentor/work with you in the event that they say no.
You’ll need to take initiative and network a bit to get a research paper done. Maybe drop into a uni after you’re done with school and visit math/physics professors to talk about a research option. Or you can just email or even call them over phone…but that might be hard if you have school.
You should really start the process now. Because it can take some time to find someone willing to work with you.
In the event that you do not get into Princeton, then you should try to negotiate with your highschool to let you stay an additional year. There are ways you can structure your courses so you stay in highschool still. Maybe look into online courses which your school could accept or nearby universities via dual enrollment. And in the summer, you should be working hard on research.
The key element for you is to talk to your high school asap to stay enrolled.
Even if it means taking some art and more humanities classes while being dual enrolled in math at a nearby university. Through that dual enrollment you will be able to talk with mathematicians.
Please be aware that you can take a maximum of three subject tests in one sitting. As others have suggested, it would make sense to skip Math Level 1.
You are an international student. Ivies do not generally like 14 students. Sorry but your chance is close to 0. My kid took Calculus BC when they were 12 and found a way to stay in HS. You really should try and find a way to stay in HS