About two years ago, I absolutely fell in love with mathematics. Since then, I have studied math almost religiously, absorbing everything I can about every subject I can. I have now established what I would call an understanding of most undergraduate topics, up to intermediate complex analysis, some abstract algebra, multivariate calculus, etc.
I really want to get into a good college for mathematics - specifically MIT. As a middle schooler, I have plenty of time before I have to submit an application, and I really want to make the most of that time. You can't exactly put down "was pretty good at math in middle school" on a college application, so I was wondering what things I can do now to get a leg up in the future, that I could put down in a college essay or in my application.
So far I've started a mathematical blog, and I am working really hard to get published by the time I finish high school. My question is - what else can I learn/do/create to give myself a head start in college and in employment as a mathematician?
Take life as it comes.
I enjoy people that take interest in mathematics at a young age - I did too. What gives me an unsettling feeling is worrying about only going to the top. I'm not saying go lower, I'm just saying be a bit realistic.
Any college application will not care about what happened in middle - heck, even the first year of high school isn't really much. Still always do your best in school no matter the circumstance.
Now, to become a good mathematician? I would say build a mentor-student relationship with your teachers, that's how it starts. This goes at any level. Once you get into high school, try attending some summer programs in STEM. Do what you can. There will be grunt work, yes, but it's something we all go through.
Keep at it. Chase your dreams. I only started grad school in January and I'm chasing a dream I have to just be good at math, to be something. I'm nowhere near the research phase now, I don't even know how to start, but I'm seeking out mentors to help me along the way. I suggest you do the same.
And when it comes to applying for college? Don't get discouraged if you get a denial letter. Be realistic - keep an open mind. Keep schools like MIT on your list, but also your local state schools. Too many people rag on state universities (and I'm at one; we have a ranked math program and one of the best engineering colleges in the country), and I don't want you to go on that path. Many state schools have great math programs. Just expand.
Reach for the stars.