Math competitions/awards will not have anywhere near the impact on a BS/MD application as they do on a normal math heavy subject undergraduate application.
You do NOT need to apply to a particular major for MIT. There are no “impacted” majors at MIT, nor do you need to commit to a course of study while you are still in HS. The combination of MIT’s required courses in math and the sciences, plus the humanities requirements, will expose you to plenty of other disciplines and many MIT students are undecided when they show up on campus.
You didn’t ask this question but it sounds like you think you need to tell MIT you want to be a math major in order to leverage the benefit of your AIME score- which is emphatically not the case. Every AO at MIT understands competition math from the top down. It will be a nice plus for your application to have done well- but so would be writing a great essay about scuba diving, or knitting, or having your chemistry teacher write that you are the kindest student she has ever taught. All of these things count and there are many kids at MIT who did not do competition math at all- many of whom end up being math majors.
You can certainly plan to major in math; you will get plenty of math (and other things) and can change your mind.
Thank you for all your help!
“Every AO at MIT understands competition math from the top down. It will be a nice plus for your application to have done well”
It’s more than a nice plus, it’s an advantage, the issue is that almost everybody that qualified for the Olympiads along with top AIME scorers like the OP will be applying to MIT, along with Cal Tech, Harvard, Stanford and other selective schools.
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Some of the answers in this chat are why cc is so toxic. I do not see how getting a 12 on AIME is common among MIT students when in reality it really isn’t. In fact, I don’t think half of the people in MIT even took the AIME. I think that getting a 6+ on AIME is considered a “spike” and anything above 10 is considered elite.
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Second this! One of my friends is at MIT now, with a comparable (slightly lower) AIME score. On his hand-written note, they mentioned his math abilities. Of course, he also did a math camp, but I have a hard time believing the AIME score wasn’t impressive at all.