Stolen entirely from https://manifold.markets/ithildulin/will-i-get-into-primesusa, posted much too late. My problem set solutions I felt were decently good (over 9/10 solves, with only leaving M4 unfinished), but my personal statement could have used some more work (it was ok, but I feel like I rushed it a little). I had 3/3 recommendation letters, each of which I feel was strong. I put down differential geometry as my main focus/research interest. I have decently strong math tournament performance and I would say around average math competition performance for the general applicant. I am willing to answer some questions in the comments below, although only some. I have previous math research experience, multiple expository works, undergraduate level math background, and gave lectures as a first year at a high school math program. I had an interview where I solved all the problems relatively quickly, and I found it a really nice interview overall :D!

I'm unsure of the exact # of applicants / # of acceptances, but I think a figure I've heard thrown around is ~4% acceptance rate.