<p>Have you visited these schools? If possible that’s where I would start if I were you. I’d also encourage you to ignore the very small difference in acceptance rates between these and other similar schools. The 1.6% difference between them doesn’t mean you have a 1.6% better chance at getting into Princeton than Harvard. Your application may appeal far more to one admissions counsellor/department than the other and frankly the difference is miniscule. </p>
<p>I am not familiar with math at Harvard, but I do know that math at Princeton is very strong and well regarded. </p>