<p>You don’t need to be a legacy to get into Princeton. I assume that you instead think that a legacy status at Harvard will get you in? It will help a bit at both schools, but Princeton won’t say “lol this kid’s not even a legacy; auto-REJECTION.” nor will Harvard automatically accept you.</p>
<p>After reading through Harvard’s math dept. website, they sync up Math 25 and 55 for the first few weeks so that you can sample both and move up and down as you see fit. You could use that to your advantage. Honestly if you can’t get past the fact that you might not get in to math 55 and think that this will rule out math research for you, you might want to consider taking a class in logic.</p>