First of all, I hear Bowdoin is great. I can’t specifically tell you anything about Bowdoin’s strength in math, but I have tagged @homerdog who has a child at Bowdoin and might be able to help more.

But in terms of math education, any top 50 university or top 20 LAC (which includes Bowdoin) offers more challenging courses than the vast majority of students can handle. Are you roughly at the 1% in terms of math skills? If so, Bowdoin can meet your needs just fine. But it is when start going further into the top 1% that you need to evaluate further. And in terms of this, there are two separate things to consider.

The first is depth of courses. For example, if you have completed Linear Algebra in your senior year of high school, you will want to look at the college course catalog and verify that there are enough courses that will keep you engaged for all four years of college. Just about any university can do that, but not all LACs can.

The second is peer group. You don’t want to be much stronger than just about everyone in your class for two reasons. First, it means that you won’t learn much from your peers, which is an essential part of the college experience. This is much more likely to happen at an LAC with 500 students in the class than a university with 3000+ students per class. Second, being much stronger than everyone in your class means that few of the classes will challenge you because they are geared at a different level.

So when does this start to matter? If you tell me that you got an A in Linear Algebra but had to work for it, or that you barely qualified for AIME, then a place like Bowdoin is still fine as long as they have the courses for all four years. If instead you tell me that you took Linear Algebra but got an easy A, or that you got a 7+ on AIME, then you probably won’t have true peers at Bowdoin. On the other hand, you will probably have a handful at Notre Dame just because there are more students there. Finally, if you have qualified for USAMO or published mathematics research papers, you should probably look beyond both Bowdoin and Notre Dame as your reach schools.