Does it ever make sense NOT to go to the most prestigious graduate school you can get into? [closed]

I'm a senior undergrad at a top-ish(say, top 15) math school. I'm a solid, not stellar, student. This year I'm taking the qualifying exam grad courses in algebra and analysis and have been taken aback by the "pressure cooker" atmosphere among grad students here. That is, even moreso than in the undergraduate program.

If I'm self driven, could going to a "less prestigious" school afford me more space(I mean in a psychological sense) to produce a more solid contribution to math? By "less prestigious", I mean a school "ranked" significantly lower than the range of schools that I could comfortably get into. For me, "less prestigious" would be ranked around 40-60 on, say, USNews or NRC.

My reasoning is that at such a school, I would be more able to learn the fundamentals at my own pace, as opposed to a pace dictated to me by the program. I know I want to do math, and I think my learning style may be better suited to going at my own pace. Thoughts?

I think that there are several important points.

First, you will learn just as much from your fellow graduate students, especially in the initial years, than you will from your professors, and far more from your fellow students if there is a good atmosphere for it. Thus, I suggest that you try to land at a school with a supportive and studious student environment. You can visit the places to find out, and talk to graduate students there. From this perspective, it is very helpful to be at a place that has many talented graduate students---they will help you rise to their level (or you will all rise together). Since the top schools tend to have stronger students, this can be a good reason to go to a top school when it is possible.

Second, most of the pressure on graduate students is self-imposed, instantiating their drive to do well mathematically. Every school, including the top programs, have some students that proceed at a different pace. So you can often resist whatever external pressure you imagine is there. (One important exception to this is at a school where financial support might be withdrawn for slow progress---so look into that at the places in which you are interested.)

Third---and actually I find this to be the most important point---you shouldn't look at the school only and make a such an important life decision based only on mathematics and prestige. Rather, look at all aspects of how the choice of a school will affect your life. You must consider the city and region as well. For example, do you prefer city living or country living? If you like the mountains, hiking and snow, then don't go to Florida, and similarly, if big city living is your preference, then don't go to small town. I find that this kind of consideration is oddly often neglected among mathematics students.

There are circumstances that could lead one to be admitted to more prestigious graduate program X and less prestigious graduate program Y and choose to attend Y. For instance, there was a graduate student at UGA a few years ago who was doing well in the program but at some point revealed to me that he had to care for a sick family member in a different state, so moved to that state and enrolled in a distinctly less prestigious program there. Of course I don't disagree with his decision -- indeed I admire it -- but there was no question that this was being done for higher reasons than his mathematical well-being and future career.

Treating this question as advice, I would say No -- you should attend the most prestigious graduate program you can get into.

Of course, graduate programs are not linearly ranked: i.e., holding up two graduate programs to each other, one may not be able to identify one as more prestigious than the other. When this is possible, it is usually the case that one is significantly more prestigious. So, to refine the advice of the previous paragraph: you should choose a maximal element of the set of graduate schools you get admitted to, partially ordered by prestige.

Included in this are considerations such as the following: you strongly believe that you want to work with a particular faculty member at a program which is overall less prestigious than some other. This is a tricky decision that I don't want to enter into here in detail, except to say: if there is any doubt in your mind that you will complete a PhD under Professor X, be very skeptical about trading more than a little in the prestige of the school.

In the OP's case, s/he seems to want to choose a non-maximal element in order to take some of the pressure off. Although I understand the sentiment, I advise strongly against this. Two points:

1) Graduate school is a high-pressure, hard-slog situation for everyone. It has to be. If you're not fully prepared for that, perhaps you're not fully prepared for a PhD program: think about it.

2) Much of graduate school does proceed at your own pace. However, the quality of the students and faculty in your program sets an example and a standard, in my experience the higher the better.

Maybe this is just getting redundant, but I think this is a slightly different point from what people has said above: while there do exist compelling reasons to go to grad schools that don't maximize prestige, it really doesn't sound to me like you have put forth any.

I think on the whole grad students are pretty naive about how big an influence where they go to grad school has on their opportunities after graduating. Of course, lots of people do manage to go to less fancy schools and go on to have good careers, but if you look at the schools in the 40-60 range you mention, most of their faculty went to more prestigious places. For example, at Oregon where I'm a professor (US News rank #56), fully half the professors who got Ph.D.s in the US got them at Harvard, MIT, Berkeley or Stanford (all in the top 5 on the USN ranking) and most of the rest at institutions in the low 2 digits (Texas, Maryland, Wisconsin, Penn). Some of this is for unfair reasons (bias, etc.), some of this is selection reasons, and some is because going to a better school give you more opportunities to be a better mathematician (more exposure to new ideas, more visitors, higher quality peers). I wouldn't give up on those things because of a nebulous fear of not liking the environment. Try it out; it's much easier to go to a Berkeley or Michigan for a year and then transfer somewhere else than the other way around.

EDIT: Just as an addendum, I thought I should emphasize here that like Pete said, prestige isn't really well ordered. There are lots of pairs where it's hard to say really conclusively which is more prestigious, in which case you should go with your gut. So I'm not talking about things like comparing Chicago and Columbia, and choosing Columbia because you'd rather be in New York, but rather the difference between going to graduate school in the 40-60 range (in USNWR or NRC), and something in, say, the top 20.