It is that exciting time of the year where some lucky few in the mathematical community get to choose a graduate school to go to. This post is for you guys. Here are my assumptions: You applied to a bunch of graduate schools and you got into a slightly smaller bunch of graduate schools. Now you think you have a problem: you have to choose one.
The first thing to realize is that this isn’t a problem at all. Very likely any choice you make is as good as any other: you are you no matter where you go. It is (in my opinion) a great privilege to be able to spend time doing math and your time in grad school is going to be perhaps the period in your life where you have the most time to do math ever. It is going to be wonderful!
On the other hand, the choice you make will likely have an enormous impact on what the rest of your life looks like. It will determine who your friends are, where you live, what you eat, etc, etc. Being a graduate student will put a new kind of psychological pressure on you and your time as a graduate student will some sometimes be horrible.
In other words, the choice you make will have an important impact on your life outside of math and I think actually that those consequences are possibly more important than the purely mathematical ones.
Before we get to deciding which school to go to, let’s think about what you will do when you get there: you will write a thesis with a thesis advisor. (To me, as an advisor, this is the only thing that matters.) In the first year or so, besides learning new material, you will choose(!?) your advisor. How will this happen? If you think about what math you understand best, then it is probably the material from the math lectures you liked most. Very likely you will end up working with the professor whose lectures you enjoy the most. I say there is no way of predicting how this will end up and I claim that it is best to go into grad school with no preconceived notion of what will happen.
Having said this, here is the Carpe Diem method of choosing a grad school:
- Go somewhere else; try something new! Don’t become a graduate student at the institution you are an undergrad at.
- If at all possible, visit the schools you got into. Talk to the graduate students there, attend a random lecture, and generally just soak in the atmosphere.
- Try not to worry about extraneous issues like: stipend, teaching, housing, etc. (Of course you may have to for some reason.)
- Don’t worry about availability of professors. You’ll find somebody to work with, but as I said above there is no telling how, when, why this will happen. If an institution has a certain track record of excellence, you can be sure this will continue in the near future. Moreover, once you are in grad school, the institution you are at has a certain responsibility to get you a PhD (provided you work hard, pass your general exam, etc, etc).
- Finally, make your choice based on where you think you will enjoy living and working the most.