by Tom Wright
It seems that picking an advisor is a hot topic on this board, so I’m joining in on the fun. However, I’ll do it more from the perspective of what you should look for.
Picking an advisor is the single most important thing you will do in graduate school. Allow me to reiterate: it is THE most important thing you will do. It’s certainly more important than your thesis topic; it’s probably more important than your choice of school in the first place.
When picking an advisor, you need to consider three things:
1.) Will I enjoy working under this person for the next 3-6 years?
2.) Does this professor graduate his advisees?
3.) Do these advisees get jobs?
I’ll explain each of them:
1.) The first one is the obvious one. If you can’t work with the person or if you don’t like the problems he or she picks, you are going to be miserable for the remainder of graduate school. I’m sure you’ve figured this out by now, but grad school is hard. You’ll spend a lot of time sequestered in a room trying to learn mathematics and solve problems. If you’re bored to tears by the area you’re studying, or if you have persistent nightmares about talking to your advisor, you probably won’t last long in grad school.
2.) This one, along with #3, are usually overlooked. A student can fail to graduate for a number of reasons, many of which have nothing to do with an advisor: family concerns, frustration with the idea of studying all the time, a sudden urge to actually make money, etc. However, if students are leaving because of difficulties like lack of direction, intractable thesis problems, or other advisor-related problems, well, that’s a concern, and you should probably do some more research on the circumstances of the students’ departures. I can’t stress this enough: if you’re not clear on what your advisor wants you to be doing, you’ll end up wasting a lot of time, and you won’t make progress, no matter how hard you work.
Related to this , think about how much oversight you would like. I have a friend who went a whole semester without talking to his advisor; this was ideal for him, as he spent the time reading books without being distracted. I have another friend who went a semester without talking to his advisor, and he played computer games for the entire semester (and subsequently dropped out of grad school). Needless to say, what works for one person may not work for another. Find out how much interaction you’ll be having with your advisor and how that interacting will occur (Does the advisor do most of the talking? Does he/she make the advisee present most of the time? Does he/she want to meet daily/weekly/monthly/not at all?) and figure out whether your potential advisor would suit your style.
3.) I should note that this one is more oriented toward those who want more research-oriented or balanced research/teaching positions. If you want a teaching position out of grad school, the advisor matters somewhat less (though having a good advisor still helps). However, if you want a research postdoc, even with the intent of eventually landing at a teaching school, this is extremely important.
Let me illustrate the third point with a story:
There’s an old comic strip that my friend always used to refer to. Apparently, the comic involves a rabbit that leaves his hole, only to get caught by a fox. Faced with the prospect of becoming lunch, the rabbit says, “Before you eat me, would you like to see my thesis on the rabbit who eats the fox?” The fox, amused, says, “This ought to be good,” and follows the rabbit back to his layer. An hour later, the rabbit emerges, and the fox is nowhere to be seen.
The next day, the rabbit is caught by another fox. Once again, he says, “Before you eat me, would you like to see my thesis on the rabbit who eats the fox?” This fox, like the one before him, amusedly accepts. Again, the rabbit emerges later on with no fox in sight.
In the final scene, the rabbit is sitting over a typewriter, typing feverishly. The rabbit’s advisor, a lion, is sitting next to him. Next to the lion is a pile of fox bones.
The moral of the story, of course, is that it doesn’t matter who you are or what your thesis is. The only thing that matters is your advisor.
Now, this overstates things a bit. If you write a paper that shows up in the Annals of Mathematics, you’ll probably get a good job. Moreover, there are a ton of other things you can do to improve your resume, many of which have been detailed on this site. However, life on the job market is always a little tricky, and this is where the weight of your advisor’s name comes into play. Every advisor’s letter of recommendation says that the advisee is the greatest mathematician since Gauss and would have cured cancer if only he or she hadn’t been busy solving his or her thesis problem; however, if Terrence Tao says this, it carries a lot more weight than someone that the committee has never heard of. If several of the members of the hiring committee are personal friends of your advisor, well, let’s just say that doesn’t hurt.
I know one advisor who has had several recent students land great jobs. I know another advisor who has had several recent students who have not found jobs and have had to leave mathematics altogether. Here’s the thing: I have no idea whether the former professor’s advisees were better mathematicians than the latter’s. Neither do you. Neither, I suspect, did the hiring committees. What I do know is that the former professor set his students up better for success, both by giving them clear direction and interesting thesis problems and by knowing people in useful places, and those students were wise enough to take full advantage of their advisor’s help.
Ultimately, your grad school experience is about you, and you have to pick an advisor that does something that you are interested in, but don’t sleep on the effect that your advisor has on your graduation or post-graduation plans.