Advising

David Molnar asks about how to evaluate an advisor. There is no objective method to evaluate advisors, faculty have different students to start with so one cannot directly compare the quality of their Ph.D.s. It's easy to advise a very intelligent hard-working student; it's advising the others that really separates the great advisors from the good ones.

To best evaluate an advisor, ask their students—both the successful ones and the ones that struggle. Keep in mind that an advisor's style that works with one kind of student might not work with another so listen to why a particular advisor is good or bad. These are especially good questions for undergrads to ask current Ph.D. students when the visit potential graduate schools.

Molnar also notes that he hasn't found many resources on how to be a good advisor. We all have different approaches and one could write a book on the topic but here are general techniques (many of which I learned from my own advisor Michael Sipser).

Have students work on problems that interest them not just you. I like to hand them a proceedings of a recent conference and have them skim abstracts to find papers they enjoy. However if they stray too far from your research interests, you will have a hard time pushing them in the right directions. And don't work on their problems unless they want you to.

Keep your students motivated. Meet with them on a regular basis. Encourage students to discuss their problems and other research questions with other students and faculty. Do your best to keep their spirits high if they have trouble proving theorems or are not getting their papers into conferences. Once they lose interest in theory they won't succeed.

Feel free to have them read papers, do some refereeing and reviewing, give talks on recent great papers. These are good skills for them to learn. But don't abuse them too much.

Make sure they learn that selling their research is as important as proving the theorems. Have them write the papers and make them rewrite until the paper properly motivates the work. Make them give practice talks before conferences and do not hold back on the criticism.

Some students will want to talk about some personal issues they have. Listen as a friend and give some suggestions without being condescending. But if they have a serious emotional crisis, you are not trained for that; point them to your university counseling services.

Once it becomes clear a student won't succeed working with you, or won't succeed as a theorist or won't succeed in graduate work, cut them loose. The hardest thing to do as an advisor is to tell a student, particular one that tries hard, that they should go do something else. It's much easier to just keep them on until they get frustrated and quit, but you do no one any favors that way.