This page reflects the experience of colleagues and friends in the form of advice for mentors of all kinds and in various stages of their careers. It should be taken with a grain of salt, as it has no basis more reliable than the experience of those who have shared their stories with me. I myself have very little formal advising experience, and already I have made some mistakes. My hope is that this list will help us learn from the successes and blunders of others. This list is by no means definitive, and will be updated as more ideas crystalize, and stories are shared. Please feel free to contact me if you have any suggestions, comments or additions.

  • Make sure to avoid superseding your students and mentees. Take on at most k students when the different kinds of problems you work on is k+1, so that you have something to work on, and no one is led to supersede anyone else in your group.
  • Try to meet regularly with your students, and offer your mentees the same opportunity.
  • Do not speak ill of others to your students and mentees, especially about other students, mentees and colleagues.
  • Allow your students some scientific freedom, but try to guide them if they wander too much.
  • Students and mentees should not work for you, write papers for you, or do you favors without some kind of reciprocity. They are often not in a position to say no, and are constantly worried about your opinion of them.
  • Provide opportunities to your students and mentees, and guide them on how to obtain it themselves.
  • Do not compete with students or mentees, or encourage competition between them. Some forms of competition may be healthy, but cooperation is usually a lot healthier.
  • Encourage students and mentees to become independent, produce a paper or two on their own, and/or work with others in the same career stage.
  • Letters of recommendation are critical for a mentee’s career, so make sure to write them on time. If for any reason you cannot write a good and useful letter, you should let the mentee know as early as possible that you cannot write them a letter.
  • Do not cosign students or mentees (or anyone else for that matter) on papers that were written, or mostly thought-out, without them. It robs them of their impetus for growth and independence, and makes them feel like imposters.
  • Be mindful of a mentee’s deadlines for job applications when writing a paper together.
  • Encourage your students and mentees to attend conferences and present their works. In such events, try to facilitate their interactions with experts in the field.
  • Try to run a seminar for students to learn and become familiarized with research on relevant problems in your area.
  • If you have already decided to take on a student or mentee, try to ensure they do not feel unworthy of your mentorship.
  • Let your students and mentees know if they do something wrong. If this happens with another’s student or mentee, let their mentors know instead of taking it up with the mentee.
  • Do not take up formal mentorship out of pity, guilt, pressure or favor, especially if you don’t think the student has a chance of finding a job later on. On the other hand, don’t dissuade a student from pursuing a career in Mathematics, since your initial evaluation of them may well be wrong.
  • Be friendly with students, but try to keep some well-defined distance from them. Students are not meant to be your friends. Becoming too friendly with students may compromise your mentorship of them, which could hurt their careers in the long run.