Advice for Students Thinking about Grad School in Math

In which I compile standard advice I’ve given over the years.
advice
Author

Mike Janssen, Ph.D.

Published

August 1, 2026

Note: the advice below is somewhat dated, as the availability of funding for basic research in the USA has been in flux in recent years. Nonetheless, it offers some things to think about. Moreover, if you are a student interested in graduate school in math, I encourage you to talk with your advisor and other professors in your department, and read the articles linked below. The sooner you do this, the better! But it’s never too late.

My advice on graduate school in mathematics

This is intended to be a general outline of advice on thinking about, selecting, and applying to graduate schools in mathematics.

Overview of graduate school in mathematics

  • One question you will need to have a good answer to is: Why do I want to go to graduate school? At the very least, your statement of purpose will need to address this question. Moreover, different departments have different sets of strengths. You should endeavor to find a department that will prepare you for what you want to do.
  • Unlike many other disciplines, you should never pay for graduate school in mathematics. Even if you don’t ultimately want to teach, you will likely do some form of teaching as a graduate student. This is good experience in general, and also comes with a considerable financial reward in the form of tuition waiver, monthly stipend, benefits, etc.
  • Usually you will start with a few years of coursework to gain breadth (and some depth) in mathematical areas of interest. You’ll also, at some point, need to pass the qualifying exams.

Selecting schools to which you want to apply

  • The usual advice, it seems, is that you should apply to somewhere around 10 schools, a few of which might be the “home run” schools, a few of which are “safety” schools, and some in between. This is probably fine advice if you can afford it (a single application fee is usually at least $50).
  • If your professors have a relationship with a particular program, this can given you an “in”. Additionally, if your university has sent students to a program and they have been successful, your professors can leverage this history to make a case that you’ll be successful, too.
  • You should have some idea of what you think you want to study, be it algebra, analysis, PDEs, applied math, discrete math, etc. However, you are allowed to change your mind after you get there! And maybe you will. Thus, I generally discourage students from applying to a school solely to work with a particular person. What if you get there and you don’t get along? What if that person is not taking students when you need an advisor? It’s better to find schools with research areas (plural!) you might be interested in and apply there. When you arrive, choose the working relationship over the work. That is, try to work with an advisor you get along with well, and do the mathematics they do.
  • Read graduate program websites carefully! They will answer a lot of your questions, particularly about admissions requirements and stipends.
  • If you can’t find an answer to a question, you can email the department faculty member in charge of the graduate program (typically called the graduate chair, or director of graduate education, or something equivalent). In general, I would discourage you from emailing a faculty member at random without a really good reason or a very specific question. Departments divide responsibilities up, so it’s best if you can find the person whose job it is to answer your questions.

Questions to ask of graduate chairs

This is a list of questions whose answers may be difficult to determine from a website.

  • What percentage of your students finish their Ph.D.?
  • What percentage of students pass the qualifying exam on the first try? Are there formal qualifying exam workshops/study groups in place to help students succeed?
  • On average, how long does it take to finish the degree?
  • What sort of travel/conference opportunities does your department make available to students? Is there dedicated grad student travel money?
  • What percentage of your graduates get jobs? What sorts of jobs (industry/academic) do they get?
  • How does your department prepare students for the job market?
  • Is there a grad student (or group of grad students) I can contact to answer some questions? (Examples of such questions are: What is the morale level like among grad students? Is it a collaborative or competitive environment?)