I’ve talked a lot about my experience as a graduate student in the math department at the University of Tennessee, and I absolutely love it, but after all this time I don’t think I’ve ever summed up why I joined a doctoral program, and why I would encourage (or discourage) or others to do the same.

As a freshman at Carnegie Mellon University, I got involved in a research project with Steven J. Miller who was visiting from Williams College at the time.

This was my first opportunity doing a pure mathematics research project, and I had gotten immense satisfaction from working on a problem whose answer was not already known, especially since I got a preview of the level of creativity needed to solve such problems.

It was also around the time I originally became more active as a writer on Quora, and grew fond of the writing aspect as well (to date I’ve written four papers co-authored with Miller, two of them already in press).

While my exact research interests have changed dramatically since this point in my life, I quickly became acquainted with the research process and also grew very fond of it. In mathematics, this largely came in the following steps:

1. Choosing a problem to solve
2. Reading related papers and books
3. Solving the problem gradually, sometimes pivoting towards a different problem part-way through
4. Writing up the results in a paper and having it peer-reviewed
5. Presenting the results at conferences and fielding questions

This is a little bit different from other sciences that may involve working in a lab, which was never my real passion anyway (I did consider majors in chemistry and chemical engineering in addition to math, but steered away from those pretty quickly).

Pittsburgh, PA, my hometown and the home of my alma mater, Carnegie Mellon University (personal photography)

So with that in mind, what is grad school, particularly a Ph.D. program, really for? RESEARCH. At least in the United States, you’ll probably also have to take classes (usually at a higher intensity than as an undergraduate), and at least in mathematics departments, you very well may be teaching as well.

So enjoying those things is important, but the main thing a Ph.D. program guarantees is the ability to do research, contributing original work to a growing body of knowledge shared among all researchers. And of course, you’ve got to write the thesis to document your newly developed expertise.

This is in many respects more demanding than a lot of other careers, despite the inherent flexibility in many cases (doctoral study is not a 9–5 job by any means), so it is definitely not for the faint of heart. Maybe you don’t know initially if you really want to do research, but if you have the time to spare, no harm done by trying.

Worst-case scenario get a master’s degree and then go do something else. But make it to the end and you’ll have developed the problem-solving, writing, and creative thinking skills to be a researcher.

Or, at the least, begun to develop these skills. My understanding is that later career advancements, be they in academia or industry, will help me continue developing them.