The reason why to do a Ph.D.

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