Which Personalities Survive A Math PhD

A math PhD is an endeavor unlike anything you’ve ever done before. Even though everyone tells you this before starting, and warns of its difficulty, if you’re an optimist you’re going to picture yourself as one of those few who ends up thriving in graduate school. Unfortunately significantly more people predict that they’ll thrive than actually end up thriving, meaning that warnings do little to reduce the next generation of grad student suffering. So, this is an attempt to explain specifically what personality characteristics allow one to succeed in the math PhD, so that even an optimistic young mathematician (as I was) might be able to make a better decision if you know yourself well enough. I’ll use the language of Jungian cognitive functions (explained via video or text) so if you aren’t familiar with those I recommend checking that out first.

The four cognitive functions that math uses the best are Ne, Ni, Ti, and Si. Introverted thinking is most obvious as effective given that the entire game of mathematics is forcing ideas into a logical framework. Whenever you learn a new proof or solve a tricky homework question or see how what you knew before about integrals actually comes from more general facts about Inter-universal Teichmüller theory, your Ti will be satisfied. Ti collects abstract connections, and abstract connections is what mathematics is made of.

Extroverted intuition also fits very naturally in the math PhD as the same sort of creative problem solving that was satisfying in undergrad classes you’ll also find in grad classes, plus the entire project of a dissertation is—once you have built up sufficient knowledge—a test of idea exploration. Ne dominants often like debates as a form of idea exploration, which is a format that you’ll have difficulty finding in the math PhD (unlike in undergrad you don’t have random philosophy or polisci majors running around) but otherwise Ne users should find themselves fairly satisfied.

Introverted intuition users also have a lot amount going for them in a math PhD, given that math has more abstract information for you to collect than perhaps any other field. Whereas the Ti users appreciate the abstract connections between mathematical concepts, the Ni users will appreciate the mathematical concepts in and of themselves. Especially as you go deeper into math, it’s not hard to find a mathematical object whose definition is built on top of a field you don’t know and that field is itself built on top of another entire field you don’t know, and so on.

And then even though math has a reputation for being abstract, there’s bountiful concrete information to dig into should you so desire. Perhaps more so on the analysis side of things, you’ll find you can usefully learn lists of hundreds of counterexamples to intuitive ideas. So strong memory and desire to collect brute facts can very much pay off for those who have introverted sensing.

Maybe the most surprising thing about the transition from undergraduate math to a math PhD is how little Fe and Te pay off. Mathematicians are not a social bunch, and if you derive any positive amount of your life satisfaction from creative positive social-emotional vibes and having the group appreciate it, you’re probably going to be in dire straits. Not only are there few group interactions, but the quality or effort you put into the social interaction is often just not something on math PhD students’ radar, so the appreciation you are looking for will be scarce. So the Ni-Ti-Fe users, INFJ and ENFJ, had better have some alternate plan for fulfilling their Fe needs if they want to feel happy in the PhD.

On the extroverted thinking side, grad school in some sense stops paying off hard work. If you really liked the challenge of being very productive in undergrad in order to get good grades in order to get into a good grad school, that system for paying off hard work sort of disappears in the PhD. Classes (and how well you do in them) become rather unimportant, and instead the two measures of external progress that you’ll see (the only two which your advisor will likely care about) are becoming a candidate and finishing your dissertation. The projects you will be working on—homework, then research—are much less about how well you can take advantage of systems around you or how hard you can work; they’re really just about how much you know and how well you can think about what you know. So the NTJ’s and STJ’s end up significantly less satisfied in a math PhD than you might’ve expected.

Introverted feeling isn’t particularly deprived or particularly fed, while extroverted sensing shows up almost nowhere in the math PhD, as one could’ve guessed.

So, my overall rankings for what cognitive functions work well in a math PhD are:

Ti > Ne > Ni > Si > Fi > Te > Fe > Se   

Which loosely corresponds to INTP and ENTP being most satisfied in a math PhD, while ENFP, INFJ, ISTP, ISFJ, ISTJ, and INTJ all should be cautious depending on how well developed your auxiliary function is, and the remaining types should prepare for some misery.

Let me know in the comments if you think rank the cognitive functions that are happy in a math PhD differently, or if you’ve done any ranking like this for any other field—I’d be curious to see!