In an email, Bonny Becker asks: *How do I go about gaining a better understanding of what my math PhD-seeking son is talking about?*

This question haunts those of us with a beloved mathematician in our lives. While most professions have a few dark rooms mysterious to outsiders, the field of mathematics feels like a palace in which *every* room is dark.

Math isn’t just mentally taxing and packed with jargon. It’s also dizzyingly abstract. At least rocket scientists and neurosurgeons can point to concrete objects that they work with—spaceships! Brains! By contrast, mathematicians work with pure ideas. Their game plays out entirely on the wrinkly fields inside their skulls. That can make it hard for outsiders to peek over the fence into the work of the mathematician.

So how do we, the spouses and parents and roommates of mathematicians, figure out what the heck our loved ones are up to? How do we make chitchat over dinner?

We’ll never understand the specifics of their research. They’ve spent years getting a handle on it, and we’re not going to catch up over the course of a single conversation. Instead, we can relate to the non-technical aspects of their profession—the curiosities that drive them, the obstacles that scare them, the relationships that give texture to their working days. Here are some suggestions for what to ask about (with an important caveat at the end):

1. *The emotional roller coaster of research.* Mathematicians spend their days tackling abstract problems that no one has ever successfully solved before. This experience can prove exhilarating, humbling, or mind-numbingly hard—sometimes all at once. Ask how it feels to prove something that no one else has ever proved. Ask how it feels to be the first human history to discern one particular truth.

2. *Teaching.* Almost all PhD students and math professors spend time as instructors. Because we’ve all been students at one point or another, the classroom is an easy (and fun) shared space to bond over.

3. *The different flavors of research.* Describing math research is like describing food, music, or dance—you can’t *quite* capture the experience, but you can evoke it. Some of a mathematician’s work involves grinding out technical details. Some involves observing elegant connections. Sometimes you’re applying an old technique to a new setting, or a new technique to an old setting. Sometimes there are dozens of hurdles to jump, and sometimes (rarely!) the path is straight and narrow. Even without delving into specifics, many mathematicians can offer colorful metaphors for the strange work they do.

4. *The student-advisor relationship*. For young PhD candidates, choosing an advisor is a crucial process. They need to consider the intellectual fit, the level of independence they want, the fertility of the research area, the advisor’s ability to make time around other obligations, the personal chemistry… It’s no accident that mathematicians refer to their advisors as their academic “parents.” (Sometimes they even extend the metaphor, with academic siblings, aunts, uncles, and grandparents.)

5. *Department politics*. Every math department (like any workplace) has its crazy stories, its bickering colleagues, its sweet moments, and its minor scandals.

6. *The intellectual fashions of mathematics*. It may surprise you, but math experiences trends and fads. Some areas within math are hip and popular. Others have fallen slowly (or suddenly) out of favor. Some topics are seen as stodgy and reliable, others as dubious upstarts, and others are all but deceased. If you’re curious about intellectual history, the varying cultures of mathematical subfields can make for surprisingly engaging storytelling.

7. *Social justice*. Academia remains a locus of power and prestige in our society, and math remains unequal in its representation of women and ethnic minorities. This isn’t a “fun” topic, so tread with care, but it can be a worthwhile one, whether your loved one comes from an underrepresented group or is simply concerned with issues of fairness and access in the profession.

A final and crucial caveat: Research can be a touchy subject. Not long ago, I was rock-climbing with a mathematician friend, and I casually asked, “How’s the thesis coming?”

He gave me a wounded look, as if I’d slapped his dog.

In any discipline, graduate school is a special, fragile time. While their college friends hop from job to job every 18 months, grad students invest half a decade or more into launching an academic career. That career will soar or plummet on the strength of their research—but research is a long, slow haul. Months may pass between pieces of meaningful feedback. And in that near-vacuum of encouragement and guidance, grad students can go a little stir-crazy.

My point is simply that mathematicians, like anyone, would sometimes rather talk about *Scandal* or *Duck Dynasty *than their own work. And that’s okay.

I don’t pretend to have a complete picture of what my wife does when she’s not sipping coffee or catching up on *The Good Wife*. But our conversations—mostly on the topics listed above—have given me a rough sketch—a bad drawing, if you will. And as we all know, math and bad drawings go hand in hand.

Your readers ask the most interesting questions and you write the best responses! I especially appreciate your caveat. My son is feeling pretty good about grad. school right now (1st year, 2nd semester) but his research hasn’t really begun yet, so I know I will be sharing your caveat with him (and also reviewing it myself) in the coming years. Thank you for your very valuable and helpful advice!

Well, thanks for asking good questions! 🙂

Now I understand why my daughter got upset (to put it mildly) when i asked her how her thesis was going. It must be very stressful to sustain effort and hope over so many years, especially because the reward at the end isn’t definite, other than being able to say you have a Ph.D.

Yeah, I think that’s exactly right. I’m sorry your daughter’s feeling tender about her thesis right now. I think all grad students (in all disciplines) experience that at least sometimes, so at least she’s not alone.

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My Grandfather is turning 95. And I would love to tell him how many times his birthday has fallen on a Friday like the day he was born. 4/1/1921. I can figure the days, months, min, but configuring with leap years I am going insane lol. Can you tell me how to do this please??

Thank you. I have literally prayed about how to talk to my PhD-seeking son. “You hungry?” is as good as it gets sometimes.

I love pure mathematics

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