My PhD cost me $1.17M (but I'd do it again)

Not from my bank account, just from opportunity cost. It’s the first time I’ve sat down and calculated that. I don’t think I was ready for the sticker shock, I just thought it could make for a catchy title. Honestly, this might say as much about big tech salaries as it does about PhDs, but the counterfactual history was a reasonable one where I took a job at Google and took a standard path to senior engineer.

To get that number, I made some salary approximations, calculated taxes and cost of living, and was naively surprised at S&P 500 returns in a zero interest rate environment, which managed to account for a substantial amount of the difference. The total gap will increase over time too, through the interminable power of compounding returns. Your ultimate career path might not have quite such inflated salaries, and zero interest rates probably aren’t coming back any time soon, but the opportunity cost for a PhD may still be much higher than you expect.

Some people hold the position that they should do their best to deter anyone and everyone they can from getting a PhD. Their belief is that you’re fit for one if and only if you ignore that advice and boldly forge ahead anyways.

I think this is unnecessary. There are plenty of real reasons not to do a PhD (I have at least 1.17M of them), and one should have a better reason to do one than an inability to absorb advice. These considerations, and my own story, are the best I can offer to you if you're a prospective student; the final decision is up to you.

The happy path of grad school

Whatever path you choose in life, you’ll take some form of opportunity cost along the way; the important thing is just to notice the tradeoff. For example, last I checked, it was quite expensive to raise children in the US. Most people go on to have children anyways, and many go on to be happier with their kids than the money would make them. An econ PhD friend of mine talks about a concept of “Life EV”: sometimes we do things that are financially suboptimal because they sufficiently improve our life along other dimensions (he often yells this as he's halfway through leaping into a clearly bad decision because it seems fun).

But just as you shouldn’t have kids for the sole reason of hoping you have someone to visit you in your nursing home, you shouldn’t only think of a PhD in terms of what comes after. The best reason to do a PhD, and one which is both necessary and sufficient, is that you simply want to experience the journey.

That journey can be a beautiful one, if you’re lucky. You’ll meet other like-minded, bright-eyed grad students. You’ll meet generous mentors who pay things forward like it is their moral duty. You’ll travel to conferences (on someone else’s dime!) across the world, and you’ll meet more people that care about your tiny corner of reality than you could have imagined existed (there were dozens of us).

You can work on the kind of problem that follows you to the shower. The kind that itches your brain at night. The kind that jolts you awake as you lay in bed, because a piece finally clicked into place and you can’t hope to sleep until you write it down. The kind that gives you an adrenaline high for days when you figure it out, because you’ve been working on it for months or years.

There are other reasons that help, too. It’s hard to believe you can tackle a challenge that no one else has, especially if the pressure of completing your thesis hangs over you. A PhD is training and proof of your ability to grapple with the unknown.

You might want to do something you can only do with a PhD, or which a PhD can open doors for. In the world of math, this could mean working at a university, but it could also mean working at a hedge fund, at a national lab, or at an AI lab of a big tech company. Most things don’t need a PhD in the strictest sense, but people do pay attention when you have one.

These things are icing on the cake, but at the end of the day, the surest way to make it a positive, worthwhile experience is to want the experience. A PhD should not feel like paying your dues, and it is not noble to suffer through one. An important corollary is that if you are decidedly not enjoying the experience, it’s ok to leave!

A note on "slack"

It can be a little paradoxical to describe grad school as a time with a lot of slack. After all, grad students have a reputation for being over-worked, under-paid, over-caffeinated, and under-rested. But it isn't always like that, and there is a unique thread of intellectual freedom through all of it.

For me, that freedom manifested as space to grow. Once I finished most of my coursework (first two years), the only expectation seemed to be that I spend a lot of time thinking. In theory, that means thinking about your research, but in practice, my mind still managed to wander for many hours a day.

That space expanded considerably in my last two years; the pandemic happened, I'd already decided to leave academia, and I had enough research to graduate. I had few expectations to fulfill, and any remaining research work was mainly tying up loose ends. This was an unusual abundance of slack, but it led to substantially more hours being alone in my head.

I used to think this time was a bit wasted. The amount of concrete things that came out of those last couple of years felt pretty dismal in number. I was probably burnt out for a substantial portion of it, and the social isolation was hard.

Looking back, those years were probably some of the richest years of personal growth that I've ever had. Among other things, I developed a lot more self-awareness and confronted large chunks of emotional baggage that I never previously noticed.

This constitutes a large part of why I would make the same choice to do a PhD, if I could go back and choose again. It also highlights another kind of opportunity cost, which is of time. Whether I spent 5 years in grad school or at Google, those 5 years would pass either way. I only got to spend my early 20s once, and I'm glad that I spent them the way I did. Just as money in the bank would compound year over year, I can benefit from that space to grow for the rest of my life.

The darker side of grad school

The PhD journey can be a beautiful one, if you’re lucky. If you’re unlucky, academia is a meat grinder. There are various opportunity costs to consider, but there are real costs too, mostly in the form of stress to the mind and spirit. From my limited view, the following things were the main culprits.

Impostor syndrome

Academia has a high density of brilliant people. Many academics, including ones you will think are far more brilliant than yourself, feel they don’t belong. They do, and you will too if you choose to join them. There is an entire post that can be written about this topic, but the short version is that it is important to know that you may feel this way, to know that it is a normal and well-worn path, and to know that there are resources for this.

Social isolation

It can be intoxicating to be consumed by your work, but the darker side is that you can end up disconnected from and left behind by your social network. PhD programs are selective, so you can’t be picky about which city you end up in. I think this is especially hard for overseas students, where even phone calls are difficult to coordinate thanks to time zones.

You’ll see other people moving on to the next stage of their life, starting their careers, starting families, buying houses, cars, vacations, and other shiny things. Your family and friends may valiantly try to understand your work, but they probably won’t. Your cohort might end up a bit south of social and outgoing (n.b. you are allowed to be the one that organizes social events!).

My advice for this is to find a hobby with a strong community around it (preferably a physical one; you get exercise and get to meet people in person). I took up rock climbing in my first year, and it changed my life.

A bad advisor relationship

Professors are people too, and in any group of people there will be unsavory individuals. Some rare professors have a reputation for dealing in politics, gossip, and lies. It is not always easy for a fresh grad student to figure out who these are, but one should do everything in their power to avoid such professors.

Some other professors have very particular (and antagonistic) approaches to mentorship. One who shall not be named would intentionally fail students on their quals. Their alleged motivation for doing so was to use the pressure to pass quals as a motivational whip or forcing function on their students. By doing so, they could compel their students to study additional foundational material for the second attempt. Think twice before working with someone like this.

Setting aside extreme examples, you might just not get along well with your advisor through no fault of yours or theirs. Working chemistry is fickle, and you’re allowed to decide it isn’t a good match. Shop around for advisors aggressively until you find a fit (or at least do the best you can with the size of your department), since from the point of picking an advisor onwards, they’ll be the biggest factor in your journey. It can be worth picking your second favorite topic if it means working with your favorite professor.

Academia or bust

One of my undergrad math professors once told me how they got their job. While preparing to defend their thesis, their advisor got a phone call from a colleague asking if he had any good students finishing soon. That was it. No interview, no postdoc needed (typically a 3 year contract), they just discovered the next day that they had a job waiting for them. That was some 60 odd years ago.

Today, you’ll fight to earn 1-2 postdocs, then fight even harder to earn a tenure track position, then work on earning tenure (usually a 6 year process). Although it’s uncommon to be denied tenure once you have a tenure-track position, that’s still a total of ~16 years from the start of grad school before you can be completely sure of stable employment. A pretty low (but not insignificant) portion of PhD students that want tenure eventually make it.

I believe in chasing dreams; if tenure is your dream, then aim for tenure. Just don’t hinge all of your expectations and happiness on that outcome. Luck is enough of a factor that brilliancy won’t inoculate you. Yitang Zhang proved a partial result of one of the most famous open problems in math in 2013. He was incredibly persistent, but prior to this major result, still found himself living out of his car and working at Subway (I think this is exceptionally unlucky though).

At the end of the day, there are plenty of other places you can do research or teach.

Unexpected regrets

Few journeys end with no regrets. 5 years is a long time for regrets to find you, and they may not be what you expect. I am happy to have done a PhD, and I wouldn’t change that decision. But my biggest regret was that it kept me away from home for what ended up being the last years of our family cat’s life. She unexpectedly passed away shortly after defending my thesis, and before I could make it home to say goodbye.

Appendix: miscellaneous advice + other articles

External links

• Read Terry Tao’s career advice, it generalizes well. Some standouts for me:
  • Does one have to be a genius to do maths?
  • Continually aim just beyond your current range
• Sara Billey’s advice on getting a PhD in a timely fashion.
  • Choose your advisor systematically. Talk to current and former grad students. Are they happy? Do they have the kind of job that you want? Do they have jobs at all?
  • 20 hours per week of focus time is enough. Hours in front of the TV don’t count. Hours interrupted by texting and checking your phone don’t count.
• John Baez’s advice for young scientists.
• A great list of questions before starting a philosophy degree.
• A list of resources by Matt Might.

On teaching

• Put your heart into it when you do it, because you have a responsibility to your students, but set reasonable boundaries, because you have a responsibility to yourself, too.
• It’s easy to put infinite time into teaching. It feels productive compared to slamming your head against a research problem with no visible progress. Resist this urge. In the language of the Eisenhower Matrix, teaching is frequently important and urgent, while research is frequently important but not urgent. The latter category contributes most to long-term success.
• Grade efficiently. If you can choose the grading rubric, simpler point rubrics are easier and faster to grade. The difference between an answer that is 2 out of 3 points and 3 out of 3 points is much easier to spot than 17 or 18 out of 20.
• Grade fairly and predictably. Students will compare grades and answers and bring papers back to you with complaints (even if you grade perfectly, students will do that anyway, it'll just cost you less time).

Other notes

• Develop connections with people outside of your department. If you're gunning for academic positions, aim for at least one recommendation letter from someone outside. Your advisor can and should help you via warm intros.
• People who brag about how much they work don’t work as much as they say they do. Don’t let it get in your head, and don’t try to catch up. Grad school is a marathon and not a sprint.
• People who brag about how little work they do often work more than they say they do. Some people really are built different, but for the most part, it isn't the norm to work very little and make visible progress.
• There’s some folk wisdom that you should go to a different institution at each stage of your career. The idea behind this is that each department (or research group/lab) has its own school of thought. This might hold true beyond grad school, but it’s overblown at the undergrad -> grad transition. Don’t be afraid to stay at your undergrad institution for your PhD.
• Prestige isn’t everything, but it still matters more than it should. If you want to stay in academia, then the prestige of your advisor can open doors for you. If you want to leave academia, people still pay attention to the university brand next to your degree.

Thank you to those who volunteered to read drafts: Alex, Felix, Ross

Feedback appreciated!