For context, I'm entering a mathematics PhD program that offers several different areas of specialization, mathematical computer science (MCS), pure maths, statistics, and more. My undergrad was in pure maths, so I feel most comfortable there, but I'm also interested in MCS, although I'm essentially a stranger there, other than a course on graph theory and a chapter of Algorithms. I'm trying to decide which track to put myself on while considering job prospects after school.

After reading several posts about job prospects for a pure maths PhD here, here, and here, I've noticed a few places where you can go with your PhD.

  1. Academia, with a notoriously tight job market, but where you get to continue doing enjoyable research, possibly gain tenure and basically continue the freedom from the same "business" demands that industry would have. I'm not sure I have the mettle to make it here, so the next options feel safer.
  2. Industry, where your skills will probably be underutilized, or even totally irrelevant, meaning you will have to learn entirely new skills -- programming, statistics, etc -- that you're perfectly capable of learning but haven't been directly taught in your PhD studies. These are jobs like actuaries, software engineers, etc.
  3. Industry Research, rare in between opportunities where research is restricted to what the company needs, but is still relatively open and free. Places like Google and Facebook labs.

There is obvious tension between the first two because a PhD is an academic, not professional, credential. It's simply not optimized to land you into option 2. If you're interested in options 2 or 3, the advice is that you should learn programming or something else on the side and use that to get your first job, and essentially leave the learning in your dissertation behind. This seems like an enormous waste to me. The effort and time spent learning esoteric pure math is essentially for fun (admittedly, a lot of fun), while you are still left to develop marketable job skills on your own.

So my question is: how can I choose my academic track/thesis topic minimize doubling my work? Am I merely butting my head against an intrinsic problem of academic vs professional credential? Should I see the PhD instead as an magical time to enjoy learning math, which will end but leave me mentally strong to tackle other, very different challenges? Perhaps instead it is merely an incubator, where I'm supported while developing a variety of skills not directly involved in the program?

Edit: Thank you for your responses. They're very helpful on a soul searching level and definitely respond to my question, but they weren't exactly what I was looking for.

I should have phrased it like this: What kinds of concrete choices -- courses, advisors, areas of mathematics, etc -- can I make while doing a PhD to maximize its' value after graduating?

For example, is MCS a better choice in terms of applicability outside of academia? Should I consider where a professor's students go after graduating when considering them as an advisor? Am I just worrying too much, and I should just find a problem I love so much that I think about it in the shower? What else am I missing?

Thank you again for your help.

  • 6
    If you see this as a problem, you should consider the option of not getting a PhD. Commented Aug 12, 2020 at 1:02

5 Answers 5


A math PhD will teach you a large number of completely marketable, industry-ready skills:

  • how to think logically and analytically

  • how to research challenging technical topics on your own, solve problems, and pursue difficult goals over an extended period of time, overcoming frustration and maintaining a good level of motivation

  • how to communicate your ideas effectively, in writing and in person (in particular, if you gain teaching experience while doing your PhD your presentation skills will end up orders of magnitude better than those of your peers who went into industry straight out of college)

  • and many other “soft” skills that are difficult to quantify and describe but are nonetheless extremely useful and important.

All of these things add up to a very attractive package for employers. It’s easy to focus on the “esoteric math” part of a PhD and conclude that it’s a “waste”. Will an industry job give you an opportunity to use your knowledge of Schur’s lemma or Brouwer’s fixed point theorem, or show off your familiarity with Radon-Nikodym derivatives? Probably not. But that doesn’t mean you will have wasted your efforts learning those things. Along the way, you will have learned to look at the world like a mathematician, and that, as it happens, is a darn useful skill almost anywhere you go.


I won't be overly worried. Just think about all the people who didn't go on to do a PhD. They got a job and probably living out their lives right now. You can definitely explore whatever you want, and all the best if your advisor is supportive or doesn't care that you are doing some work on the side (mine wasn't so flexible), although full fledged courses will definitely put you behind on your thesis and research. I have not figured out the best solution, however there are plenty of MOOCs or even certificates, e.g., Oracle, Microsoft, which you can get.

That being said, math PhD will definitely put you in a niche in terms of future career and set you back money/youth-wise. Read this excellent answer https://academia.stackexchange.com/a/11208/78834 It is not good to start life when you are 30 in today's economy. I'm saying this because I don't want to gaslight you about the harsh reality of today's job market. No, you are not better prepared for a tech interview than a highschool student who spent his entire life hacking computers because you did a PhD.

And it is not about the lack of knowledge, it is about the lack of experience, and accumulation of experience over the years. We are in a fully experience/skill-based market as compared to a degree/whatever-is-in-your-head based market. Think about the thousands of PhD scientists who work on climate change that gets their finding rebuked by people in charge with no science degrees whatsoever. We are living in this era/climate and we can't deny this.

Ok, so you learned C++ while doing your PhD. Now you are out of the program, and you will have to compete with undergrads or highschool students who maybe doing C++ many years longer than you. Who will be hired? (Not you, because every job nowadays literally wants at least 5 years of professional software development experience.) Think about that.

Not to scare you further, but my friend in graduate school (who is much more robust in the technical-skills than me), got rejected from a bunch of high-tech companies. He taught C++ and was a TA bunch of other software courses as a master student. There is literally no person more knowledgeable in when it comes to memory management in C than him. We spent a week lamenting how industry hands out rejection letter like candies and how it is so much harder to get into a good tech company than passing the PhD oral defense. Then we forgot about it. Mind you however, those were some top companies. I'm pretty sure he could easily work as a code monkey.

  1. A nearly necessary ingredient to doing well in pure math is the conviction / delusion that your research question is important, your efforts are relevant, and you will make a meaningful contribution to the world. A cynic doesn't think this way. A rational thinker performing Bayesian reasoning based on existing empirical evidence about past outcomes, placements, and job market realities, does not think this way, either. It's clear that you don't have this conviction / delusion -- this itself makes it harder for you to do well in, say, abstract homotopy theory. Pure maths sounds idealistic and romantic, until you come to the realisation that pure maths actually treats its younger colleagues like shit. If pure maths really loves us, why it is making us hardworking and gifted people suffer from such job insecurity, low wage, and tremendous stress? If your romantic partner says that he or she truly loves you verbally, but they always act abusively towards you, would you stay with them just for their sweet promises?

  2. One of the biggest favours you can do to yourself during graduate school is to become genuinely interested in coding, machine learning, and statistics. Stats has a better academic job market than pure math; statistical learning would not be wasted double effort; and the connections of stats professors and students are closer to industry jobs. Some maths PhDs are smart kids, so they can wait till year 4 to have their big realisation, leetcode for a year, and still land reasonable jobs. They then give you self-justificatory coping narratives of how their previous 4 years of intellectual exploration have been fulfilling and meaningful -- this is just copeism. If we modify their interests from abstract number theory to machine learning, while controlling for every other factor including the level of intelligence, then the same kids would be just as happy if not happier, would have completed their PhDs one year earlier, and would have been better placed in the industry. Despite all their copeism, deep down in their hearts, the 4th year leetcoders fully know that it's a tremendous pity that abstract algebraic topology will never show up in their professional life anymore, ever.

  3. You seem to be under the impression that pure math has more intellectual challenge and enjoyment than coding, ML, and Stats. The former is what you'd do if you had all the money in the world; the latter is what you do to pay the bills. This is the cross-discipine prejudice that pure mathematicians often exhibit. I don't think this is fair. Look - The Invention of C, C++, and Neural Nets are among the top ten most significant technological achievements in the history of Humanity. Proving theorems about Neural Nets actually says something important, and nobody has solved the problem. Mathematically formulating and explaining the empirical phenomena achieved by Stochastic Gradient Descent on deep neural nets is a mathematical challenge deeper and greater than the one faced by von Neumann, which was doing the same for Quantum Mechanics, and we needed to invent the theory of operator algebras to do that. These are fields where a lot of activities are happening. They give you the skills and knowledge that our free market economy is rewarding - and free market is the best exsiting definition of what our society considers to be of "value."

In short, if you only genuinely and passionately love number theory, then, why, go fucking do it. But if there's any intellectual possibility that you can be genuinely and passionately be interested in statistics and maching learning, then why don't you go ahead and develop this interest?

  • 1
    This seems to conflate two related but distinct issues: "pure maths" versus "proving things about ML and stats"; and "aspiring to academia" versus "preparing for industry". Some of the things you rhapsodise about in your third paragraph are not necessarily what someone would end up doing in industry.
    – Yemon Choi
    Commented Jul 15, 2023 at 2:48
  • 1
    Might I also suggest that the first half of your first paragraph makes the point well enough, and so you don't need to include the second half which is more argumentative/subjective?
    – Yemon Choi
    Commented Jul 15, 2023 at 2:52
  • I didn't go to grad school for any of the reasons you suggest. I did it because for me it was something I was good at, had fun doing, did not find stressful, and allowed me to live in a city I loved with pay that was sufficient for me at the time (as someone who grew up relatively poor). If I didn't like the job of being a grad student I would have quit and found a different job that I liked better. Commented Jul 15, 2023 at 20:14
  • @NoahSnyder Noah, I appreciate your sharing. I’ve noted that if someone’s parents are affluent, then the economic prospects after grad school aren’t really a worry; if someone’s parents are relatively poor and grad school stipend is already more than how much the parents make, then the economic side of grad school is deemed quite favourable. PhD student could also be the only job to get a first-world country visa. But those with parents who are in between are those the most worried about the compensation they are receiving and are missing out. OP seems to be from this in-between group. Commented Jul 20, 2023 at 23:23

I believe that the mindset to pursue a PhD should not be this.

Landing a good paying/mentally satisfactory job in tech is always a challenge and won’t be easy for anyone, and it does not require a PhD in particular. So if getting a tech job is priority to you in your life, I suggest not pursuing a math PhD.

However, PhD studies are not just some very specific topic you will study like crazy for a couple years and then forget all about it. Being in a PhD program strengthens you socially, psychologically and mentally. One acquires more than some coding skills in a PhD program if they are doing it for the right reasons. Also, one requires more than just a desire to get a job to be doing a PhD for the right reasons.

I think one should pursue PhD if and only if they are interested and passionate about a certain topic so much that even in the shower they are thinking about it. Doing a PhD for the right reasons requires you to be married to your topic, just because you are interested in it beyond reason. Otherwise it is a waste of time and it is better to do a masters where you can learn some skills required in industry and go directly into the real life.


I don't feel there's a tension between the two at all. Your PhD will give you lots of time to work on topics that you are hopefully interested in. It will also teach you the importance of communication, collaboration, and how to teach yourself new topics. When you say you will leave your learning behind, well, that's probably the same as if you went to do a postdoc in a different field (for example). There's a very strong chance that you will never use the exact things you did in your PhD in future. You have learnt far more than just the topic of your thesis. To use your example of learning to program, given your courses, you will more than likely pick some up. Once you know the basics, what's far more important is how you think about problems.

If you want intellectual work outside academia, look for interesting companies, simple as that. Bear in mind that what a company advertises isn't necessarily what they are currently doing... There are many, many people in industry who would have been more than capable of doing a PhD, and I would advise not to consider yourself above them, simply for having taken a different path.

So, enjoy exploring interesting topics, take time to see what other people are doing, get experience of communicating (reading, writing, and presenting), and you'll be well set.

  • Downvote without a reason - any input?
    – awjlogan
    Commented Aug 12, 2020 at 12:59

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